Credit Derivatives: An introduction to the products, applications, participants and pricing. Michael Duncan (31384161)
[email protected]
Supervising Professor: Rae Weston MGSM 952 Research Project Macquarie Graduate School of Management MBA Programme November 2004 London
Credit Derivatives: An introduction to the products, applications, participants and pricing.
Table of Contents Executive Summary ........................................................................................................................ 3 Introducing Credit Risk ................................................................................................................... 4 What is Credit Risk? ................................................................................................................... 4 Major Risk Categories ................................................................................................................ 5 Market vs. Credit Risk ................................................................................................................ 6 Sources of Credit Risk Exposure ................................................................................................. 7 Credit Ratings & Credit Events ................................................................................................... 7 Credit Spreads .......................................................................................................................... 10 Economical Rationale for Managing Credit Risk ....................................................................... 12 Credit Derivative Products ............................................................................................................ 14 Credit Derivatives Defined ........................................................................................................ 14 Classification of Credit Derivatives ........................................................................................... 14 Credit Event Instruments ........................................................................................................... 14 Credit Spread Instruments ......................................................................................................... 21 Total Return Instruments ........................................................................................................... 22 Total Return Instruments ........................................................................................................... 23 Credit Derivative Applications ...................................................................................................... 25 Risk Reduction ......................................................................................................................... 25 Credit Line Management ........................................................................................................... 26 Capital Management ................................................................................................................. 27 Balance sheet Management ....................................................................................................... 28 Enhancing Yields ...................................................................................................................... 28 Market Access .......................................................................................................................... 29 Market Making ......................................................................................................................... 31 The Credit Derivative Market ........................................................................................................ 32 Market Size .............................................................................................................................. 32 Participants ............................................................................................................................... 33 Products .................................................................................................................................... 35 Reference Assets ....................................................................................................................... 36 Contract Size & Maturity .......................................................................................................... 37 Credit Default Swap Spreads ..................................................................................................... 37 Relationship with other Credit Markets ..................................................................................... 37 Regulatory Treatment of Credit Derivatives .............................................................................. 38 Credit Default Swap Valuation ...................................................................................................... 39 Key Pricing Variables ............................................................................................................... 39 Default Probabilities and Recovery Rates .................................................................................. 40 Intuition behind CDS Pricing .................................................................................................... 43 “Back of Envelope” Valuation .................................................................................................. 44 Replication Approach to Valuation ........................................................................................... 45 Model Approach to Valuation ................................................................................................... 47 Bibliography ................................................................................................................................. 52 Books ....................................................................................................................................... 52 Articles and Reports .................................................................................................................. 52 Electronic Reference ................................................................................................................. 54
This document is copyright 2004. This document may not be copied, reproduced, exhibited, sold, rented, lent by anyone, by any means whatsoever, without express written permission of the author.
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Credit Derivatives: An introduction to the products, applications, participants and pricing.
Executive Summary Credit derivatives and structured credit instruments are relatively new compared to derivatives related to that of market risk only and have won through a major revolution in the past few years. Indeed credit derivatives are still subject to continual innovation as the credit derivative market continues to develop, growing both in size (nothing to over US $ 5 trillion in less than 10 years) and in complexity. The interest in this developing market lies not only in the large margins that banks can raise with complex, esoteric and difficult-to-price products but more importantly in the fact that the emergence of this market has truly “completed” the financial markets; by segregating credit risk completely from market risk. Creating both arbitrage opportunities on previously poorly priced credit risk and allowing corporate and financial intermediaries to mange their credit risk exposure. Despite the interest and potential for the market, credit derivatives as a product class are still generally misunderstood and have gained a mystic as a result. This mystic has quite possibly been reinforced by much of the literature on the subject, tending to lie at one of two extremes:
Highly quantitative - this as a consequence can be very intimidating to those without a PhD. Highly descriptive – taking about but not actually showing how to value credit derivatives.
This report provides a middle ground; a general overview of the credit derivatives market is covered in an easily comprehensible manner. Mathematical formulae are used where necessary; however examples are provided and are designed to be readily replicated by the reader. Aspects of the credit derivatives market that are covered in this report include:
Introducing Credit Risk - the concept of credit risk and its implications to participants within the financial markets. Credit Derivative Products - what they are, how they work and how they are distinguished from one another. Credit Derivative Applications - applications of credit derivatives products. The Credit Derivative Market - addressing the size, growth, products used, participants, motivations and it‟s relationship with other credit markets (i.e. cash debt market) Credit Default Swap Valuation - describing the intuition behind the valuation of credit default swaps and critiquing some of the more common methodologies and techniques that can be used. Moving away from the theory, practical examples of deriving default probabilities and actual valuation of a credit default swap are provided.
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Credit Derivatives: An introduction to the products, applications, participants and pricing.
Introducing Credit Risk1 The following section provides an overview of the basic risks that arise when dealing with financial market instruments and contracts. Concentration is focused toward that of credit risk and how this particular type of risk category fits into the spectrum of financial risk. However credit risk cannot be readily understood without some idea of the other risk categories (especially market risk). The aim being to introduce the reader to the world of credit risk and the rationale for managing this risk both effectively and efficiently.
What is Credit Risk? Credit risk can generically be described as the risk that a loss will be experienced as result of the counterparty to a financial contract (whether it is a security, loan or derivative) defaulting on their contractual obligations. This description although correct, does not necessarily convey the full „flavour‟ of credit risk, nor the aspects of its subtypes. To provide a more comprehensive picture of what credit risk is, three principal credit risk subtypes; counterparty risk, default risk and credit rating migration are discussed below.
Counterparty Risk For the purchaser of a derivative contract, the primary risk is that of counterparty exposure. The purchaser loses money if their counterparty (the seller of the derivative contract) does not honour the contract obligations. Counterparty risk/exposure can be calculated from the mark to market value of a derivative contract (Basle rules require a further „add-on‟ component to this for banks). As a consequence of this mark-to-market valuation, the risk a purchaser has to a counterparty will fluctuate on a daily basis according to market movements. It follows that as a contract becomes increasingly in the money (has intrinsic value) for the purchaser, counterparty risk increases. Similarly as the value of the contract deteriorates, the counterparty risk decreases. This is known as the current exposure. In addition to this there is the potential future exposure, which is a measure on how the current exposure may develop in the future with some degree of statistical confidence. Counterparty risk is only applicable when the contract the purchaser holds is in the money, when it is out of the money the counterparty risk for the purchaser is zero (however the seller of the contract will now have counterparty risk arising from the purchaser). Do note that in longer-term contracts (i.e. OTC derivatives with lengthy maturities still to run, such as swaps) even with the current exposure being zero; the potential future exposure will result in some level of counterparty risk being derived for the contract.
Credit Default Risk Credit default risk arises when an issuer of a debt obligation (i.e. a bond) cannot honour their contractual commitments as a result of; bankruptcy, insolvency, or repudiation and subsequently default on any payments that it owes. In instances of an issuer defaulting on an obligation, the investor loses money by way of the fact that payments due to them (principal and interest) by the issuer are no longer made. Recovery of money owed via litigation can take years and will not necessarily result in all or any of the amount owed being recovered. Although credit default risk and counterparty risk sound one and the same, they are not. Consider the case where an investor holding Telstra bonds seeks to protect themselves from a potential default; it is possible to hedge potential default risk on Telstra by purchasing a credit derivative; however in doing so counterparty risk with the seller of the credit derivative is created.
1
Giesecke, k., Credit Derivatives and Structured Credit Products, Class Lecture Notes, Cornell University, April 2002.
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Credit Rating Migration A further credit risk subtype that is particularly import is that of credit rating migration. This is essentially the risk that a party will suffer adverse affects from a credit rating movement. This can include the company concerned and/or an investor with a debt or equity position in the company (long or short). Credit ratings are essentially a guide to the credit worthiness of a company, by an independent rating agency (such as Moody‟s, Standard & Poor‟s or Fitch). The higher a companies credit rating, the greater the desire and amounts that banks are willing to lend and the cheaper the rate of interest on the loans. Similarly banks are prepared to offer bigger credit lines (size of loans/derivatives exposure that they are prepared enter into with a specific company) and cheaper prices on derivative contracts (as the credit risk is reduced) the better a companies credit rating is. Aside from a company‟s perspective, ratings migration will have an adverse affect on holders of a company‟s loans or debt securities (or derivative contracts on these). As a company's rating deteriorates the relative risk of a company increases, which is subsequently reflected by a widening of credit spreads (more about these later). This translates into a higher risk premium (i.e. higher yields) required for an investor to purchase the companies debt or equity and the consequence is that debt and equity issued by the particular company decrease in value. Similarly tighter credit spreads resulting from a company‟s rating improving, translate to increases in value for debt and equity issues by the company.
Major Risk Categories Market Risk The risk derived from changes in market prices or rates. Market risk exposures result when positions are taken in the following asset classes; equity, interest rates, currency and commodities. The use of options on these asset classes also results in an additional market risk element, that of volatility. Volatility is the relative rate at which an assets price increases and decreases, the higher the rate of the price movement the greater the volatility (or probability of a change in price).
Operational Risk This is the risk of loss due to a possibility of mistake or breakdown in the management of risk exposures. Types of loss from operational issues in the past include: Mispricing of instruments – in an age of increasing complexity of financial instruments there is no such thing as a small pricing error. Incorrect assumptions about pricing model inputs or indeed the actual pricing models themselves can result in huge losses. Natwest Markets are infamously known for their losses from their swaptions book as a result of a trader using a flat volatility surface (even worse their systems were not able to capture this). Not understanding the risk involved – organisations can quickly disappear due to the actions (or inactions) of a select few. Even today banks become involved with markets and products that they have no real understanding of and as a consequence cannot realistically assess any of the risks that result. Fraud (i.e. the „rogue trader‟) – illegal activity by an individual can result in serve losses or even bankruptcy for a bank affected. Nick Lesson brought down Barings Bank as a result of successfully hiding his substantial losses made from illegal trades on Singaporean and Tokyo Futures exchanges. Systems failure – this is where internal systems (technical and management) breakdown to the extent that mispricing, fraud and mismanagement of exposures is possible in an organisation. Legal exposure – the possibility that a derivative contract or structure may be deemed illegal or unsuitable for sale to specific clients/counterparties. As a consequence of bankruptcy by Enron and WorldCom (just 2 of many examples) various investment banks have been indicted in the US in relation to the creation of special purpose vehicles (SPV‟s) designed to distort the earnings and true financial status of these companies. Compliance – the risk arising from violations of laws or rules and regulations. This results from uncertainties regarding some legal issues, appropriate regulatory capital and reporting treatment.
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Liquidity Risk Is the inability to adjust a position (long or short) without significant adverse price movement. Effects of increasing liquidity risk are: Bid/offer spreads widening dramatically in a short time period. Access to credit deteriorating with the result being that not only is funding (i.e. borrowing) harder to obtain, but it is also more expensive (reflecting higher risk premiums that are demanded by lenders). This risk is not as important for parties taking positions as hedges as they simply maintain the position until expiry.
Systemic Risk This can be described as a market wide liquidity breakdown or contagion style correlated defaults. Some relatively recent examples are the Russian and Asian crises in the late 1990‟s and the downfall of the telecommunications industry in the early 2000‟s.
Market vs. Credit Risk Basically, credit risk is a part of market risk. However there exist illiquid contracts for which market prices are not readily available, for example loans. Other factors, which distinguish between these two types of risk, are: Market vs. Credit Risk Market Risk Credit Risk Time horizon short (days) long (years) Hedging standardised customised Information market related asymmetrical Data abundant sparse
Time horizon – Market risk is short term in nature, with exposures generally held for only short periods of time (often intra day). Credit risk exposure conversely tends to be in periods of years rather than days; as the instruments are generally of a longer-term nature (e.g. bonds tend to be issued with tenors greater than 3 years). Hedging – Market risk exposures are readily hedged using standardised instruments such as: swaps, FRAs, forwards, options, swaptions, futures and the physical underlying. All these instruments whether OTC or exchange traded, are standardised to a certain degree (the only term to agree on is the size of the notional). Credit risk is altogether a different matter, with contract details considerably more customised and individualised (though the ISDA master agreements are improving this) but also the number of instruments and variability in tenor 2 of instruments available, is significantly less than for market risk. Information –For market risk exposures, information is not only easy to obtain, but it could be argued as excessive. A view on anything from oil to interest rates can be obtained from economists, analysts, independent think tanks, industry associations and of course your friendly taxi driver 3 (to name just a small list of possible sources). Whereas for credit risk exposures, information is asymmetrical, with one party of a transaction often knowing more than the other and third parties frequently precluded entirely. Typically it is the borrower/issuer4 that knows more about their debt servicing ability and general credit worthiness than the lender/buyer, however, it can be possible for the reverse to be true. Data – Much as with information, data for market risk exposures is abundant in supply and can be readily obtained from sources such as Bloomberg, Reuters and Bridge or your local financial newspaper. The flipside for credit risk is that although data available on exposures is increasingly expanding, it still can be sparse and infrequent for all but the top names.
2
Liquidity for credit default swaps is concentrated in the 5-year tenor and decreases significantly the further away from this point of the curve. Taxi drivers globally, are an excellent source of debate on current political and economic issues. 4 Company financial statements increasingly seem to more a wok of fiction that fact these days. 3
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Sources of Credit Risk Exposure Credit risk exposures can originate from various types of financial transactions, the most significant being: Exposure to the credit risk of an underlying counterparty. This can be through the purchase of a corporate or sovereign bond, making a loan (corporate or retail) to a borrower or by guaranteeing the debt of a company. This type of action is a conscious decision to take on credit risk exposure. Exposure to the credit risk of an Over-the-Counter (OTC5) derivative counterparty. Entering into any form of OTC derivative contract; such as swaps, options, forwards and even a combination of these instruments, results in a risk that the counterparty to the derivative contract will default on their obligations. With an OTC derivative instrument, the primary motive of the purchaser is to either hedge or gain exposure to market risk (whether interest rate, currency or equity), a side effect being the creation of a credit risk exposure. Combinations of both; such as asset swap packages. An asset swap is generally a fixed rate (fixed coupon) bond that is converted into a floating coupon by way of a fixed-for-floating interest rate swap (i.e. corporate bond + IRS swap). Subsequently the purchaser of such a package picks up credit risk exposure from the bond issuer and also from the counterparty to the swap.
Credit Ratings & Credit Events Credit Ratings A credit rating performed by an independent (private6) rating agency such as Moody‟s or Standard and Poor‟s (S&P) essentially provides a description of the credit worthiness of issuers bonds. In doing so a credit rating addresses some key questions an investor will have:
How financially sound is the company that I want to invest in? Does this company have sufficient income and cashflow to cover any liabilities?
Credit ratings for the two rating agencies range from that of AAA/Aaa (the best) to that of CCC/Caa (the worst for a not defaulted company) 7. Ratings BBB/Baa and above are classified as investment grade (translation, little likelihood of default) and ratings BB/Ba and below are classified as non-investment grade. Company‟s bond issues with a non–investment grade credit rating are often referred to as “junk” or “highyield” due to the fact that to attract investors they have to offer higher coupons relative to that of investment grade issues. As a consequence these companies bonds are much riskier than investment grade issues and have a higher probability of defaulting. In addition to the two ratings classified above, there is non-rated (NR) and default (D) classifications. A nonrated rating simply means that a company has not been rated by a rating agency. This does not imply that a company is so bad that it won‟t get even a bad rating (though it can), but more often than not means that a company is not sufficiently active in the capital markets or is too small to justify the expense of paying a rating agency to assess them. A company with a default classification is as the name describes, in default (i.e. not repaying their debt). The table below shows the primary credit rating scales for S&P8 and Moody‟s9. Credit Rating Scales Classification S&P Moody's AAA Aaa AA Aa investment grade A A BBB Baa BB Ba non investment B B grade CCC Caa NR NR not rated D D default 5
Exchange traded derivatives do result in credit risk exposure, however it is to a clearinghouse for which the risk of default is negligible.. S&P and Moody‟s are the two largest and most recognised but there are a number of others, Fitch especially is making inroads. 7 Actually these are simple ratings, more detailed ratings include a +/- on the rating (i.e. A+ or A-) to provide additional granularity. 8 www.standardandpoors.com 9 www.moodys.com 6
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Additionally the rating agencies also provide a differentiation between that of long and short term credit quality of a company by offering long and short term ratings. Note that a credit rating should not be taken as dogma, rating agencies do get it wrong and a credit rating does not excuse the sensible investor from undertaking their own research. Parmalat and Enron are just two recent examples of companies that had investment grade credit ratings, that are now bankrupt or in the process of restructuring. Taking the credit rating concept a stage further, the table below 10 shows the historical relationship between a company‟s credit rating at the start of the year and at year-end. This can be thought of as a credit rating migration or transition table. Average One-Year Transition Rates (1981-2003) Rating at year-end (%) Rating at start of year AAA AA A BBB BB B CCC
AAA
AA
A
BBB
BB
B
CCC
D
NR
88.07 0.59 0.05 0.03 0.03 0 0.08
6.81 87.37 2.01 0.19 0.07 0.07 0
0.6 7.5 87.42 3.91 0.37 0.24 0.25
0.14 0.57 5.54 84.46 5.09 0.31 0.51
0.06 0.07 0.43 4.56 76.32 4.88 1.36
0 0.1 0.16 0.84 7.53 73.88 9.32
0 0.02 0.03 0.22 1.02 4.42 46.27
0 0.01 0.05 0.37 1.36 6.08 30.85
4.33 3.77 4.31 5.41 8.21 10.12 11.36
source: S&P EU 2003 Annual Default Study and Rating Transitions
What this table demonstrates is the probability of a company‟s credit rating moving higher or lower in a oneyear period. As an example for companies with an initial credit rating of BB, by year-end the following credit rating migrations will have occurred: 0.03% will be upgraded to AAA 0.07% will be upgraded to AA 0.37% will be upgraded to A 5.09% will be upgraded to BBB 76.32% will have their rating unchanged at BB 7.53% will be downgraded to B 1.02% will be down graded to CCC 1.36% will be in default 8.21% will no longer be rated Likewise company default data is also available with the table below, Cumulative Average Default Rates 11 showing the cumulative probability of default per rating category over time. Cumulative Average Default Rates (1981-2003) % Year 1 Year 2 Year 3 Year 4 Year 5 Rating 0 0 0.03 0.06 0.1 AAA 0.01 0.04 0.1 0.19 0.31 AA 0.05 0.15 0.28 0.45 0.65 A 0.37 1.01 1.67 2.53 3.41 BBB 1.36 4.02 7.12 9.92 12.38 BB 6.08 13.31 19.2 23.66 26.82 B 30.85 39.76 45.47 49.53 53 CCC source: S&P EU 2003 Annual Default Study and Rating Transitions
The table provides evidence that there is a strong relationship between a company‟s credit rating and the probability of default. That is, the higher a company‟s credit rating, the lower the cumulative average default rates (and of course vice versa).
10 11
S&P, EU 2003 Annual Default Study & Rating Transitions; Feb 13, 2004. S&P, EU 2003 Annual Default Study & Rating Transitions; Feb 13, 2004.
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A secondary relationship that is shown is that of the time horizon. The greater the time horizon of a company's obligations, the higher the probability of the company defaulting on those obligations regardless of a company‟s credit rating.
Credit Events A credit event can be thought of as the credit quality change of a firm; generally it is either that of a default or credit rating migration (e.g. a credit rating gets lowered from AA to A). The 1999 International Swap and Derivatives Association (ISDA) Credit Events Definitions 12 documentation, defined six possible trigger events that can be applied to credit derivative contracts:
Restructuring- an event as a result of which an agreement between the parties to a reference obligation, as agreed by the reference asset and the holders of the relevant obligation, have become less favourable to the holders that they would otherwise have been due to the terms of the reference obligation being changed. Examples of changes can include; a reduction in the principal amount or interest payable under the obligation, a postponement of payment, a change in ranking in priority of payment or any other composition of payment. Obligation Default – obligations of a least a specified minimum amount have become capable of being declared due and payable because of a non-payment default (i.e. a default other than a failure to pay) by the reference asset. Bonds and loans generally contain various covenants, the violation of which can give the lender the right to accelerate (i.e. demand repayment immediately). Notably these violations can be technical nature (such as failing to send a report on time) as well as reflecting deterioration in credit quality (taking on additional debt or failing to meet minimum financial ratios). Obligation Acceleration – obligations of a least a specified minimum amount have been declared due and payable because of a non-payment default (i.e. a default other than a failure to pay) by the reference asset. To trigger a credit event, the non-payment default must lead to the reference obligation actually being accelerated. Failure to Pay - a failure of the reference asset to make when due, any payments of a specified minimum amount under one or more obligations after any Grace Period. Repudiation/Moratorium - where the reference asset (a governmental authority as this trigger event is only applicable to sovereigns) disaffirms, disclaims or otherwise challenges the validity of the relevant obligations thus resulting in a Failure to Pay. Bankruptcy- a reference assets‟ inability to pay debts. Whether the insolvent debtor petitions for such action or the debtor's creditors make the petition, the objective is the same: an equitable distribution of assets to eliminate as much of the outstanding debt as possible.
Unfortunately these definitions (even after the 2003 update) are broader than those used by the major rating agencies. As a consequence some commentators13 have estimated that the probability of a credit event under the ISDA definitions is about 30% higher than observed historically by the agencies. Moody‟s 14 take a particular dislike to the ISDA definition of bankruptcy as being excessively wide in scope. Arguing that the act of a reference asset even contemplating the merits of bankruptcy (e.g. hiring advisors to discuss options) if publicly reported could trigger a credit event payment, even if the reference asset does not ultimately enter bankruptcy. Thus a key point that should be made abundantly clear in dealing with credit derivative instruments is to know what exactly constitutes a credit event (under which a default payment will be made), within the parameters of the contract.
12
ISDA., ISDA Credit Event Definitions, 1999 and 2003. Ernst & Young., Credit Derivatives; Financial Services, Ernst& Young LLP, London, 2003. 14 Tolk, S., Understanding the Risks In Credit Default Swaps; Structured Finance Special Report, Moody‟s Investor Services Inc, New York, 2001. 13
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Credit Spreads A credit spread is the difference in yield between that of a defaultable and a risk-free (non-defaultable) security. The spread is the excess yield, which compensates an investor for incurring the credit risk associated with that of a defaultable security.
Credit Spreads Maturity Benchmark Corporate Yields Yields (years) (%) (%) 1 2.53 3.38 2 2.93 4.12 3 3.25 4.81 4 3.53 5.41 5 3.77 5.99
Credit Spreads (%) 0.85 1.20 1.55 1.88 2.22
There are two general formats of credit spreads: The credit spread relative to the risk-free benchmark, known as the absolute credit spread (i.e. corporate vs. risk free security). The credit spread between two credit sensitive securities, known as the relative credit spread (i.e. corporate vs. corporate security). Defaultable securities are generally corporate or emerging market sovereign issues, whilst risk-free securities in the financial literature largely refer solely to US Treasuries, the risk free benchmark also includes Sovereign issues from the G11 countries (such as Gilts, Bunds, JGB‟s and Australian Commonwealth securities). However Libor15 based benchmarking is increasingly becoming standard. The credit spread itself is calculated by subtracting the yield of the defaultable security from that of the riskfree security. The mathematics of the bond price/yield relationship with that of credit spreads is presented below. There are two types of bonds: risk-free and defaultable
T
B*t is the price at time t of a risk-free zero coupon bond paying 1 at maturity (or T) * The bond yield y * (T ) satisfies the equation B *Tt e y (T )T
BtT is the price at time t of a defaultable zero coupon bond, paying 1 at maturity (or T).
The bond yield y(T ) satisfies the equation BtT e y (T )T
The credit spread S (T ) is then
(2)
1 BtT S (T ) y(T ) y (T ) ln T T B*t *
(1)
(3)
The term structure of credit spreads is the schedule of S (T ) against maturity (T). The Term Structure of Credit Spreads Credit Spread (%)
2.50 2.00 1.50 1.00 0.50 0.00 0 15
1
2
3
Time (years)
4
5
6
London Interbank Offered Rate.
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The workings of the formulae discussed, can be best demonstrated by providing a tangible example from the credit spreads table. Taking y* (3) 5.50% and y(3) 6.20% as the respective yields for the risk-free and the defaultable zero coupon bonds maturing 3 years from now, from the credit spreads table above. It is a quick calculation to determine that the credit spread is S (3) y (3) y* (3) 6.20% 5.50% 0.70% using equation (3). We can also derive the 3 year credit spread of the corporate bond over the risk-free bond by using the T
respective bond prices of B*t e.0553 0.847894 and BtT e.0623 0.830274 . Taking the formula
1 3
from equations (1) and (2) for the bond prices, a quick calculation of ln
0.830274 results in an answer 0.847894
of 0.70%. Generally the credit spread is often solely attributed to that of default risk, with the respective widening and tightening of spreads explaining the financial market‟s current sentiment regarding an issuer‟s likelihood of default. Thus a widening (decrease in bond prices) in spreads can be interpreted as the market view that an issuer has a increased probability of default on any securities outstanding and a tightening (increase in bond prices) in spreads can be interpreted as the market view that an issuer has a reduced probability of default on any securities outstanding. Intuitively attributing credit spreads to that of relative default probability does make sense. However even a brief observation of the financial markets in action, will show that spreads experience considerably more volatility than can be rationalised by this logic. Indeed spreads for some issuers can fluctuate by more than 20 basis points (0.02%) in a day (e.g. from a cut or increase in base rates), without any obvious change in the respective issuers financial circumstances, such as a rating change or deterioration in profitability. This indicates that other factors are at play in driving the credit spreads for an issuer other than the default probability. These additional factors include; tax, recovery, liquidity, interest rates and other market factors (such as supply and demand for an issuer‟s bonds). Some academics 16 have produced research, which show that for AAA rated firms only 5% of the credit spread can be directly attributed to that of default probability (for BBB firms this increases to 22%) with the balance of spreads derived from the additional factors mentioned above.
16
Delianeis, G. and Geske, R., The Components of Corporate Credit Spreads: Default, Recovery, Tax, Jumps, Liquidity and Market Factors, University of California, Los Angeles, 2001. MGSM 952, Research Project, November 2004, London
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Economical Rationale for Managing Credit Risk The Modigliani-Miller 17 theorem, states that in the absence of taxes, bankruptcy costs, asymmetric information and perfect capital markets, a firms value is unaffected by how it chooses to finance itself, whether by debt or equity, nor by what it‟s dividend policy is. Going further, the theorem holds that addition or subtraction of financial risk will similarly have no bearing on a firm‟s value. The reality however is somewhat different, capital markets are far from perfect and as a matter of fact, none of the theorems required conditions are actually met. Moreover a firm‟s capital structure (the combination of it‟s debt and equity capital) is very closely monitored by market participants and will ultimately affect its valuation. Similarly excessive leverage or risk taking by a firm is punished by the markets placing a discount on both debt and equity issues, as high-risk strategy. Although the strategy can often result in higher rewards (i.e. profitability) in the short term, it can ultimately result in higher losses (i.e. a greater probability of not being able to service debt and higher probability of bankruptcy) in the long term. Ultimately the economic rationale for managing credit risk within a bank is the impact it can have on the bottom line. Successful management of credit risk enables a bank to not only avoid costly and embarrassing losses when counterparties default, but also enables profits to be enhanced with the use of leverage and assertive balance sheet management. Non-financial companies can also benefit from management of credit risk. Prior to the introduction of credit derivatives in the late 1990‟s the traditional method of managing credit risk was via credit rationing (limiting any further transactions with a specific counterparty) and/or asset sales for loan and bond exposures. This was only partially effective and very inefficient. Although bank assets can be sold in the secondary market, the riskier asset exposures that a bank is most likely to want to reduce will not necessarily have liquid secondary markets. This is especially the case in loans; in 1996 primary loan syndication origination in the U.S. exceeded $900 billion, whilst secondary loan market volumes were less than $45 billion 18. This can and often leads to a bank incurring a capital loss on the asset sale (as the market prices in a discount on the assets “fair value” and subsequent “fire sale” nature of the sale), a loss of interest income and a possibly soured relationship with the clients concerned (potentially leading to lost future business). Similarly it was also relatively difficult to short the market, as to do so requires that bonds are first borrowed via the repo19 market, before they can be sold to create a short position. Not only is the corporate repo market fairly illiquid (except for the most global names), but also these short positions have to be funded. This left the credit risk from OTC derivative transactions (such as swaps, options and forwards); the only way of reducing this exposure (while remaining in the market) was to set up netting agreements 20 and/or require collateral from counterparties. Both of these options have distinctive drawbacks; netting doesn‟t really reduce exposure, merely allowing an exposure to a specific counterparty to be managed better, collateralisation does reduce counterparty risk considerably; but requires active management in itself of posting/receiving and calling collateral (also reducing the relative attractiveness of an OTC derivative to that of an exchange traded one). Assignment (selling) of counterparty contracts to a willing buyer offers a more dramatic alternative of credit reduction. However assignment tends to result in the buyer obtaining a derivative portfolio for a substantial discount, as it can signal that the seller is either in trouble or withdrawing from the market (i.e. “fire sale” prices). 17
Modigilani, F and Miller, M,. The Cost of Capital, Corporation Finance and the Theory of Investment, American Economic Review, June 195 8. JP Morgan,. The J.P. Morgan Guide to Credit Derivatives; Risk Publications, London, 1999. 19 A repurchase agreement (repo) is an agreement between two parties whereby one party sells the other a security at a specified price with an obligation to repurchase the security at a later date for a specified price. 20 If counterparties have multiple offsetting obligations to one another - e.g. multiple interest rate swaps or forward contracts-they can agree to net those obligations. In the event that a counterparty defaults, the outstanding contracts are all terminated. They are marked to market and settled with a single net payment. This technique eliminates "cherry picking" whereby a defaulting counterparty fails to make payment on its obligations, but is legally entitled to collect on the obligations owed to it. 18
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As you can appreciate, a bank that can not only measure and quantify their credit risk, but can also isolate the specific aspects of credit risk embedded in financial contracts (e.g. bonds and derivatives) has a distinctive advantage over their competitors. Why? Because a bank, which can disaggregate the various risk components, is then able to assign each a value. In terms of credit risk, a bank can determine whether or not they want to hold the specific credit risk associated with a financial contract (i.e. is it cheap or expensive?). Similarly by being able to value credit risk accurately; a bank derives a more complete picture of their credit risk exposures. Credit risk that they do not wish to hold can be transferred to other parties and likewise credit risk that they want to hold or increase exposure to, can be purchased from the market. Despite the obvious advantages that can be gained from actively managing credit risk, most banking orgainisations are not doing so yet. Even in some of the world‟s largest banks, credit risk management is limited to that of a process of setting and adhering to notional exposure limits and pursuing very limited portfolio diversification strategies. In the worst run examples, such as the German Landesbanks 21 (as just one of numerous examples than could have been chosen) the term credit risk “management” was a misnomer (rather “mismanagement”), although exposure limits were set and adhered to, borrowers were never seriously monitored22. Thus as long as a counterparty line for a specific borrower was not fully utilised, bank lending officers could continue lending regardless of the borrowers current or future debt servicing capability. Also because of political interference (Landesbank owners are German State governments) loan activity was frequently directed to government favoured industries and companies, on very cheap terms (which did not incorporate a risk premium).
21
The Landesbanks lose their government guarantee in 2005 as a result of a European decree that the gurantee was a form of government subsidy. As a result the Landesbanks credit ratings will drop from AAA to ratings determined by their respective financial performance. 22 From 1998 to 2003 WestLB lost more than EUR 1 billion annually from losses on loans and provisions for doubtful debt. MGSM 952, Research Project, November 2004, London
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Credit Derivative Products Credit Derivatives Defined Credit derivatives can be defined23 as bilateral financial contracts that isolate specific aspects of credit risk from an underlying instrument (also known as the reference asset or entity) and transfer that risk between two parties. In so doing, credit derivatives separate the ownership and management of credit risk from other qualitative and quantitative aspects of ownership of financial assets. Notably the above definition, in substance captures numerous credit instruments that have been consistently used for years; including letters of credit, guarantees and loan participations. Raising the question, why is this relatively new group of products (credit derivatives) so significant? The feature of credit derivatives, which distinguishes them from that of the more traditional credit instruments, is the precision with which credit derivatives are able to isolate and transfer the component parts of credit risk (i.e. default, spread, credit migration, restructuring) from an underlying asset, as opposed to credit risk in it‟s entirety.
Classification of Credit Derivatives The classification of credit derivatives differs slightly from that of other financial derivative types, whereby instruments are classified as either: forwards, swaps, or options. These distinctions are less clear-cut with credit derivatives, as a credit default swap can resemble an option by way of the contingent payoff. Thus credit derivatives are generally classified 24 on the basis of whether they are:
Credit Event Instruments Credit Spread Instruments Total Rate of Return Instruments
The instrument payoffs are based on reference assets, which are associated with either single names, or multiple names. Additionally the reference asset can be either a cash instrument (such as a loan or bond) or a synthetic instrument (such as another credit derivative). Settlement of the contingent payment for a credit derivative can be either: cash settlement (the difference between the par value25 and market value of the reference asset is paid by the protection seller) or by physical delivery (the reference asset is transferred to the protection seller in return for the par value of the asset) in the event of a credit event/spread occurring (i.e. an asset that might be valued at $0.20 after a default, is exchanged for par).
Credit Event Instruments These are instruments where contingent payments are made depending on the occurrence of a pre-agreed credit event. The most commonly known is the single name credit default swap. Instruments within this class are:
Credit Default Swaps (CDS) Baskets (1st to default and nth to default) Credit Indices Credit linked notes (CLN) Collateralised Debt Obligations (CDO)
23
JP Morgan., The J.P. Morgan Guide to Credit Derivatives; Risk Publications, London, 1999. Das, S., Structured Notes and Derivative Embedded Securities, Euromoney Books, London, 1996. 25 The par or face value of a bond is generally $1.00. 24
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Credit Default Swaps (CDS) A credit default swap is a contract that enables two counterparties to isolate and transfer the credit event risk from a reference asset, without transferring ownership (unless a credit event has occurred and there is physical settlement). Credit default swaps involve a protection buyer (payer), who pays a periodic fee to a protection seller (receiver) in exchange for a contingent payment if there is a credit event. Credit default swaps are the largest product segment of the global credit derivatives market with approximately 51% of credit derivative market share26.
C re d it D e fa u lt S w a p P e r io d ic f e e ( X b p )
P r o te c tio n B u y e r
P r o te c tio n S e lle r C o n tin g e n t P a y m e n t f o llo w in g c r e d it e v e n t
R e fe re n c e A sse t C r e d it E v e n t T ra n s fe r o f d e fa u lte d re fe re n c e a s s e t if p h y s ic a l d e liv e r y
Basket Default Swaps27 A basket default swap is similar to a single asset default swap except that the underlying is a basket of assets rather than one single asset. There are several types of basket default swaps, the most popular being first-todefault basket default swaps. With a single asset, a credit event is usually a default of the lone asset issuer. With a first-to-default basket swap, a credit event occurs the first time any of the issuers in the basket defaults. Default protection against losses is provided for the first issuer to default only, as the contract terminates following this initial default.
F irs t-to -D e fa u lt B a s k e t
P e r io d ic f e e ( X b p )
In v e s to r (p ro te c tio n s e lle r)
P o rtfo lio M a n a g e r (p ro te c tio n b u y e r) C o n tin g e n t P a y m e n t f o llo w in g c r e d it e v e n t
$ 3 0 m P o rtfo lio : 3 R e fe re n c e A s s e ts of $10m each
C r e d it E v e n t T ra n s fe r o f d e fa u lte d re fe re n c e a s s e t if p h y s ic a l d e liv e r y T e r m in a tio n o f c o n tra c t
Nth to default 28 basket swaps provide an extension to that of first-to-default concept. Instead of the contingent payment being determined on the first issuer to default, it can be based on the 2 nd 3rd 4th to 10th etcetera issuer in the basket to default. The basic valuation method and payoffs remain the same as the first-to-default swap.
26
British Bankers Association., BBA Credit Derivatives Report 2003/2004. Tavakoli, J., Credit Derivatives: A guide to instruments and applications, John Wiley & Sons, 1998. 28 Capital Markets Quantitative Research., Portfolio Credit Derivatives Insights – A framework for managing tranche and Nth to default transactions, The Royal Bank of Scotland, London, 2004. 27
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Unlike a CDS, a Basket Default Swap introduces the concept of correlation. As such basket instruments are best suited to that of investment grade reference assets, with low correlation (even better is to use reference assets with the same credit ratings as well). The higher the correlation between the reference assets in the basket, the greater the likelihood, that if one defaults the remaining assets will also follow suit (e.g. a basket with three reference assets all in the car manufacturing industry; Ford, General Motors and Toyota.). Thus the greater the correlation between a baskets reference asset components, the worse the credit protection. It may be cheaper than buying individual credit protection on each of the reference assets, but this is at the cost of reduced protection. Basket structures work best when the investor seeks to gain protection to a number of reference credits that have either very low or negative correlations (e.g. financials and miners) as the cost of obtaining credit protection is reduced, without giving up too much of the credit protection.
Credit Indices29 Credit indices are offered as either single notes or multiple name CDS, which offer exposure to a broad credit market and are rated. Their returns are based on the performance of a series of CDS comprising the names in the index. Indices generally reference 25, 50 or 100 of the most popular corporate names for a specific geographical region, investment grade or sector.
C re d it In d e x - C D S F o rm P e r io d ic f e e ( X b p )
P r o te c tio n B u y e r
P r o te c tio n S e lle r C o n tin g e n t P a y m e n t f o llo w in g c r e d it e v e n t
R e fe re n c e A s s e ts C r e d it E v e n t T ra n s fe r o f d e fa u lte d re fe re n c e a s s e t if p h y s ic a l d e liv e r y R e d u c tio n o f th e In d e x n o m in a l a m o u n t b y th e in d e x w e ig h tin g o f th e d e fa u lt re fe re n c e a s s e t P o s t c r e d i t e v e n t t h e p r e m i u m o n t h e I n d e x is p a i d o n t h e r e d u c e d n o m i n a l ( s u b je c t t o f u r t h e r c r e d i t e v e n ts )
Credit derivative indices offer both liquidity and flexibility, allowing investors to take pure sectoral views (i.e. exposure to financials or corporates only) and to place and unwind exposures rapidly. Similarly investors are able to take negative views by shorting a single note or CDS. Similarly the inclusion of a broad selection of credits and industry sectors provides indices with strong diversification and limited exposure to the default of any single reference name. These benefits were previously impossible to obtain with small transactions sizes, without buying into a fund and paying the associated fees and charges.
C re d it In d e x - N o te F o rm SPV [S e lle r/M T N Issu e r]
C ash
In v e s to r In d ex sp read (X b p )
C ash
C r e d it E v e n t Is s u e r p a y s in v e s to r c a s h s e ttle m e n t a m o u n t I n v e s t o r ‟ s r e d e m p t i o n a m o u n t r e d u c e s b y t h e i n d e x w e ig h t i n g o f t h e d e f a u l t r e f e r e n c e a s s e t ( i . e . P a r is n o t p a i d a t m a t u r i t y o f t h e n o t e ) P o s t c r e d i t e v e n t t h e p r e m i u m o n t h e I n d e x is p a i d o n t h e r e d u c e d n o m in a l (s u b je c t to fu r th e r c re d it e v e n ts )
29
R e tu rn fro m p o r tf o lio
R e fe re n c e p o rtfo lio - 1 0 0 N am es of $1m each
www.indexco.com
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Indices have made a dramatic entrance to the credit derivatives market, in less than two years these products have captured 11%30 of market share, from 0% less than two years previously. Indeed these instruments may be a major driver of future growth of the market as a whole, as the first exchange traded credit derivative products will be futures contracts, based on the most popular credit derivative indices. The emergence of credit derivative futures should promote increased growth in the OTC market as well (if it behaves as the interest rate derivatives market has).
Credit Linked Notes A Credit Linked Note31 (CLN) is a note issuance with an embedded credit default swap. Under a CLN structure, the coupon of the note is linked to the performance of a reference asset. It offers borrowers a hedge against credit risk, and gives investors an enhanced yield on the note, relative to that of other note issues for accepting the additional exposure of a specified credit event.
C re d it L in k e d N o te H ig h G ra d e C o lla te ra l R e tu rn
C ash
SPV [S e lle r/M T N Issu e r]
P e r io d ic f e e ( X b p )
P r o te c tio n B uyer C o n tin g e n t P a y m e n t f o llo w in g c r e d it e v e n t
C LN Coupon + P e r io d ic f e e ( X b p )
C ash
R e fe re n c e A s s e ts
In v e s to r
CLN are created through the use of a Special Purpose Vehicle32 (SPV) structure, which is collateralised with high rated securities and is at “arms-length” from the deal arranger. They can be structured as either a Credit Linked Deposit (similar to buying a collateralised CDS protection) or Credit Linked Loan. Investors buy the notes from the SPV (the issuer) that pays a fixed or floating coupon during the life of the note. At maturity, the investors will receive par unless the referenced asset defaults or declares bankruptcy, in which case they receive an amount equal to the recovery rate. The SPV enters into a default swap with the deal arranger (generally the bank that created the SPV). In case of default, the SPV pays the dealer par minus the recovery rate in exchange for an annual fee, which is passed on to the investor in the form of a higher yield on the notes. The investor is exposed to both the note issuer (SPV) and to the reference asset.
Collateralised Debt Obligations33 One of the largest segments 34 of the credit derivatives market with around 16% of market share, are portfolio products more commonly known as Collateralised Debt Obligations (CDO).
30
BBA., Credit Derivatives Report 2003/2004, London, Sep 2004. http://www.investopedia.com/terms/c/creditlinkednote.asp 32 Also referred to as either: an SPC, SPE or bankruptcy-remote entity, whose operations are limited to the acquisition and financing of specific assets. The SPV is usually a subsidiary company with an asset/liability structure and legal status that makes its obligations secure even if the parent company goes bankrupt. 33 www.riskglossary.com/articles/collateralized_debt_obligation.htm 34 British Bankers Association., BBA Credit Derivatives Report 2003/2004. 31
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CDO is the general moniker given to a variety of instruments these include: Collateralised Bond Obligations (CBO) and Collateralised Loan obligations (CLO) which respectively hold only bonds or loans. Just to make things slightly confusing, CDO can be further distinguished by whether they are:
Balance Sheet vs. Arbitrage Cash vs. Synthetic Static or Managed Cashflow or Market Value
CDO are constructed with the objective being to transfer the credit risk associated with these portfolios of obligations. These portfolios often consist of bonds or loans held by a bank, but may also consist of mortgages, credit card receivables and even derivatives. A CDO is a securitisation in which a portfolio of assets as described above is transferred to a SPV, which in turn issues multiple tranches of debt securities of varying levels of seniority and size in order to fund the SPV‟s purchase of the portfolio. The tranches levels of seniority are catergorised according to their degree of credit risk as:
Senior Mezzanine Subordinated/Equity
If there are defaults or the CDO's collateral otherwise under performs, scheduled payments (known as a Waterfall) to senior tranches take precedence over those of mezzanine tranches, and scheduled payments to mezzanine tranches take precedence over those to subordinated/equity tranches.
C a s h C D O S tru c tu re T ru s te e C ash
A s s e ts tr u e “ s a le ”
O rig in a tin g B ank
S en io r N o te (A A A )
SPV C ash
C D O n o te is s u a n c e
M e z z a n in e 1 (A ) S tru c tu re s c a n h a v e 5 + tra n c h e s .
R e fe re n c e A s s e ts (b o n d s , lo a n s e tc )
T h e “ e q u ity ” is th e f ir s t lo s s p ie c e a n d is u s u a lly u n r a te d . S u b o r d in a tio n is m a in f o r m o f c r e d it e n h a n c e m e n t. L e v e l o f p r o te c tio n f o r A A A n o te c a n r a n g e f r o m 1 0 -3 0 % in c a s h f lo w C D O s . O th e r c r e d it e n h a n c e m e n ts a r e o v e r c o lla te r lis a tio n a n d e x c e s s s p r e a d .
M e z z a n in e 2 (B B B )
S u b o rd in a te d (E q u ity )
Senior and mezzanine tranches are typically rated, with the former receiving ratings of A to AAA (normally represents around 70% to 90% of the notional amount of the CDO structure) and the latter receiving ratings of B to BBB. The equity tranche is usually unrated and carries the first loss in the event of any defaults. Ratings reflect both the credit quality of underlying collateral, as well as how much protection a given tranch is afforded by tranches that are subordinate to it. Similarly the level of rating in effect determines the yields paid to the various tranches. The highest rated tranches receiving the lowest yields and the equity tranche receiving the highest yield (say LIBOR + 500 bp, whereas a AAA tranche may receive LIBOR + 20 bp). The returns on CDO securities are dependent on the joint default performance of the assets in the collateral pool. A CDO has a sponsoring organisation, which establishes the SPV to hold the collateral and issue securities. Sponsors can include banks, other financial institutions or investment managers. Expenses associated with running the SPV are subtracted from the cashflows to investors. Often, the sponsor retains the equity tranch of a CDO (or at least a portion of it) so that it maintains a significant interest in the management of the relationship with the obligors (and because the equity tranche can be very hard to sell).
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Balance Sheet vs. Arbitrage CDO 35 These CDO correspond to the respective motivations of the sponsor. With a Balance Sheet CDO, the sponsor is a bank or other institution that holds, or anticipates holding, loans or debt that it wants to remove from its balance sheet in order to liberate economic or regulatory capital. Similar to a traditional ABS 36, the CDO is a vehicle for it to do so. Assets can comprise: investment grade and sub-investment grade term loans, revolving credit lines etc. Arbitrage CDO are motivated by the opportunity to add value by repackaging collateral into tranches according to investor demand for specific risk and to exploit the differences in funding costs of assets and liabilities. This is the same motivation for most CMOs. In finance, the law of one price suggests that the securities of a CDO should have the same market value as per its underlying collateral. In practice, this is often not the case. Accordingly, a CDO can represent a theoretical arbitrage. Assets can comprise: high yield or emerging market bonds, ABS/MBS37 and even other CDO. Much of the arbitrage in an Arbitrage CDO arises from a persistent market imperfection related to the somewhat arbitrary distinction between investment grade and sub-investment grade debt. Many institutional investors face limits on their ability to hold sub-investment grade debt. This can take the form of regulations, capital requirements, and investment restrictions imposed by management. Insurance companies, pension plans, banks and mutual funds can all face some sorts of limitations. As a result, sub-investment grade debt often trades at spreads to investment grade debt that are wider than might be explained purely by credit considerations. With a CDO, a portfolio of sub-investment-grade debt can be repackaged into tranches, some of which receive investment grade and even AAA ratings.
Cash vs. Synthetic CDO Cash CDO expose investors to credit risk by actually holding collateral that is subject to default. By comparison, a synthetic deal holds high quality or cash collateral that has little or no default risk (purchased with proceeds of the tranche proceeds). It exposes investors to credit risk by adding credit default swaps to the collateral. Synthetic CDO can be static or managed. They can be balance sheet or arbitrage deals.
Synthetic CDO Structure Trustee Portfolio CDS premium
Originating Bank
Cash
Senior Note (AAA)
SPV CDO note issuance
Contingent payment Risk free cashflow
Cash
G11 Govt Securities
Mezzanine 1 (A)
Mezzanine 2 (BBB)
Subordinated (Equity)
Arbitrage synthetic deals are motivated by regulatory or practical considerations that might make a bank want to retain ownership of debt while achieving capital relief through CDS. In this case, the sponsor has a portfolio of obligations, called the reference portfolio. It retains that portfolio, but offloads its credit risk by transacting CDS with the CDO.
35
Choudhry, M., Fourth-Generation CDO Structures: Credit Trading via the Managed CDO, Bloomberg Seminar, July 2002. Asset Backed Securities 37 Mortgage Backed Securities 36
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For arbitrage synthetic CDO, two advantages are An abbreviated ramp-up period (for managed deals), and The possibility that selling protection through CDS can be less expensive than directly buying the underlying bonds. This is often true at the lower end of the credit spectrum. The biggest advantage to (balance sheet or arbitrage) synthetic CDO is the fact that they don't have to be fully funded. For a cash CDO to have credit exposure to $100 million of bonds, it must attract $100 million in investment so it can purchase those bonds. With a synthetic CDO, a mere $150 million in high quality collateral can support credit exposure to $1,000 million in obligations. In such a partially funded deal, the entire $1,000 million reference portfolio is tranched, but only the lower-rated tranches are funded. In this example, the most senior $850 million tranch would be called a super senior tranch. It might be retained by the sponsor or sold off as a CDS. The funded piece might comprise USD $100 million of investment grade tranches and $50 million of mezzanine and unrated tranches. In arbitrage deals, partial funding offers higher capital relief than does full funding under the Basle capital requirements38. For synthetic deals, it is generally less expensive to sell the super senior tranch as a CDS than it would be to fund that tranch.
Static vs. Managed CDO39 With a Static CDO, collateral is fixed through the life of the CDO. Investors are able to assess the various tranches of the CDO with full knowledge of what the collateral will be. The primary risk they face is credit risk. With a managed CDO, a portfolio manager (usually the sponsor) is appointed to actively manage the collateral of the CDO. The life of a managed deal can be divided into three phases: 1. Ramp-up which lasts about a year, during which the portfolio manager initially invests the proceeds from sales of the CDO securities. 2. The reinvestment or revolver period lasting five or more years. The manager actively manages the CDO's collateral, reinvesting cashflows as well as buying and selling assets. 3. In the final period, the collateral matures or is sold. Investors are paid off. In a managed deal, investors do not know what specific assets the CDO will invest in (these assets will change over time); at the time they purchase the CDO securities. All the investors know is the identity of the portfolio manger and the investment guidelines that they will work under. Accordingly, investors in a managed CDO face both credit risk, in addition to the risk of poor management. For this lack of transparency, investors have the privilege of paying portfolio management fees. Most CDO are generally managed deals.
Cashflow vs. Market Value CDO A Cashflow CDO is similar to a CMO40. Cashflows from collateral are used to pay principal and interest to investors. If such cashflows prove inadequate, principal and interest is paid to tranches according to seniority. At any point in time, all immediate obligations to a given tranch are met before any payments are made to the less senior tranches. With a market value deal, principal and interest payments to investors derive from both collateral cashflows as well as sales of collateral. Payments to tranches are not contingent on the adequacy of the collateral's cashflows, but rather the adequacy of its market value. Should the market value of collateral drop below a certain level; payments are suspended to the equity tranch. If it falls even further, more senior tranches are subsequently affected. An advantage of a market value CDO is the added flexibility they afford the portfolio manager. They are not constrained by a need to match the cashflows of collateral to those of the various tranches. Analysing CDO is difficult. Not only is there an entire portfolio of credits to analyse, in managed deals, an investor won't know what collateral will be purchased. On top of this is the added complexity of the tranching, which must also be analysed. Sophisticated portfolio credit risk models should be used. Needless 38
Basle Committee on Banking Supervision., Basle II Third Consultative Package, Overview of The NEW Basle Capital Accord, April 2003. Choudhry, M., Fourth-Generation CDO Structures: Credit Trading via the Managed CDO, Bloomberg Seminar, July 2002. 40 Collateralised Mortgage Obligation. 39
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to say, there is much potential for manipulation or abuse by sponsors. However CDO appeal to investors because of the attractive yields they offer, but with these instruments moreso than others, it is case of caveat emptor.
Credit Spread Instruments 41 The payoff of credit spread instruments; depend on the movement in credit spreads, regardless of the reason for the movement. Credit spread credit derivatives enable the isolation of:
Relative credit value changes, independent of interest rates. Trading forward credit spread expectations. Trading the term structure of credit spreads.
Credit spread products are generally forwards or options on the future spread between two financial assets; either to a credit spread to the risk free benchmark (absolute spread) or between two credit-sensitive assets (relative spread). Instruments within this class include:
Credit spread forwards (or credit spread swaps). Credit spread options.
At present the market for such instruments is not yet particularly liquid, while credit event instruments have gained significant and growing liquidity.
Credit Spread Forwards The structure of a credit spread forward is that of a forward contract on the credit spread between two reference assets. Unlike a CDS, the structure of a credit spread forward need not require periodic cashflow exchanges, between the contract counterparties. Rather, the structure can be that of a simple forward contract, such as a Forward Rate Agreement (FRA) 42 where there is a net cash settlement based on the difference between the agreed spread at contracts start date and the actual spread at the contracts expiry. Counterparties to a credit spread forward contract are obligated to make or receive payments on pre agreed spread levels at the start of the forward contract, thus both parties have the potential to lose or make money on the contract, dependent on the change in credit spreads at expiry. An example may be an investor holding a corporate bond which they intend to sell in six months time, worried that the credit quality may deteriorate (reflected by a widening of the credit spread between corporate bonds and treasuries), affecting the price that the investor will receive on the bonds sale. A credit spread forward can enable the investor to receive a spread of 20 bp in six months regardless of what the actual credit spread is at that time. If credit spreads widen beyond 20 bp the investor makes a gain on the contract, similarly if credit spreads tighten below 20 bp the investor makes a loss on the contract.
41 42
Das, S., Structured Notes and Derivative Embedded Securities, Euromoney Books, London, 1996. A FRA is a forward contract on interest rates.
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Credit spread options Credit spread options are similar to that of credit spread forwards with payoffs also dependent on the future level of credit spreads, the distinguishing feature being that the option buyer has the right and not the obligation to buy or sell the spread (depending on whether they have purchased a put or call). As such the option seller has an unlimited loss and limited profit potential (the option premium), the option buyer having limited downside (the option premium) and unlimited profit potential. Credit Spread options are commonly structured to "knock-out" (i.e. expire worthless) upon a default occurring, so that they separate the change in credit spread from the default risk. Credit spread put options - enable the buyer the right to sell the credit spread, and benefit from an increasing (widening) credit spread. Credit spread call options - enable the buyer the right to buy the credit spread, and benefit from a decreasing (tightening) credit spread.
Credit Spread Option
Option Premium at Start Date
Protection Buyer
Protection Seller
Contingent payment at Exercise Date
Credit Spread
Credit Spread Options - Payoffs Payoff at Expiry Credit Spread Call Nominal * Max (Strike - Credit Spread, 0) Credit Spread Put Nominal * Max (Credit Spread - Strike, 0)
Long Put
Long Call
Gain
Gain
Strike 0
Strike Credit Spreads
Option Premium Loss
MGSM 952, Research Project, November 2004, London
Credit Spreads
0 Option Premium Loss
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Total Return Instruments These are instruments where the payoff depends on both the behaviour of spreads as well as on events such as default. As such the objective of this particular type of structure is the replication of the total performance of a reference asset (i.e. a loan or a bond). Key features of a total return instrument are:
The investor (total return receiver) assumes all risks and cashflows of the reference asset. The total return payer passes through all payments derived from the reference asset. The total return receiver in return, effectively makes a payment to the payer equivalent to that of a funding cost plus a margin.
By definition it can be argued that total return instruments are not in actual fact a credit derivatives, rather that of financial derivatives with a credit element (in so much that the asset can default). Because of this credit element they generally fall within the mandate of the credit derivative trading desks at investment banks and securities brokers and as a consequence have become classified as credit derivatives. The most popular instrument types within this category are total return and asset swaps.
Total Return Swap: (total rate of return swap) 43 A total return swap is a contract that enables an investor to obtain the cashflow benefits of owning an asset without having to actually hold the physical asset on their balance sheet. The total return payer owns the reference asset and pays the absolute return (income plus any capital appreciation or depreciation) of the asset to the total return receiver in exchange for a periodic payment (LIBOR plus a fixed spread). With this type of instrument the total return payer for all intents and purposes, is effectively lending their balance sheet to the total return receiver.
Total Rate of Return Swap Appreciation
Total Return
Total Return Payer
Total Return Receiver
LIBOR + X bp
Depreciation
Reference Asset
43
Tavakoli, J., Credit Derivatives: A guide to instruments and applications, John Wiley & Sons, 1998.
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Asset Swap Asset swaps44 are essentially synthetic floating rate notes. They are a tailored structure that enables an investor to purchase a fixed rate bond (or loan) and then hedge away the interest rate risk by swapping the fixed interest payments for floating. The investor assumes the credit risk that is economically comparable to purchasing a floating rate note issued by the fixed rate bond issuer. There are two components to an asset swap, the first is the fixed rate bond and the second is a fixed for floating interest rate swap of the same maturity as the bond.
Asset Swap Asset Purchase Cash
Investor
Issuer/Dealer Asset
+ Coupon Swap Fixed payment
Asset
Fixed payment
Swap Counterparty
Investor Floating payment
44
Oldfield, M., Only For the Sophisticated Investor, Euromoney-International Bond Investor, Autumn 1994.
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Credit Derivative Applications Section one introduced the concept of credit risk and the economic rationale for managing it. Section two described the credit derivative building blocks (or key instruments) currently used in the financial markets. This section describes how various market participants can apply credit derivative instruments to their businesses and subsequently enhance economic performance. The principal applications 45 of credit derivatives to enhance economic performance for organisations, whether financial or otherwise are summarised below46:
Risk Reduction Credit Line Management Capital Management Balance Sheet Management Enhancing Yields Accessing Markets Market Making (trading)
Specific credit derivative end user applications are presented in the table below.
Credit Derivative User Applications Risk Reduction Credit Line Management Capital Management Balance Sheet Management Enhancing Yields Market Access Market Making
Commercial Banks
Securities Houses
Corporations
Insurance Companies
Fund Mangers Government Bodies
Risk Reduction Risk reduction (hedging) is driven by an organisations need or desire to reduce unnecessary credit risk exposures. In essence it revolves around the isolation of unwanted credit risk, whether for a one-off credit concern (such as a single deal) on ongoing business activity and the transference of that credit risk to another party. Credit risk exposure for an organisation can be broken down to that of: Single name (or obligor) - such as a major supplier or counterparty. Multiple or portfolio names - such as exposures to specific industry groups or segments. Country exposures – An organisation may have concerns that a large proportion of revenues derive from a particular country or countries. Thus adverse economic growth or political uncertainty of these countries can have a detrimental effect on revenues. Generally, risk reduction requires the purchase of credit derivative protection (equivalent to being short a bond), being that most organisations seeking to hedge exposures can be said to be long credit. This is probably the easiest and simplest means for which to achieve the risk reduction objective (i.e. buy a CDS or basket default swap). 45 46
CIFT Ltd., Masterclass in Advanced Credit Derivatives, Public Course, London, June 2004. Kasapi, A., Mastering Credit Derivatives: a step-by-step guide to credit derivatives and their application, Financial Times, London, 1999.
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However there are occasions where an organisation (e.g. a corporation) may be expressly prohibited47 from dealing in financial derivatives of all but the most vanilla 48 variety. In these cases, organisations that are able raise capital via the bond markets by issuing bonds, can remove credit risk by the use of structures such as CLN or CDO. These structures provide the ability to directly or indirectly remove credit exposure from the balance sheet and transfer it to a willing party.
Credit Line Management Credit lines are the internal limits that an organisation places on its exposures to borrowers, trading partners or traditional derivatives counterparties. Although generally more associated with banks and securities houses, credit lines can also be applicable to corporations, fund managers and insurance companies. Credit lines can be allocated into groupings such as, counterparty, industry segment, country and even product type. Unlike risk reduction, credit line management is concerned with the successful management of credit lines, which does not necessarily mean the reduction of credit risk. Rather, the objective is to facilitate ongoing business relationships with favoured borrowers, trading partners and counterparties. Credit derivatives can be used in two ways to successfully manage credit lines:
The first is to reduce credit exposures via the purchase of credit derivative protection, such as CDS. Essentially freeing up credit lines, enabling the organisation to continue business activity as normal or even to increase it. To increase credit exposures via the sale of credit derivative protection for credit lines where exposure does not meet targeted levels (this could be because a bank is not active or does not have access to a specific industry segment or market).
Where credit derivatives come into their own is that exposure to certain counterparties can be transferred to a third counterparty (the credit protection seller) without the original counterparty otherwise aware. This is particularly important for organisations seeking to maintain relationships with clients. If a bank is seen to be selling its loans to a major corporation on the secondary market, that major corporation is not going to be likely to want to continue borrowing from that bank. Worse still the corporation can decide that other business with the bank (i.e. financial advice, financial markets products and corporate finance), will go to a competitor that wants “all” their business. Frequently loan covenants (especially in Europe) require that if the lender (i.e. bank) is to sell a loan to a third party, they have to first obtain permission from the borrower. Using a credit derivative, the loan exposure remains on the balance sheet of the lending organisation, yet the credit risk is removed. In most orgainisations the notional of credit derivatives, are treated as a “loan equivalent” and the credit line reduced accordingly. So if $100 million notional of credit derivative protection is purchased, this translates to that of a $100 million reduction in the credit line utilisation (though it does create a new counterparty exposure to the seller of the protection). The cost of this credit line management is that potential returns from a counterparty name, or industry are reduced slightly in the shorter term. To pay for the protection, the spread (or margin) on the business activity is reduced. However over the medium to longer term, returns are increased as, the organisation continues doing business as normal or even increasing it with the affected counterparty (i.e. a greater increase in business, at a smaller margin, can be more profitable than low business volume at high margin). Of course the organisation stays within internal credit lines, which thereby limits potential loss from a default from the counterparty or industry.
47
Often companies prevent company officers from making transactions in certain derivative products, such as options in the hope this will avoid potential trading losses or rogue traders. However the weakness with this type of restriction is that most sophisticated financial deri vatives can be readily replicated synthetically, using simple products. 48 Vanilla is the term applied to derivative instruments of a very basic or simplistic nature – such as futures and analytical options. MGSM 952, Research Project, November 2004, London
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Indeed some of the first uses of credit derivatives in the late 1990‟s were banks hedging credit lines to major derivative counterparties and loan exposures (i.e. buying credit protection).
Capital Management Capital management is the process whereby management determines the business activities for which their organisations limited capital resources are invested. Desired business activities can be either ones that offer high returns or alternatively offer low risk to invested capital. In essence capital management can be described as a process of balancing risk against that of reward. Capital management is widely employed by organisations that wish to be, or remain successful. It can be used to strategically determine which business activities/projects to pursue and also to assess potential trades or deals with counterparties. Individual transactions, projects or deals are accepted or rejected based upon the capital utilised and the expected profits that will be generated, measured against a stated threshold. In the context of banking, capital is managed/allocated in two ways:
Internally as per management degree – this is known as economical capital. By external regulation and legislation (domestic and international), on a matrix based system known as regulatory capital.
Economic capital management This is usually performed using sophisticated models that assess the risk and return characteristics of potential transactions. One of the first models to emerge was the risk-adjusted return on capital (RAROC) model, which was developed by Bankers Trust in the early 1980‟s. Other banks further extended the model to that of risk-adjusted return on risk-adjusted capital (RARORAC). The idea being that the models can rank transactions (or potential transactions) according to their expected returns adjusted in some manner for their risk. If a transaction is above a stated threshold, it is accepted, if not it is rejected. Credit derivatives can be used with respect to economic capital management in instances where a proposed transaction may initially not meet the required threshold return levels, for example a proposed loan to a favoured corporate client. Rather than reject the loan outright which could sour any client relationship, the loan can be still be made. However the loan would incorporate a simultaneous purchase of credit derivative protection. This in essence enables the bank to mitigate any credit risk and to also lock-in a guaranteed risk less49 margin over the loans tenor. The locked in margin, calculated as the loans spread (including funding) less the cost of credit protection. Admittedly this guaranteed margin, is not going to be huge (or always possible), and is dependent on a banks individual cost of funds. However what happens is that the risk adjusted return (although small), divided by the risk adjusted capital use (which is going to smaller) results in a large multiple and thus clears the threshold (e.g. in basis point terms 5/0.5 = 10). Regulatory capital management Regulatory capital is the requirement set by bank regulators following the Basle Accords. Basle held that for risk-based assets (i.e. loans or bonds) a minimal proportion of the assets nominal value is to be held aside as regulatory capital. This proportion of capital is matrix based and is dependent on the type of asset in question. The original 1988 Basle Accord50 provided a matrix that was applicable to both on and off balance sheet assets. Risk Based Capital = 8% x Nominal of the Underlying Asset x Risk Weighting x Conversion Factor
(4)
As an example it required that banks hold capital equal to: 0% for OECD governments and central bank debt 20% for holdings in OECD incorporated banks 100% for Corporates 49 50
Guaranteed to the extent that the credit protection seller does not default, if there is a default by the borrower. Basle Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards, Basle, July 1988.
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The levels that these weightings required were subject to much debate and discussion amongst the banks ever since, leading to numerous updates and of course to Basle II (which is set to be implemented in 2005/2006). In practice this means that for each $100 million nominal of bonds purchased or loans made to an OECD incorporated bank, a bank is required to support this holding with 8% or $8 million of tier one capital (which can be holdings of OECD government debt, cash, or equity). So as you can see the choice of asset has an immediate economic consequence, the riskier the asset, the greater the regulatory capital required to support it51, which in turn effectively lowers an assets potential return (there is an opportunity cost on the regulatory capital used). Like credit line management, credit derivatives can be used to reduce capital exposures with the purchase of credit derivative protection and subsequent credit offsets, thus reducing regulatory capital utilisation. Similarly assets sales, asset hedging and portfolio diversification (not just credit related) also assist in the reduction of regulatory capital usage.
Balance sheet Management A key feature of derivative products, which makes them as popular and versatile as they are, is there off balance sheet nature. This off balance sheet nature, when applied specifically to credit derivatives enables an organisation to assume unfunded credit exposures. Prompting the question, what is so significant about whether an asset goes on or off the balance sheet? The answer is financing. Because prior to an asset being acquired, the purchase amount (i.e. cash) has to be obtained from somewhere. Either it comes from existing cash reserves reducing the organisations liquidity, or the amount is borrowed resulting in interest payments (and the creation of a new liability) for the term of the loan. The net effect is that any returns from holding the asset are subsequently reduced 52. Thus any organisation that can replicate an on balance sheet credit exposure, off balance sheet is not only managing their balance sheet more efficiently, but also enhancing the return on assets or capital employed (because capital use is minimised) and subsequently increasing profitability. Off balance sheet credit exposure can be created with the sale of credit derivative protection (providing a long credit exposure for the seller), this provides a consistent return over the duration of the protection (as the spread received is agreed at the initiation of the contract and does not change over time) for zero outlay. Should the reference asset default, the credit protection seller is required to make a contingent payment to the credit protection buyer. The loss given default (LGD) from this situation for the credit protection seller would be identical to having had purchased the cash asset and it subsequently defaulting. Assets can also be removed from the balance sheet through the use of cash and synthetic CDO, asset sales and SPV53. The transfer of physical assets is generally regarded as a sale and as a consequence may not be popular with borrowers.
Enhancing Yields In today‟s rampant chase of ever increasing yields (i.e. returns) over what is currently available in the market, credit derivatives can provide the investor with the ability to boost yields to a desired level. Unfortunately credit derivatives instruments are not a “magic bullet” for yield aspirations, they are merely a tool with which used correctly, have the potential to enhance yields over which would otherwise be available
51
Actually that is not necessarily the case, see my earlier point regarding how the Basle has lead to much debate and discussion. Henry, D., Fuzzy Numbers, Business Week, European Edition, Number 3886-1216, October 4 2004. 53 Enron was but one company known for their use of SPV structures to manipulate financial statements. 52
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in the cash credit market (i.e. corporate bonds and loans). This is because potential returns can only be increased at the expense of magnifying risk (unless you have insider information). It is worthwhile to note that structured financial products, (not just credit derivatives) are sold on the back of their high yields, yet the marketing of AAA rated products such as a CLN or CDO will tend to only mention the increased risks in the small print of the contracts (understandable really, investment bankers have to make a living too). In fairness to investment bankers it is commonly acknowledged that the credit markets (both for cash and derivatives) are a professional market place (retail investors cannot be involved as they can in the equities markets) with market participants being professional investors (hedge and mutual funds, corporate treasuries and banks and other investment banks). Thus it is ironic that when these structured instruments go wrong 54, these so called “professional” investors call in the lawyers at a moments notice and sue the investment banks that originally created these products for them. These “professionals” are smart enough to buy these products when they are the current fad, yet at the same time not smart enough understand the basic principal of investing that: “greater returns can only be obtained at the expense of greater risk”. Preamble aside, the application of credit derivative instruments with respect to enhancing yields is achieved in three ways: Coupon returns are exchanged for optionality payoffs. Where the coupons from a standard credit investment are used to fund the purchase of a series of credit options, which is a common feature in structured notes. The advantage here is that short of default, potential losses are restricted to that of the coupon payments only, however the upside profit potential is theoretically unlimited The investor sells credit protection. CLN‟s are the perfect example of this application in practice; the boost in yields is achieved via the investor selling credit protection to an SPV. The investor receiving the normal coupon yield, plus x basis points per annum over the duration of the CLN. The investor can use leverage. A secondary aspect of credit derivatives being an off balance sheet and unfunded instrument, is that they can provide an investor with more “bang for their buck” by allowing credit exposures to be readily magnified to desired levels. This is achieved by increasing the nominal on an underlying credit derivative contract, whether you are a buyer or seller of protection. For example consider a total rate of return swap; on a nominal of $10 million the potential returns may not excite an investor. However if the exposure is increased by a multiple of ten, to that of a nominal $100 million suddenly potential returns increase by 1,000% (the converse is that potential losses are also magnified by the same amount). The measures used to enhance yields can range from the simple; such as single name products to that of the more complex; such as baskets or other multiple name products. These methods of enhancing yields are not inherently wrong by any means, but like all tools they should be used appropriately and with the end users fully aware that they can result in unexpected losses. Similarly the appropriateness of using yield-enhancing methods also requires consideration prior to investing in these products. Should a corporate treasury be making bets on the credit performance of other reference assets? Maybe - if they are a profit centre, no - if they are not.
Market Access One of the many benefits of the emergence of the credit derivatives market is that it has enabled nontraditional participants to become involved credit markets, thereby increasing liquidity to both the cash and derivatives markets for credit. The market for loans was once restricted primarily to financial institutions such as banks, due to the requirement for specialist skills in assessing loan applicants, economies of scale and also regulatory restrictions (such as the Glass-Steagal Act 55). In those days credit as a consequence was not viewed as a
54 55
Finance and economics editor., Credit derivatives: Russian doll, The Economist, Volume 372, Number 8394, 25 September 2004. A United States 1933 Banking Act that separated commercial and investment banking activities.
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tradable commodity, lenders in most cases held loans (and often corporate bond issues) until they matured which in turn discouraged participation in the market by non-banks. The creation of credit derivatives in the late 1990‟s, almost overnight, revolutionized the perspective of credit as a tradable commodity. Because the credit risk from cash products could now be isolated, it could then be traded in its own right and thus a new asset class was born. Better still participants could become involved in the market without the need to be concerned with the issues and costs of aspects such as administering loans or even dealing with the borrower. Indeed the underlying reference assets for the credit derivatives did not even have to exist as such; they could be based on the perceived credit perception of companies, industries or even countries. As a result new participants became attracted to this newly emerging market, such as fund mangers, investment bank traders, insurance companies and even sovereign nations, all looking to profit or benefit in some way from the isolation of credit as a tradable commodity. Some of the key constraints of the cash market for credit, which can limit organisations from participating, include: Corporate issuers can have preference for bank loans rather than bond issues for debt financing (especially in Europe). This market constraint essentially removes a non-bank from participating in the provision of credit to a desired corporate. A lack of liquidity for specific bond issues/tranches. One of the drawbacks with numerous corporate bond issues/tranches is that they are too small (less than $100 million). This has a tendency to make them unattractive to a lot of potential investors, as this small size discourages an active secondary market for the issue. The limitation of issue size is also evidenced with respect to an issuer providing multiple tranches of a debt issue in order to construct a yield curve (i.e. issuing in key tenors such as 1, 3 5 and 10 year maturities) for investors. A corporation may choose not to borrow (whether from banks or by issuing bonds), because they have no need for debt capital financing. Regulatory restrictions (such as the requirement that lenders be licensed banks) and lack of location presence can also prevent a potential player from participating directly in a market for credit (e.g. a specialist business bank may seek to gain exposure to agricultural sector, but not have the sales force to achieve this). Internal restrictions that an organisation can impose on its employees in order to prevent rogue traders or “hedging” debacles. These can be can include specific; assets classes (such as debt or equity), countries, products and often derivatives. These constraints subsequently create an imbalance between investor demand and issuer supply, in turn providing credit derivative products with the opportunity to address the imbalance. How can credit derivatives be utilised to provide market access? Creating “synthetic longs” - exposure to a desired reference asset can be created through the sale of credit derivative protection (i.e. a CDS). Similarly this method also addresses the investors preferred maturity exposure, as protection can be sold at the desired maturity. Purchasing structured credit products – For potential investors unable or unwilling to sell credit protection an alternative is to purchase credit derivative instruments such as CLN and CDO. Investment banks can tailor these products to specifically incorporate an investor‟s desired credit exposure. Replicating the credit exposure payoff – A third alternative is to replicate the desired credit exposure though the use of a TRORS. This instrument also has the ability to potentially circumvent internal restrictions on products, if a desired cash exposure cannot be acquired directly just replicate the payoff via a swap.
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Market Making An important application that credit derivatives have that generally tends to be overlooked in most texts regarding credit derivative applications is that of market making. This is where an investment bank or securities house will make a two-way market (i.e. quoting bid and offers) for credit derivative instruments. Other applications for credit applications that were described earlier either create investor demand for or supply of credit protection. However this demand and supply is not often simultaneous, which without organisations willing to make a market, would result in the credit derivatives market experiencing periods of either excess demand for or excess supply of credit protection, huge credit spreads and most likely low liquidity as a consequence. Market makers by way of the fact that they are prepared to quote bid and offer prices for customers, create depth for the market and facilitate its continued development by creating liquidity. Market makers are primarily rewarded for this function by retaining what is known as the bid offer spread. A quote of 100/120 for 5 year Ford protection means that the market maker is willing to pay 100 basis points (bp) annually for protection and sell it at 120bp, the difference of 20bp (less transactions costs, i.e. brokerage fees) is where they make their profit. Say the market maker sells protection to the customer at 100bp 56, the market maker can then either: Retain the bid/offer spread - closing the synthetic long credit position in the reference asset (i.e. short CDS position) which has been created for the market maker, by doing the opposite of the original transaction and purchasing 5 year credit protection via a credit derivatives broker or dealing directly with another market maker. Warehouse the exposure - maintaining a short CDS position on the reference asset and manage the risk accordingly, the market maker would then have the view that CDS spreads for that particular reference asset will narrow. This is known as trading and the profits from trading can be dramatic (as can the losses). On $5 million nominal (average market size is $5 to $10 million) the 20bp translates to $10,000 annually for 5 years (or $50,000), this income is for a single transaction, a busy market making desk at a top tier investment bank can be doing more than 200 transactions like this a day. The secondary reward that market makers derive from this flow business as it is called, is market intelligence. The knowledge that market makers derive from customer flows can be harnessed to create profit opportunities from: Trading – The knowledge of what your customers are doing and in the size they are doing it, at the most basic level allows a market maker to front-run customer orders (if a customer sells $100m of nominal, the market maker sells $120 million keeping the first $20 million for themselves and the larger of the change in spreads from any move in credit spread). Similarly knowing what is driving the customer flows, allows the market maker to strategically take views (these can be as simple or as complex as the trader desires) on the markets future direction, with a greater probability that the market maker (trader) will be correct. Structuring – A better understanding of the drivers behind the customer flows, creates the opportunity for an investment bank‟s (or securities house) structuring desk to specifically target selected clients and tailor for them structured credit derivatives (i.e. CLN, CDO or packages so esoteric they are not commonly known in the market) that meet a customers investing or hedging objectives. Significantly for the investment banks, the margins (50bp to 100bp or more) for arranging these structured products can be substantially greater than market making. The income derived from these deals (aside from arranging) can incorporate; management fees, advisory fees, placement fees and anything else can get away with (on top of the bid offer spread from any underlying credit derivatives purchased or sold as part of the structure).
56
Similarly if the market maker buys credit protection at 120bp, they have the same options available, only they do the opposit e.
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The Credit Derivative Market This section provides a snapshot of the credit derivatives market as it stands today. Key aspects, which are addressed, include:
Market size Participants Products Reference assets Relationship with other credit markets Regulatory treatment
Market Size The theme that is common among all the surveys is that growth of the credit derivatives market has increased dramatically, continually surpassing the expectations of market participants. At the end of 2003 57 the global market (excluding asset swaps) measured in terms of outstanding nominal was estimated at USD$ 3.5 trillion, an increase of 82% over the previous year. This growth is expected to continue, with the market growing by a further 42% in 2004 to USD$ 5 trillion and reach USD$ 8.2 trillion by 2006.
The primary drivers of this growth can be attributed to the following:
57
A wider understanding and greater awareness of the benefits of credit protection following recent high profile corporate and sovereign defaults (i.e. Worldcom, Enron, Parmalat, Argentina). Increased acceptance of credit derivatives as an alternative means with which to take both long and short credit exposures. The higher returns on capital provided by credit derivatives compared to more traditional investments (particularly those with funding costs) have encouraged participants to enter the market. Improvements in risk management techniques, along with improved credit derivative valuation. Enhancements to the original ISDA credit derivative documentation improving the clarity of contracts, which as a result has led to less disputes following the occurrence of credit events. The migration of employees from established institutions to the less advanced, which has broadened the industry‟s participants and assisted in the standardisation of structures and documentation. The rapid growth and increasing liquidity is to a certain extend self-reinforcing; as liquidity, price transparency and depth of the market increase, it attracts additional participants to the market, in turn promoting further liquidity.
BBA., Credit Derivatives Report 2003/2004, London, Sep 2004.
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Recent surveys released by the ISDA58 show that the credit derivatives market 59 first overtook that of the OTC equity derivatives market at the end of the 2nd half of 2003, with USD$3.8 trillion nominal outstanding against USD$3.4 trillion. For the 1 st half of 2004 the nominal outstanding for credit derivatives and equity derivatives increased respectively to USD$ 5.4 trillion and USD$ 3.8 trillion. Despite this impressive growth, the credit derivatives market is still small relative to the OTC derivatives market as a whole. The ISDA market survey shows that credit derivatives accounted for only 3.1% of the overall total (USD$173 trillion) of derivative transactions.
Participants The credit derivatives market can be essentially divided into three segments; buyers of protection, sellers of protection and intermediaries. Commercial banks are by far the largest buyers with over 50% of global market share 60. The primary drivers behind the banks usage of credit derivatives are twofold. The first is that they provide an efficient way of reducing their credit exposures, as it is frequently cheaper (and definitely easier) than securitising debt or selling loans on the secondary market, and does not affect the relationship with borrowers. The second reason is regulatory; the current capital requirement on investment grade corporate debt is higher than the internally imposed economic capital requirements, thereby providing banks with an incentive to transfer the risk to entities operating under a different capital regime.
Credit Derivative Market Participants Buyers End of:
2001
Sellers 2004
2001
(forecasted)
Commercial Banks Securities Houses Fund Managers Insurance Companies Corporations Government Bodies
52% 21% 15% 6% 4% 2%
51% 16% 16% 8% 7% 2%
2004 (forecasted)
39% 16% 10% 33% 2% 0%
32% 15% 16% 33% 4% 0%
Source: BBA Credit Derivatives Report 2001/2002
However, credit derivatives are not yet widely spread throughout the banking sector, largely remaining the province of the larger banks. Counterparty risk is heavily concentrated among the top 10 global banks and broker dealers, which together account for around 70% of all credit derivatives transactions 61. Indeed JP Morgan Chase is a counterparty in just over 50% of credit derivative transactions in the US 62. As the market develops, this concentration among the top ten banks is expected to reduce significantly (only a couple of years ago the top 10 had a 99% share of the market).
Top 10 Counterparties 2003 1 2 3 4 5 6 7 8 9 10
Name JP Morgan Chase Deutsche Bank Goldman Sachs Morgan Stanley Merrill Lynch Credit Suisse First Boston UBS Lehman Brothers Citigroup Bear Sterns
Source: Fitch Ratings ISDA., ISDA Market Survey 1987 – 2004 (1H), New York , 22 Sep 2004. The ISDA only includes credit default swaps in their survey, thereby understating the true size of the credit derivatives mark et. 60 BBA., Credit Derivatives Report 2001/2002, London, Sep 2002. 61 Fitch Ratings., Global Credit Derivatives: A Qualified Success, 24 Sep 2003. 62 OCC., OCC Bank Derivatives Report Second Quarter 2004, Administrator of National Banks, Washington DC, 2004. 58 59
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Banks and securities houses also play the role of intermediaries in the market, providing liquidity for the market via trading or through the creation of credit structures (both for buyers and sellers). Credit trading has become an important new source of profit in its own right (see the section on applications) and many banks and securities houses are now entering this market. Indeed many are combining their CDS and corporate bond trading desks (a lot of CDS traders are ex corporate bond traders) in order to encourage traders in identifying arbitrage opportunities between the two markets. Intermediaries are also using credit derivatives as a means of managing credit risk arising from OTC derivative transactions (i.e. interest rate swaps, a practice known as line management). The major net sellers of protection are insurance companies, with several companies devoting substantial resources to underpin this business (especially financial guarantors). Estimates suggest that the insurance companies‟ involvement in the market has enabled banks to transfer over USD 260 billion of credit risk 63. There are a number of reasons for this involvement: 64 Insurance companies generally calculate capital based upon premium, whereas banks calculate it on nominal value. Transfer of credit risk can represent a net capital saving across the two sectors. This may explain why the most highly rated insurers such as monolines are prepared to invest in large amounts of low premium, senior and super senior tranches. Credit liabilities represent a major, relatively new, asset class that can enable insurance companies to diversify their normal investment risks. Insurance companies generally have a broad cultural tolerance for difficult risk. This tolerance is assisted by the fact that at the moment insurers can hold risks for long periods of time without having to mark-to-market65. Insurance pricing is based upon long-run actuarial assumptions, rather than the much more shortterm dynamic bank pricing, so it is possible than in a transaction both the buyer and seller achieve a bargain. This may explain why several international Property & Casualty insurers and reinsurers have been buying mezzanine and principal-protected equity tranches. The great prominence of the insurers may also explain the rapid growth of portfolio transactions. Many insurance companies are restricted in their use of derivatives, but are able to invest in credit linked securities and CDO tranches along with their normal asset classes. Fitch66 also discovered that European regional banks such as the German Landesbanks were major sellers of protection, using the exposures to enhance the low yields that are otherwise available in their low margin domestic markets. Fund managers are active on both sides of the market, buying protection on their investments as well as, to a lesser degree, enhancing yield by purchasing tranches. The nature of the fund tends (i.e. whether a pension, mutual or hedge fund) to dictate the seniority of the investment, with pension funds buying senior tranches and hedge funds the mezzanine and equity tranches. Hedge funds are also becoming increasingly active in trading credit derivatives (in particular credit structure arbitrage - which is the arbitrage of; cash vs. credit derivatives vs. the equity of a reference asset). Non-financial corporations are generally net buyers of protection, but their direct activity in the market has been limited to date, with only a handful of large multi national corporations involved. There are, however a number of credit derivative applications that can be readily adapted for use by corporations. Examples may be a company using a CDS to buy protection against credit extended to customers or against a major supplier defaulting. Successful marketing of the advantages of credit derivatives by the investment banks to corporations is likely to result in this area of the market increasing activity. Participation from government bodies and supranationals (i.e. World Bank and IMF) has been very limited. Similar to corporations, these entities are natural buyers of credit protection examples may include; mitigating the credit risk of major long term project financing (e.g. construction of bridges and roads) or an Export Development Agency (EDA) reducing the credit risk form holding emerging market sovereign 63
Fitch Ratings., Global Credit Derivatives Survey: Single-Name CDS Fuel Growth, 7 Sep 2004. Ernst & Young., Credit Derivatives; Financial Services, Ernst& Young LLP, London, 2003. 65 Daily valuation of an asset at current market prices, leading to unrealised profit and losses. 66 Fitch Ratings., Global Credit Derivatives Survey: Single-Name CDS Fuel Growth, 7 Sep 2004. 64
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exposures to markets they wish to develop for export. It is surprising that these participants have not been more active in the market. Retail investors are currently precluded from the credit derivatives market entirely, by way of its OTC nature. The absence of any retail investor credit derivative products is due principally to the fact the market is so new. Currently there are a number of exchanges looking to list credit derivative futures contracts on credit indices, of which the Singapore Exchange will launch the first in late 2004, based on the Asian Trax X indexes67. Such a development makes the market more accessible to small participants such as retail investors and smaller banks, owing to the small size of contracts and the absence of counterparty risk (due to margin and daily margin requirements of open futures positions). Credit derivative traders expect that credit derivative futures will result in greater transparency to the market as a whole (as prices are easily disseminated) thereby improving liquidity and subsequently growing the market further.
Products The latest BBA Credit Derivative report 68 has shown that the most popular credit derivative product by market share continues to be credit default swaps with 51% of the market in 2003, up from 45% in 2001. One of the key drivers behind the popularity of CDS is their use by both intermediaries and investors to delta hedge their portfolio credit derivative exposures69, thus as portfolio products experience growth so do CDS. The BBA note that one of the main developments since the previous report in 2001 was the introduction of credit derivative indices, which already accounted for 11% of the market at the end of 2003. Expectations are that this market share will further increase to 17% by 2006. Global Market Share of Credit Derivatives Products 2003 51.0% 16.0%
11.0% 1.0% 3.5%
3.5% 3.5%
7.0%
Credit Default Swaps Portfolio/Synthetic CDOs Indices Credit Linked Notes Asset Swaps Total Return Swaps Basket Products Credit Spread Products Equity Linked Products
3.5% Source: BBA Credit Derivatives Report 2003/2004
With the exception of Credit linked notes, no other product type captured more than 7% market share in 2003 and were not predicted to do so in the near future.
67
Trinephi, M., Credit indexes: Exchanges look to futures, Asiarisk, Apr 2004. BBA., Credit Derivatives Report 2003/2004, London, Sep 2004. 69 Fitch Ratings., Global Credit Derivatives Survey: Single-Name CDS Fuel Growth, 7 Sep 2004. 68
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Reference Assets Credit protection written on sovereign names were prevalent as reference assets in the early days of the credit derivatives market, however the share of sovereigns as reference assets has declined from over 50% in 1997 to less than 10% in 2003 70. In contrast, corporate names have become the most common, accounting for 65% of all reference assets in 200371. This growth in corporate names as reference assets is reflective of the rapid growth of the corporate bond market from the mid 1990‟s 72. Similarly the notable reduction in debt out-standings by a number of corporate issuers (i.e. calling bonds) over the past year is most likely to maintain the dominance of corporate names as the majority reference assets. This is due to market participants switching from cash to credit derivatives in to maintain credit exposure to specific corporate names. Global Reference Assets by Type 2003 Corporate 65%
Sovereign 6%
Financials 17%
Other 7%
Source: Fitch Ratings
Asset Backed Securities 5%
The number of actively traded corporate names is around 500 to 1,000, although trades have occurred on up to 2000 names73. The majority of these companies are rated by the major agencies with approximately 82% investment grade (BBB ratings and above), though as the market develops further it is likely that the percentage of sub-investment grade reference assets will increase. The rationale behind a move to lower credit grade reference assets intuitively makes sense, as the demand for credit protection will increasingly be for riskier reference assets 74. Similarly Fitch75 note that the reduction in demand for senior and super senior protection (CDO), combined with the launch of high yield CDS indices, provide a further explanation for this ratings shift. Hedge funds are also thought to have increased interest in trading high yield names. These factors have contributed to the increase of sub-investment grade credit exposures to 18% in 2003, up from 8% in 200276. Global Credit Derivative Exposures by Rating 2003 AA 10%
AAA 17%
A 25%
Sub Investment Grade 18%
Source: Fitch Ratings
BBB 30%
70
Nomura Fixed Income Research., Credit Default Swap (CDS) Primer, New York, 12 May 2004. Fitch Ratings., Global Credit Derivatives: A Qualified Success, 24 Sep 2003. 72 Nomura Fixed Income Research., Credit Default Swap (CDS) Primer, New York, 12 May 2004. 73 Ernst & Young., Credit Derivatives; Financial Services, Ernst& Young LLP, London, 2003. 74 Unless an investor is very risk adverse, why buy credit protection against a reference asset that has a very low probability of default? 75 Fitch Ratings., Global Credit Derivatives Survey: Single-Name CDS Fuel Growth, 7 Sep 2004. 76 Fitch Ratings., Global Credit Derivatives Survey: Single-Name CDS Fuel Growth, 7 Sep 2004. 71
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The most actively traded reference assets for the month of July 2004 were: Ford Motor Co, General Motors, Altria Group, Daimler Chrysler, General Electric, Verizon Communications, Duke Energy Corp, MBIA Insurance, Eastman Kodak and Rolls Royce PLC 77.
Contract Size & Maturity One of the key features distinguishing OTC derivatives from their exchange traded (ET) brethren is the fact that contract size and maturities are non-standardised. Like other OTC derivatives, credit derivatives have no limit to either the size or maturity of a specific contract. However, the average size of contracts traded ranges from a nominal of USD$5 to USD$20 million, with the USD as the most favoured currency denomination. Maturity of contracts ranges from 1 to 10 years, with the 5-year maturity being the most popular tenor. As the market continues to increase both its liquidity and depth, it is expected that activity in other tenors (especially around the five-year tenor) will experience notable increases.
Credit Default Swap Spreads78 The premium paid for protection by a buyer to the seller is called a CDS spread It is quoted in basis points per annum of the contracts nominal value and is usually paid quarterly. It should be noted that the spread quoted on a CDS is NOT the same as the credit spread of a corporate bond to a government bond. The CDS spread is the annual price of protection for a reference asset and not based on any risk-free bond or any benchmark interest rates (think of it in a similar capacity as an annual insurance premium, which is fixed for a stated period). For example, the 5-year default swap quote for Ford Motor Corp (the top reference entity) is 168.77/172.66 as at 8 October 200479. This means that a protection buyer of Ford on a nominal value of USD$ 10 million would pay 172.66 basis points, or USD$ 43,165 every quarter until expiry 80 of the contract, as the premium for the protection received.
Relationship with other Credit Markets Credit derivatives have fostered improved liquidity in the cash credit markets by making it easier to access a diversified portfolio of names and, when desirable, actively short credit risk. Originators of credit, as a result, are less capacity constrained in terms of industry and obligor exposures. Moreover, the market does appear to be moving toward greater liquidity and diversification as more reference entities are actively traded 81. Similarly the credit derivatives market leads to a convergence in prices on loans, bonds, asset swaps and CDS. As differences in relative credit spreads (funding costs aside) allow traders to arbitrage the market, in turn removing pricing anomalies. Prices on these products are unlikely to converge completely: as loans may contain clauses and covenants that allow lenders to take pre-emptive action to protect their exposure more easily than bondholders or banks may under price loans in order to attract future business with a borrower. Similarly there are the funding costs to consider on cash products, whereas credit derivatives are unfunded (the exception being structures such as CDO and CLN). There is now anecdotal evidence that the credit derivatives market is now leading the cash market, as CDO structures hedged with CDS are having a greater effect on the current general tightening of credit spreads of cash products than that of traditional cash market spread drivers. Similarly the growth of structured credit derivative products is essentially reinforcing the expansion of the credit derivatives market as a whole. This is because traders are hedging these structures with vanilla credit derivative products such as CDS and credit indices.
77
www.fitchratings.com/corporate/sectors/crdt_drvtvs/cdx_index.cfm Nomura Fixed Income Research., Credit Default Swap (CDS) Primer, New York, 12 May 2004. 79 Bloomberg L.P., CDSD (Ford), 11 Oct 2004. 80 Unless prior to expiry, the protection buyer closes out the contract with the originating seller or the reference entity defaults. 81 Fitch Ratings., Global Credit Derivatives: A Qualified Success, 24 Sep 2003. 78
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Regulatory Treatment of Credit Derivatives 82 Regulatory treatment of risk transfer by banks using credit derivatives has been and remains important to the growth of the market. It is not a mere coincidence that more CDO transactions occur towards the end of the year, prior to financial and regulatory reporting dates. Bank regulators presently do not have a common internationally agreed approach to the affects of credit derivatives on bank capital requirements. Consequently making it possible for banks to arbitrage regulatory regimes and locate units in countries that provide favourable treatment. Similarly it is possible for institutions, especially insurers and hedge funds (which are not subject to the same regulation as banks) to create significant concentrations of correlated credit risk without the necessity to identify theses positions to regulators. Changes to the Basel Accord83 include a standardised treatment of credit derivatives. Protection provided by non-banks of high credit quality (such as insurers) can reduce the risk weight of a bank‟s underlying exposure, provided the credit derivative includes defined credit events that mirror the ISDA definitions. There are two approaches available to banks calculating their capital requirements: Standardised approach – based on external ratings. Internal ratings approach (IRB) – based on internal ratings set by the lending bank with reference to the probability of default. For protection buyers, the banking book treatment for exposures protected using the standardised approach would be calculated with the following formula:
r * ( w r ) (1 w) g
(5)
where r* = effective risk weight of the position, taking into account the risk reduction from the CDS r = risk weight of the underlying obligor w = residual risk factor, set a t 0.15 for credit derivatives g = risk weight of the protection provider. The risk weights of the obligor (r) and the protection seller (g) will depend on their respective external ratings. Consider for example a AAA rated insurer (20% weighting) selling protection on an underlying exposure which was a B rated corporate (100% weighted), a bank with a required 8% capital ratio would see its capital requirement on an unprotected $100 million exposure, decrease from $8 million to $2.56 million with the inclusion of CDS protection. 100% 8% $100m $8m (unprotected exposure) (15% 100%) (85% 20%) 32% (the effective risk weight) to 32% 8% $100m $2.56m (final capital requirement for exposure protected with a CDS) The (w) factor is intended to capture any residual risk that protection purchased using CDS might be unenforceable, leaving the bank with an unhedged exposure to the underlying obligor. A similar formula, using probability of default rather than risk weights, is proposed for banks using the IRB approach. Banks using the Advanced IRB are permitted to use their own methodology to estimate default probability for exposures protected by CDS. For the trading book, Basle II also has an affect on the specific capital charge applied to trading book positions hedged with credit derivatives. In this case the process is much simpler, allowing an 80% offset for positions hedged using CDS or CLN, providing the reference asset, maturity and currency of the underlying position are an exact match. The offset is applied to the side of the hedged transaction with the higher capital charge. In instances whereby the reference asset is identical and only the maturity and currencies are mismatched, only the higher of the specific risk capital charges for the two sides of the hedge would apply.
82
Rule, D., The credit derivatives market: its development and possible implications for financial stability Bank of England- Financial Stability Review, Jun 2001. 83 Basle Committee on Banking Supervision, Consultative Document: Overview of the New Basel Capital Accord, Basle, Apr 2003. MGSM 952, Research Project, November 2004, London
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Credit Default Swap Valuation This section covering the pricing/valuation84 of CDS is an area that much of the research and literature published on the subject has a tendency to unnecessarily overcomplicate. Like many financial derivatives instruments, the valuation of CDS is essentially a case of deriving the present value of actual and possible cashflows and arriving at a net present value. Valuation for this section focuses entirely on that of CDS despite the numerous credit derivative products that exist today. The rationale behind this is that CDS are the leading credit derivative product (in market share and liquidity) and as a consequence they are a building block for many other credit derivative products. Specific areas that are addressed include the following: Key pricing variables Default probabilities and recovery rates Intuition behind CDS valuation With respect to valuation, three popular approaches are examined which include: “Back of envelope” Replication Modeling In order to move away from pure theory to that of practical application, an example of CDS valuation using the JP Morgan model 85 is provided. Unlike many academic papers on CDS pricing, this example is presented in an easily comprehensible format (i.e. it can be readily replicated by the reader), using current market data.
Key Pricing Variables 86 When valuing any type of financial instrument, it is absolutely crucial to understand not only the variables going into a methodology (and why), but also what assumptions (if any) the methodology makes, for it to be valid. In essence a participant should know what drives a specific methodology or model, it sounds obvious but there are a lot of people that trade products using methodologies and models like a “black box” (i.e. they don‟t know what input variables drive the valuation output). So how do you determine how much CDS protection should cost? First, define the variables that are incorporated into the methodology used, and then understand which variables are excluded (and why). The most important variables for valuing a CDS are. Probability of default and the recovery rate are somewhat subjective and can be obtained in numerous ways (which are described in detail later). Correlation between the reference asset(s) and the protection seller is important, being that buying protection on a reference asset that is highly correlated with the protection seller is in essence like giving away cash and quite stupid (e.g. buying protection on the US Investment bank JP Morgan from JP Morgan). The higher the correlation between the two, the greater the likelihood that if the reference asset defaults, so too does the protection seller. Nevertheless many models make the assumption that the correlation is zero and can thus be ignored because (a) it simplifies the model and (b) lessons in stupidity would have to be taken to make such a mistake. If correlation is incorporated into a model then so too must the joint probabilities of default. Maturity of the contract is the most simple, being that it is purely objective. Yet the maturity of protection is a major determinant in the final value of a CDS (intuitively a long-dated CDS is going to be more expensive than a short-dated one).
A distinction drawn between that of the CDS price and it‟s value, is that the price is the CDS “fair” value (i.e. Par CDS spread, in basis points) and the value is the present value of the CDS in dollar terms. However both terms can be readily interchanged. 85 JP Morgan., Par Credit Default Swap Spread Approximation from Default Probabilities; JP Morgan Inc. Credit Derivatives, New York, Oct 24, 2001. 86 Tavakoli, J., Credit Derivatives: A guide to instruments and applications, John Wiley & Sons, 1998. 84
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Other variables, which require some level of consideration, yet are generally overlooked in most quantitative valuation methodologies are: Demand and supply for credit protection has a direct bearing on current CDS par spreads (high demand causes CDS par spreads to widen, whereas excess supply causes CDS par spreads to narrow) and subsequently their values, yet by their nature are very hard to model in any quantitative form. Economic research can be utilised to assess whether or not the reference asset‟s credit quality will improve or deteriorate (assuming of cause that the research is any good) and thus provide and idea of the future direction of CDS spreads.
Default Probabilities and Recovery Rates Central to most CDS valuation models are the default probabilities and the expected recovery rate, as without these key variables any model valuation is going to close useless. It can be argued that the key distinction between the various types of models available for valuing CDS, are in the methods utilised to determine the default probabilities (and to a lesser extent the recovery rate). There are no hard and fast rules to obtaining either default probabilities or recovery rates. Methodologies available range from the simple to the highly complex, each with their own inherent pros and cons. The most common of which are:
Historical data - This method is arguably the most basic, both default probabilities and recovery rates can be taken from published historical data from the many rating agencies (see the section Introducing Credit Risk for an example). Nothing easier, however there are pitfalls with this method: the data is historical and does not necessarily predict future performance, data may not be specific enough with the user perhaps having to use an industry sector as a proxy for their reference asset (especially so for sovereigns) - resulting in CDS valuations based on an industry sector rather than that of a specific reference asset (i.e. incorrect values). Even if this data is obtained from proprietary databases, the same drawbacks apply. Transition ratings - similar to using historical data (see the section Introducing Credit Risk for an example), transition ratings can be obtained from publicly available data or from proprietary databases (or even a combination of both). However whereas the historical data method uses historical default events per industry sector, transition ratings focus on the likelihood of a reference asset‟s credit rating changing. From here the user can apply the historical default rates for a specific credit rating and multiply by the probability of a change in each rating (i.e. using matrix algebra). CDS Spreads – Given a curve of par CDS spreads (i.e. CDS spreads of varying maturities) each with a net present value of zero, an algorithm can be constructed that calculates the implied default probability by using a bootstrap procedure. This particular method is probably the most accurate of the methodologies available, as it is the most reflective of market sentiment. The drawback is that it is only useful for the most liquid of the underlying reference names (i.e. the top 100) for CDS. A less popular reference name means that either a proxy default curve is calculated or that the default curve is implied from illiquid spreads (and is wrong). Issuer (credit risky) yield curves – Assuming that the credit spreads between risky bonds and riskfree bonds are purely reflective of the likelihood of default - then this is an awesome method to use. As market sentiment changes this is immediately shown in a change in the credit spread, and thus default probability. Unfortunately credit spreads do not just reflect the market view on an underlying bonds default probability87, they also incorporate factors such as: supply and demand, tax, liquidity, interest rates and the bonds level of seniority (which affects any expected recovery rate). This approach also relies on obtaining a recovery rate from some other source (see historical data or transition ratings matrices). Despite the drawbacks, examples of Hull‟s methodologies for deriving default probabilities from issuer yield curves are demonstrated in the following section. Use of equity prices – The above methodologies are all generally reliant to at least some degree on a company‟s credit rating. Because ratings agencies generally only review credit ratings annually, any ratings changes (unless a company is under a credit watch) follow after the market has already
87
Delianeis, G. and Geske, R., The Components of Corporate Credit Spreads: Default, Recovery, Tax, Jumps, Liquidity and Market Factors, University of California, Los Angeles, 2001 MGSM 952, Research Project, November 2004, London
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digested any pertinent information that will affect a company‟s default potential (lawsuits, losses etc). Leading many market analysts and academics to argue that equity prices are more relevant for deriving default probabilities. The Merton88 model is a derivation of the well-established BlackScholes model89 and shares the same assumptions. The model was originally proposed as a means of assessing credit risk by characterising a company‟s equity as a call option on its assets. The equity in a firm is a residual claim; equity holders receive the residual of the cashflows left after other financial claim-holders (e.g. lenders or accounts payable) have been satisfied. On liquidation the same principle applies, equity holders receive the balance of any cash or assets once all outstanding debts and other financial claims are paid off. Thus equity can then be viewed as a call option on the firm, whereby exercising the option requires the firm to be liquidated and the face value of the debt (treated as the exercise price) to be paid off. The firm is the underlying asset and the option expires on maturity of the debt. The default probability is obtained by calculating the equation N (d2 ) 90. The intuition behind the model is perfectly sound; unfortunately the model‟s assumptions (such as a single debt issue) and its simplicity require that the model be modified significantly before it can provide any tangible use. KMV91 is a big exponent of this type of technique; they apply a transformation to the probabilities derived from Merton‟s model to produce default probability estimates, which in turn are calibrated into „real‟ default probabilities using monotonic mapping based on historical experience.
Probability of Default Assuming No Recovery 92 Hull is a popular reference for both professional and aspiring professionals in the financial markets. Thus it is appropriate to demonstrate the derivation of default probabilities from issuer yield curves using Hull‟s methodology, because it is commonly accepted and widely known. where y*(T) is the yield on a T-year risk free zero coupon bond y(T) is the yield on a T-year corporate zero-coupon bond Q(T) is the probability that the corporation will default between time zero and time T Using the equations (1) and (2) the value of a T-year risk free zero coupon and a similar corporate bond with principal of $1is e y
e
y* ( T ) T
e y (T )T
*
(T )T
and e y (T )T . The expected loss from default is therefore
Making an assumption that nothing will be recovered from the corporate defaulting, the calculation of Q(T) is quite easy. There is a probability Q(T) that the corporate bond will be worth zero at maturity and a probability of 1-Q(T) that it will be worth 1. The bonds value is then
Q(T ) 0 1 Q(T ) e
y* (T )
1 Q(T ) e y (T ) *
The yield on the bond is y(T), such that
e y (T )T 1 Q(T ) e y (T )T *
meaning that
e y (T )T e y (T )T *
Q(T )
e y (T )T *
reducing to
88
Merton, R., On the Pricing of Corporate Debt: The Risk Structure of Interest Rates; Journal of Finance, Vol. 29, pgs 449-470, 1974. Black, F. and Scholes, M., The Pricing of Options and Corporate Liabilities; Journal of Political Economy, Vol. 81, pgs 81 -98, 1973. 90 See Merton for a full break down of the model and its inputs. 91 http://www.kmv.com 92 Hull, J., Options, Futures and Other Derivatives: Prentice Hall, 5th Edition, 2000. 89
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Q(T ) 1 e
y (T ) y* (T ) T
(6)
This methodology is demonstrated using current market data93 in the following table. Probabilities of Default Assuming No Recovery Maturity Benchmark Corporate Expected Default zero rate zero rate default loss probability (years) (%) (%) (%) in year (%) 1 2.53 3.38 0.8489 0.8489 2 2.93 4.12 2.3653 1.5164 3 3.25 4.81 4.5555 2.1902 4 3.53 5.41 7.2370 2.6815 5 3.77 5.99 10.4852 3.2482
Probability of Default Assuming Recovery The assumption that nothing will be recovered in the event of default is not particularly realistic. Upon bankruptcy, creditors owed money by the defaulting company file claims against the company‟s assets. The liquidator then sells these assets and the proceeds are used to pay off as much of the claims as possible. These claims are categorised by seniority of the debt for which the more senior the debt, the greater the priority of those debt holders claims (i.e. senior bond holders get paid before more junior debt holders, and equity holders only receive any remaining residual amounts after the debt holders have been paid) Therefore the above equations can be thought of as that of a primer to default probabilities incorporating a recovery rate, which follows. Hull and White94 define the recovery rate as the proportion of „claimed amount‟ received in the event of a default. Making the assumption that the claimed amount for a bond is the no-default value of the bond, the calculation of the default probability of default is simplified. The same notation as the earlier equation (6) is used with the addition of R as the expected recovery rate. Thus in the event of a default the bondholder receives a percentage (R) of the bond‟s no-default value. If there is no default, the bondholder receives 1 (on principal of $1). The bond‟s no-default value is e y
*
(T )T
and the probability of a default is Q(T)
The value of the bond is thus
1 Q(T )100e y (T )T Q(T )100Re y*(T ) so that
100e y (T ) 1 Q(T )100e y*(T )T Q(T )100Re y*(T )T which gives
e y*(T )T e y (T )T Q(T ) (1 R)e y*(T )T which can be reduced to
1 e Q(T ) 1 R
y (T ) y*(T )T
(7)
93
Bloomberg L.P., SWDF, 27 Oct 2004. Benchmark and Corporate zero curves were derived from their respective par curves (i.e. discount rates from par curves were used to derive the respective zero curves) 94 Hull, J., Options, Futures and Other Derivatives: Prentice Hall, 5 th Edition, 2000. MGSM 952, Research Project, November 2004, London
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This is demonstrated using the same financial data as previously in the following table. Probabilities of Default with 40% Recovery Maturity Benchmark Corporate Expected Default zero rate zero rate default loss probability (years) (%) (%) (%) in year (%) 1 2.53 3.38 1.4148 1.4148 2 2.93 4.12 3.9422 2.5274 3 3.25 4.81 7.5925 3.6503 4 3.53 5.41 12.0617 4.4692 5 3.77 5.99 17.4753 5.4136
Note that in calculating the default probability with a recovery amount, it results in a default probability that is higher than if no recovery amount is assumed. Which is a slight problem, as the probability of default should in theory be independent of the expected recovery amount (as recovery occurs after a default).
Hazard Rates95 Much of the literature on CDS valuation refers to hazard rates rather than that of default probability density (i.e. default probability). This can potentially result in confusion for the practitioner unless the relationship between the two is defined. The hazard rate h(t) at time t is defined so that h(t)dt is the probability of default between time t and t + dt, conditional on no earlier default (i.e. h(t)dt is the probability of default between time t and time t + dt conditional on no default between time zero and time t). The default probability density, q(t) is defined such that q(t)dt is the unconditional probability of default between times t and t + dt as seen at time zero. Either h(t) or q(t) can be utilised in describing default probabilities. They provide equivalent information and the relationship between the two is t
q(t ) h(t )e 0
h ( ) d
(8)
The table below shows the relationship between that of hazard rates and default probabilities. Hazard Rates Vs. Probabilities of Default Assuming (No Recovery) Maturity Benchmark Corporate Default Hazard zero rate zero rate probability Rates (years) (%) (%) in year (%) (%) 1 2.53 3.38 0.8489 0.8562 2 2.93 4.12 1.5164 1.5532 3 3.25 4.81 2.1902 2.2947 4 3.53 5.41 2.6815 2.8907 5 3.77 5.99 3.2482 3.6287
Intuition behind CDS Pricing A CDS consists of two legs (like an interest rate swap), a fixed leg and a contingent leg. On the fixed leg side, the protection buyer (payer) makes a series of fixed periodic 96 payments of CDS premium until the earlier of; contract maturity or default of the reference asset. With the contingent leg, the protection seller (receiver) makes a single payment, only in the event of the reference asset defaulting (hence the term contingent).
95 96
Hull, J., Options, Futures and Other Derivatives: Prentice Hall, 5 th Edition, 2000. Generally quarterly payments, but they can be monthly, semi annual or annual payments.
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The net present value (NPV) of the CDS is simply the algebraic sum of the present values of its two respective legs. Again like an interest rate swap, at inception the market premium on a CDS is set such that the value is set to zero. Value of CDS = PV [contingent leg] – PV [fixed leg]
(9)
An illustration of the cashflows of a CDS is shown below.
Credit Default Swap Cashflows (a) no default X bp
X bp
X bp
X bp
t3
t4
X bp
Protection buyer
t0
t1
t2
X bp
X bp
t5
Protection seller
(b) default X bp
X bp
t3
t4
Protection buyer
t0
t1
t2
t5
Protection seller
(1-R)
The payment made by the protection seller following a default by the reference asset is usually (1-R), where R is defined as the recovery rate of the reference asset, multiplied by the nominal amount of the CDS contract. As an example, if the expected recovery rate on a reference asset is 40% of it‟s par value, then following default the protection seller will pay 60% of the remaining value.
“Back of Envelope” Valuation97 A quick and dirty way of obtaining an approximate valuation for an existing CDS is to use a “back of envelope” method. This approach although not particularly accurate is useful in capturing the “flavour” of a change in CDS value following a move in CDS spreads (and time) and also demonstrates that you do not need a Doctorate to get a quick valuation for a CDS. What is the value of the following CDS? Bought protection 4 ½ years to maturity Nominal is USD$10 million Current CDS spread is 110 bp „Dealt‟ CDS spread was 100bp What is the hedge of the CDS? The holder of the above CDS can hedge themselves by selling protection now. In the situation whereby the existing CDS was not hedging any other credit exposures, the profit from this strategy is the current CDS spread less the initial CDS spread (10 bp), multiplied by both the remaining maturity and the nominal of the contract. PV = (Current CDS spread – Dealt CDs spread) x remaining maturity x nominal PV = (110-100) x 4 ½ x $10 million PV = 45 bp x $10 million PV = $45,000
(10)
As such this approach has the PV equal to the total income over the remaining life of the trade and its hedge.
97
CIFT Ltd., Masterclass in Advanced Credit Derivatives, Public Course, London, June 2004.
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Unfortunately the above method is only useful where there is a low probability of default and changes in CDS spreads are fairly low as contingent payments are not incorporated in the approach.
Replication Approach to Valuation98 This methodology values a CDS by evaluating the cost of a portfolio that replicates the cashflows/payoffs arsing from the CDS. The approach by Duffee is summarised in the table below.
Short Default Protection (sell CDS) Long Default Protection (buy CDS)
=
Long Risky Bond
+
Short Risk-free Bond
= Short Risky Bond
+
Long Risk-free Bond
However although correct, why use bonds when asset swaps are a more efficient alternative?
Asset swaps99 Because a CDS can be synthetically replicated, CDS valuation does not have to be model dependent. Similarly it is a reasonable assumption to consider that the underlying cash market is efficient, on average. Asset swaps provide a pricing source for valuing default risk. Asset swaps provide a context for relative value, as reference assets have transparent prices. This approach also makes it possible to tie expectations about cash bond pricing to expectations about the valuation of a CDS – an important consideration when constructing any form of hedging. The following picture shows how a CDS can be replicated. In this example the investor is selling credit default protection (i.e. equivalent to a short CDS).
R e p lic a tin g C D S E x p o s u re – p ro te c tio n s e lle r C o rp o ra te B ond P r in c ip a l
T + C o rp o ra te s p re a d T + S w ap sp read
Sw ap M a rk e t
In v e s to r L ( L ib o r )
C o lla te r a l
R e p o ra te (L - X ) P r in c ip a l * ( 1 – h a ir c u t)
R epo M a rk e t
In replicating the trade the investor undertakes the following: Purchases a cash bond with a spread T + Sc for par. Pays fixed on an interest rate swap (T + Ss) with the same maturity as that of the cash bond, and receives Libor. Finances the position (i.e. the purchase of the cash bond) in the repo market. The repo rate is quoted at a spread to Libor (L - X). Pledges the bond as collateral and is charged a haircut by the repo counterparty. Each of the four trade components may not be self-explanatory to investors unfamiliar with hedging and financing, thus these steps are expanded upon.
98 99
Duffie, D., Credit Swap Valuation, Financial Analysts Journal, Volume 55, no 1, Jan/Feb 1999. Kasapi, A., Mastering Credit Derivatives: a step-by-step guide to credit derivatives and their application, Financial Times, London, 1999.
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Interest Rate Hedge The interest rate swap component of the trade eliminates the interest rate exposure of the cash bond (i.e. the PV01 and the convexity). If this exposure were left unhedged the structure would simply equate to that of a leveraged long position in the fixed rate corporate bond (T + Sc – (L-X)). Why the interest rate hedge is via a swap and not a treasury (risk-free bond) as per Duffie. Libor is a consistent benchmark of value – there are anomalies associated with pricing an asset to a treasury given the high volatility of its term financing. As a result, Libor based benchmarking is increasingly becoming standard. Libor is also the benchmark for the bank loan market. Lock-in cashflows for term of the swap – if the short were structured with treasuries and repo, the financing would need to be rolled every three months, whereas when using a swap, financing is set for the term of the structure. Favourable economics– it is cheaper to hedge with a swap that a treasury. The cost of the hedge is net cash flow, not the cash market spread between the asset being hedged and the spread on the swap to treasury. It may seem strange to pay the swap spread (T+ Ss) rather than the treasury coupon (T). But the swap hedge will receive the lower treasury repo rate. Financing of cash position As CDS is being replicated, financing has to be introduced into the structure. This is achieved with a corporate or sovereign bond repo. The purchase of the bond is funded via a collateralised loan to a repo dealer. There are two important components to this trade Haircut- charged by the lender, which is the difference between the securities purchased and money borrowed for the loan. Haircuts vary widely according to the type of collateral, the credit of the counterparty, the term of the repo agreement and the type of funding. It is designed to protect the lender from market risk of the collateral. The interest earned on the haircut is compensation for assuming the counterparty risk. Moreover since the haircut represents the capital in the trade, institutions with the cheapest cost of capital will be able to assume the credit exposure for the lowest net cost. Repo Rate- the financing charge is the repo rate for the specific collateral. The rate will vary depending on the demand to borrow (or lend) the security. This rate is denoted as L-X, since several liquid credits have repo rates that are usually, but not always less than Libor.
Cashflows of CDS Replication Receive Pay Cash bond T + Sc $1 Swap hedge L T + Ss $1 (L - X) Repo Transaction Sc - Ss + X Sc=Corporate spread, Ss=swap spread ( no haircut)
Closer examination of the CDS Replication table (above) reveals that the cashflow nets to (assuming a haircut of 0% for simplicity)
(Sc Sc) X If the repo rate of the bond were Libor flat (X=0), the exposure would be the asset‟s swap spread (Sc –Ss). The remaining cashflow looks very much like the payment made to a protection seller of a CDS, a simple annuity stream expressed in basis points for the life of the trade. If the bond were to default, the repo would be terminated and the investor would lose the difference between the purchase price and recovery price of the bond. However payments on the interest rate swap continue to be exchanged until maturity. The asset swap pricing approach is an efficient way to gauge CDS “fair value” because if the actual CDS pricing differs significantly from that of the synthetic pricing (i.e. the asset swap), arbitrage opportunities MGSM 952, Research Project, November 2004, London
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will emerge. Mispricing opportunities can be arbitraged most efficiently by the market makers, which have the lowest transactions costs and institutions with the highest credit quality, which can exploit their relative advantage in funding costs. Any mispricing between markets (or products) has to be large enough to account for both the basis risk and any transactions costs (slippage, brokerage). This pricing approach provides a means to assess value in the CDS market. The table below, cashflows of a CDS spread lock demonstrate a possible arbitrage.
Cashflows of CDS Spread Lock Receive Pay Cash bond (Short) L - 20 L + 45 CDS 85 Net 20 The table uses the example of a five-year cash bond trading at L+45. Five-year protection for the bond is quoted at 85/90 bps. Thus a protection seller would pay an implied repo rate of L-40, and the spread lock would equate to 20bps of arbitrage profit. This trade assumes a term corporate bond repo market, which may be difficult to find in most markets. The repo would most likely have to be rolled on a short-term basis, rather than for the term of the swap. If this arbitrage did exist, the protection sellers would eventually drive the CDS spread down toward the asset swap level, eliminating the mispricing between the two markets. Aside from arbitrage constraints, CDS par spreads will vary with supply and demand conditions, just like any other type of financial instruments.
Model Approach to Valuation It can be readily argued that the best approach with which to value a CDS is via the synthetic replication as described above. However this approach can only be utilised in cases where the reference asset, has issued bonds that are available to trade via the secondary market. Which introduces the modeling approach to CDS valuation, here two specific models are examined; the first is the Hull and White model 100 and the second is the JP Morgan model 101. Both of these models (and their modifications) are commonly used by practitioners in the market. To convey a practical understanding of this type of valuation methodology, the JP Morgan model is demonstrated in an easily followed example using default probabilities calculated from equation (7) and current market data102.
Hull and White Model103 Hull and White developed a reduced form valuation model, for which their approach was to calibrate the model based on traded bonds of the underlying reference asset on a time series of CDS prices. Like many other approaches the Hull and White model assumes that there is no counterparty default risk. Other key assumptions of the model include; independence of default probabilities, interest rates and recovery rates and that the claim in the event of a default is the face value plus accrued interest. For the valuation of a CDS with $1 nominal principal, the notation used is as follows: T q(t) R
is the life of the CDS in years is the risk-neutral probability density at time t is the expected recovery rate on the reference asset in a risk neutral world (independent of the time of default)
100
Hull, J. and White, A., Valuing Credit Default Swaps I: No Counterparty Default Risk, Journal of Derivatives, 8, 1 Fall 2000. JP Morgan., Par Credit Default Swap Spread Approximation from Default Probabilities; JP Morgan Inc. Credit Derivatives, New York, Oct 24, 2001. 102 Bloomberg L.P., SWDF, 27 Oct 2004 103 Hull, J. and White, A., Valuing Credit Default Swaps I: No Counterparty Default Risk, Journal of Derivatives, 8, 1 Fall 2000. 101
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u(t) e(t) v(t) w s
π A(t)
is the present value of payments at the rate of $1 per year on payment dates between time zero and time t is the present value of an accrual payment at time t equal to t - t* where t* is the payment date immediately preceding time t (both t and t* are measured in years) is the present value of $1 received at time t is the total payment per year made by the protection buyer is the value of w that causes the value of the CDS to have a value of zero is the risk-neutral probability of no credit event during the life of the CDS is the accrued interest on the reference asset at time t as a percentage of the face value
The value π is one minus the probability that a credit event will occur by time T. This also known as the survival probability and can be calculated from q(t) T
π 1 q(t )dt
(11)
0
The payments last until a credit event or until time T, whichever is first. If default occurs at t (t
w q(t ) u(t ) e(t )dt w u (t ) T
0
Given the assumption about the claim amount, the risk-neutral expected payoff from the CDS contract is derived as follows
1 R 1 A(t ) 1 R A(t ) R The present value of the expected payoff from the CDS is
1 R A(t )Rq(t )v(t )dt T
0
The value of the CDS to the protection payer is the present value of the expected payoff less the present value of the payments made by the payer
1 R A(t )Rq(t )v(t )dt w T
T
0
0
q(t ) u(t ) e(t ) dt w u(T )
The CDS spread, s, is the value of w that makes the equation zero, simply rearrange the equation to be
1 R A(t ) Rq(t )v(t )dt T
s
(12)
0
T
0
q(t ) u (t ) e(t ) dt w u (T )
The variable s is referred to as the credit default spread or CDS spread. It is the payment per annum, as a percentage of the nominal principal, for a newly issued CDS.
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JP Morgan Model104 The JP Morgan model is essentially the same as the Hull and White model. Minor distinctions between the models are: The JP Morgan model is a discrete form of valuation, whereas the Hull and White model is continuous. The JP Morgan model takes the claim amount in the event of a default as par less the recovery rate (1-R), whereas the Hull and White model uses par less the recovery rate less any accrued interest owed (1-R-A(t))R All other assumptions are the same. As stated earlier a CDS has two cashflow legs; the fee premium leg and the contingent cashflow leg. To determine the CDS par spread (or premium of the CDS) the net present value of both legs must equal zero (i.e. both legs have the same value). The valuation of the fee leg is approximated by PV of No default Fee payments = SN x AnnuityN or N
PV S N DFi PNDi i i 1
where SN DFi PNDi Δi
is the par spread (CDS premium) for maturity N is the risk-free discount factor from time T0 to Ti is the no-default probability from T0 to Ti (for the specific reference asset being valued) is the accrual period from Ti-1 to Ti
If the accrual fee for the CDS is paid upon default, then the valuation of the fee leg is approximated by PV of No default Fee payments +PV of Default Accruals = S N x AnnuityN + SN x Default AccrualN or N
N
i 1
i 1
PVNoDefault DefaultAccrual S N DFi PNDi i S N DFi PNDi 1 PNDi
i 2
where (PNDi-1-PNDi) is the probability of a default occurring during period Ti-1 to Ti Δi is the average accrual amount from Ti-1 to Ti 2 The valuation of the contingent leg is approximated by PV of Contingent = ContingentN or N
PVContingent (1 R) DFi PNDi 1 PNDi i 1
where R is the recovery rate of the reference asset
104
JP Morgan., Par Credit Default Swap Spread Approximation from Default Probabilities; JP Morgan Inc. Credit Derivatives, New York, Oct 24, 2001. MGSM 952, Research Project, November 2004, London
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Thus for a par CDS it is known that Valuation of fee leg= Valuation of contingent Leg or N
N
i 1
i 1
S N DFi PNDi i S N DFi PNDi 1 PNDi
N i (1 R) DFi PNDi 1 PNDi 2 i 1
this can be rearranged to give an equation for the CDS spread as follows N
SN
(1 R) DFi PNDi 1 PNDi i 1
(13)
DFi PNDi i S N DFi PNDi 1 PNDi i 2 i 1 i 1 N
N
Pricing Example Consider a hypothetical CDS trade on Ford Motor Co; The CDS has a 5-year maturity with a nominal amount of $10 million, the CDS spread is 202 bps (CDS par spreads is 213.39 bp) with payments made semi-annually and the recovery rate is assumed to be 40% of the par value. Discount rates and survival probabilities for each respective payment date are shown below (default probabilities are derived using equation (7)). CDS Valuation Example Term
(years) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
(1) (2) (3) (4) (5) Risky Discount Survival Fixed Expected PV of Fixed Curve Factors Probability Periodic Value of Fixed Payment Par Rates to Period Payment Payment (4) x (1) (2) x (3)
(bps) ($) 0 0 105.95 104,335.18 3.0787 105.19 101,745.23 3.2874 104.00 98,450.73 3.6421 102.49 94,531.33 4.0031 100.71 90,337.77 4.3179 98.59 85,644.80 4.6378 96.33 80,914.81 4.9074 93.83 76,000.25 5.1756 91.06 70,962.30 5.4273 88.05 65,826.46 5.6783 Sum of PV ($) 868,748.85 Nominal Amount = $ 10,000,000, CDS Par spread = 213.39 bps (sa), Recovery Rate = 40%
1.
(%)
(%)
1 0.9848 0.9673 0.9466 0.9224 0.8970 0.8687 0.8400 0.8100 0.7793 0.7476
100 99.30 98.59 97.48 96.06 94.39 92.41 90.29 87.94 85.35 82.52
(bps) 0 106.70 106.70 106.70 106.70 106.70 106.70 106.70 106.70 106.70 106.70
(6) Default Probability for the Period 1 - (2) (%) 0 0.6981 0.7168 1.1092 1.4182 1.6656 1.9847 2.1201 2.3491 2.5907 2.8230
(7) Expected Accrued Payment (3)/2 x (6) (bps) 0 0.75 0.78 1.21 1.58 1.88 2.29 2.51 2.85 3.24 3.65 Sum of PV ($)
(8) PV of Accrued Payment (7) x (1) ($) 0 738.60 750.36 1,149.26 1,452.95 1,688.81 1,990.54 2,104.39 2,308.69 2,523.81 2,728.60 17,435.99
(9) Expected Contingent Payment (1-R) x (6) (bps) 0 41.88 43.01 66.55 85.09 99.94 119.08 127.20 140.95 155.44 169.38 Sum of PV ($) NPV$
(10) PV of Contingent Payment (9) x (1) ($) 0 41,245.07 41,599.39 62,997.28 78,485.49 89,644.32 103,439.32 106,846.55 114,169.62 121,130.96 126,628.19 886,186.18 1.34
Valuing the Fixed Leg –Fixed periodic payments
The present value of all expected fixed payments is found by multiplying each period‟s fixed payment by the respective survival probability (1 minus the cumulative default probability), discounted using the discount factor and summed over the term of the CDS. The bottom number of row (5) in the table above, $868,748.85, is the present value of this component. 2.
Valuing the Fixed Leg – Accrued payments
On the basis that a credit event occurs, midway through the time interval between two payment dates, the value of the accrued premium payment if a credit event occurs is 53.3475 bp (106.7 bp x 0.5). Then the expected value of the accrued payment for each period in 53.3475 bp multiplied by the probability of default for that period, as in column (7) in the above table. Discount these values for all periods and then sum them MGSM 952, Research Project, November 2004, London
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up over the term of the CDS. The resulting present value is $17,435.99 (see the bottom of column (8)). Note that on a relative basis this number is quite small, but this is expected, as the total is a product of the default probability for each period and an accrued payment, should a credit event occur - both of which are small numbers. Taking these two component values above and adding them together provides the present value of the fixed leg (or the PV of the expected payments by the protection buyer over the full 5-year term), which is $868,748.85 + $17,435.99 = $886,184.84. 3.
Valuing the Contingent Leg
Finally the contingent leg can be calculated. The expected value of the contingent payment in the case of a credit event occurring in each period is (1-R) multiplied by the default probability for that period (column (9) in the table). Taking a recovery rate of 40%, the expected contingent payment is 0.60 multiplied by each period‟s default probability. Discount this value for each period and then sum them over the term of the CDS contract. The resulting value is $886,186.13 as in column (10), which is the present value of the expected contingent payments. From here the value of the CDS to the protection buyer (or the fixed payer) when the CDS spread is 213.39 bp per annum as: Value of CDS = PV [contingent leg] – PV [fixed leg] = $886,186.13 - $886,184.84 =$1.34 To view this result intuitively, the average default probability of the term of the CDS is 3.5% per annum (as the survival rate after 5-years is 82.52%) and with a recovery rate of 40%, the average expected loss per year is (1 - 0.40) x 3.5% = 2.1%. The CDS spread is 213.39bp per annum, meaning that in this example the buyer has protection for credit risk with the expected loss of 210 105 bps (on Ford).
105
Actually the Par CDS spread is 213.390323 bp (i.e. when the CDS NPV is zero).
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Bibliography Books Das, S., Structured Notes and Derivative Embedded Securities, Euromoney Books, London, 1996. Hull, J., Options, Futures and Other Derivatives: Prentice Hall, 5 th Edition, 2000. JP Morgan., The J.P. Morgan Guide to Credit Derivatives; Risk Publications, London, 1999. Kasapi, A., Mastering Credit Derivatives: a step-by-step guide to credit derivatives and their application, Financial Times, London, 1999. Steiner, R., Mastering Financial Calculations: A step-by-step guide to the mathematics of financial market instruments, Financial Times, London, 1999. Tavakoli, J., Credit Derivatives: A guide to instruments and applications, John Wiley & Sons, 1998. Wilmott, P., Paul Wilmott on Quantitative Finance-Volume One, John Wiley & Sons, London, 2000. Wilmott, P., Paul Wilmott on Quantitative Finance-Volume Two, John Wiley & Sons, London, 2000.
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Duffee, G. and Zhou, Chunsheng., Credit Derivatives in Banking: Useful Tools for Loan Risk Management?; Federal Reserve Board, Washington DC, Feb 1997. Ernst & Young., Credit Derivatives; Financial Services, Ernst& Young LLP, London, 2003. Finance and economics editor. Credit derivatives: Russian doll, The Economist, Volume 372, Number 8394, 25 September 2004. Fitch Ratings., Global Credit Derivatives: A Qualified Success, 24 Sep 2003. Fitch Ratings., Global Credit Derivatives Survey: Single-Name CDS Fuel Growth, 7 Sep 2004. Gieseck, K., Credit Derivatives and Structured Credit Products, Lecture notes, Cornell University, April 2002. Geske, R., The Valuation of Compound Options; Journal of Financial Economics, Vol 7, 1979. Henry, D., Fuzzy Numbers, Business Week, European Edition, Number 3886-1216, October 4 2004. Hull, J, Nelken, I. and White, A., Merton‟s Model, Credit Risk and Volatility Skews; Working Paper, , University of Toronto, Feb 25, 2003. Hull, J. Predescu, M, and White, A., The Relationship Between Credit Default Swap Spreads, Bond Yields and Credit Rating Announcements; Working Paper, University of Toronto, Mar 2003. Hull, J. and White, A., Valuing Credit Default Swaps I: No Counterparty Default Risk, Journal of Derivatives, 8, 1 Fall 2000. Hull, J. and White, A., Valuing Credit Default Swaps II: Modeling Default Correlations; Journal of Derivatives, 8, 3 Spring 2001. ISDA., ISDA Credit Event Definitions, 1999 and 2003. ISDA., ISDA Market Survey 1987 – 2004 (1H), New York , 22 Sep 2004. JP Morgan., Par Credit Default Swap Spread Approximation from Default Probabilities; JP Morgan Inc. Credit Derivatives, New York, Oct 24, 2001. Merton, R., On the Pricing of Corporate Debt: The Risk Structure of Interest Rates; Journal of Finance, Vol. 29, pgs 449-470, 1974. Modigliani, F and Miller, M., The Cost of Capital, Corporation Finance and the Theory of Investment, American Economic Review, June 1958. Nomura Fixed Income Research., Credit Default Swap (CDS) Primer, New York, 12 May 2004. OCC., OCC Bank Derivatives Report Second Quarter 2004, Administrator of National Banks, Washington DC, 2004. Oldfield, M., Only For the Sophisticated Investor, Euromoney-International Bond Investor, Autumn 1994. Ring, J., Credit Derivative Pricing Models and Methodologies; Models and Methodologies Group Corporate Risk Management, Nomura International Plc, London, May 1999. Rule, D., The credit derivatives market: its development and possible implications for financial stability Bank of England- Financial Stability Review, Jun 2001 S&P, EU 2003 Annual Default Study & Rating Transitions; Feb 13, 2004. MGSM 952, Research Project, November 2004, London
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Skora, Richard, K., Rational Modeling of Credit Risk and Credit Derivatives; Skora & Company Inc. Credit Risk Management, New York, 1998. Skora, Richard, K., The Credit Default Swap; Skora & Company Inc. Credit Risk Management, New York, 1998. Tolk, S., Understanding the Risks In Credit Default Swaps, Structured Finance Special Report, Moody‟s Investor Services Inc, New York, 2001. Trinephi, M., Credit indexes: Exchanges look to futures, Asiarisk, Apr 2004.
Electronic Reference Bloomberg L.P., CDSD (Ford), 11 Oct 2004 Bloomberg L.P., SWDF, 27 Oct 2004
http://www.bis.org http://www.creditmetrics.com http://www.defaultrisk.com
http://www.fitchratings.com/corporate/sectors/crdt_drvtvs/cdx_index.cfm http://www.indexco.com http://www.investopedia.com/terms/c/creditlinkednote.asp. http://www.kmv.com
http://www.moodys.com http://www.riskglossary.com/articles/collateralized_debt_obligation.htm http://www.riskmetrics.com http://www.standardandpoors.com
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