1. Options 3 2. Swaps Interest Rate Derivative Instruments Credit Default Swaps Key Formulas 63

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1 1. Options 3 2. Swaps Interest Rate Derivative Instruments Credit Default Swaps Key Formulas Allen Resources, Inc. All rights reserved. Warning: Copyright violations will be prosecuted. Any use of these materials without the express written consent of the publisher is a violation of federal and/or international copyright laws. 17-1

2 Credit Default Swaps 4. Credit Default Swaps Learning Objectives This summary includes a review and an analysis of the principles set forth by CFA Institute. Upon review of this summary, you should be able to: Discuss the main types of credit default swaps (CDS) and their major characteristics...pg. 50 Explain credit events and their effect on settling CDS contracts...pg. 52 Describe the pricing of CDS contracts...pg. 54 Explain how credit exposure can be modified with CDS, including attempts to capitalize on expectations of changes in the credit curve...pg. 58 Explain how CDS may be used to attempt to profit from discrepancies in valuation of correlated instruments in different markets...pg Allen Resources, Inc

3 Study Session 17 Overview Credit derivatives are used by hedge funds, commercial banks, investment banks, insurance companies, mutual funds, pension funds, corporations, and governments. Not surprisingly, they often are used to manage credit risk (the risk that a borrower will default on its obligations), to achieve the goals of hedging and/or diversification. Credit derivatives also are used to gain exposure to credit risk to increase expected returns and to implement relative value investment strategies (including arbitrage). In addition, credit derivatives may be packaged together to form collateralized debt obligations (CDOs) and other types of structured credit products. The most prevalent type of credit derivative is the credit default swap (CDS). Sometimes, those exposed to credit risk wish to reduce or even eliminate this risk via a CDS. The protection buyer pays a periodic premium (and sometimes an upfront fee also) to the protection seller for a period of time, and if a certain pre-specified credit event occurs, the protection seller pays compensation to the protection buyer. (A credit event can be a bankruptcy of a company, called the reference entity, or a default of a bond or other debt issued by the reference entity.) Unless and until a credit event occurs during the term of the swap, the protection buyer continues to pay the premium until maturity. Should a credit event occur before the contract s maturity, the protection seller owes a payment to the protection buyer, thus insulating the buyer (at least in part) from a financial loss. CDS terminology can be a little confusing. The buyer of a CDS is taking a short position in the credit quality of the underlying issuer, whereas the CDS seller is taking a long position in the credit quality of the underlying issuer. It is noteworthy, and controversial, that the protection buyer need not be a debtholder of the reference entity, nor is the reference entity required to give consent to the CDS agreement. Unlike traditional insurance, there need not be insurable interest. It is solely a contract between the protection seller and protection buyer, and speculation on credit risks is permitted in most jurisdictions. Types of Credit Default Swaps Learning Objective: Discuss the main types of credit default swaps (CDS) and their major characteristics. The main types of credit default swaps are single-name entities, index CDS, and tranche CDS. A single-name entity CDS involves just one reference issuer (say, Coca-Cola) for a given reference debt obligation (typically unsecured). A credit event for obligations ranked at that level or higher will trigger a compensating payment from the swap seller. The amount of settlement payment is determined by the cheapest-to-deliver obligation with the same seniority as the reference obligation Study Guide for the Level II 2015 CFA Exam - Reading Highlights

4 Credit Default Swaps An index CDS pools together the credit risk of multiple borrowers, similar to an exchangetraded fund of equities. Sector concentrations are possible, but if credit risks are highly correlated in the pool, the cost of protection will be commensurately higher. A tranche CDS also pools together the credit risk of multiple borrowers, but only up to a specified level of loss, similar to tranches in mortgage-backed securities. Main Characteristics of CDS In a relatively short amount of time, the CDS market has grown rapidly and become organized like many other financial markets. For example, there is a governing body (The International Swaps and Derivatives Association, ISDA) which has developed a standardized master agreement that parties to a CDS may use. Such standardization fosters liquidity in CDS markets, as does the development of clearinghouses for exchange and settlement of CDS contracts. The main characteristics of CDS are: 1. Reference entity - a single company (or its successor; special rules apply in spinoffs) or a government, the debt of which is protected from loss (up to the notional amount) by the CDS. A basket CDS has multiple reference entities; the first-to-default kind provides compensation for losses from the first reference entity but none thereafter. An index CDS may have over 100 reference entities and offer protection on all, with each entity having a share of the notional amount (the amount of protection). Protection may also be issued on specific obligations, rather than on companies. 2. Notional amount - represents the amount of protection purchased. The notional amount need not be limited to the credit exposure of the buyer as noted earlier, the buyer does not need to have any exposure at all to speculate on credit risks. [CDS swaps that involve investors with no existing exposure to the credit quality of the underlying are termed naked credit default swaps.] 3. Credit event - the event(s) on which payment of the credit protection is contingent. For example: Failure to pay in full or on time the interest or principal due on a credit obligation Bankruptcy filing Debt restructuring (lowering coupon payments, extending maturity) Repudiation of debt (usually only applies to sovereign risks in emerging markets) Violations of bond covenants (technical, not often used) 4. Settlement method - how the protection seller pays the protection buyer should a credit event occur. Physical settlement - the protection buyer delivers the defaulted debt of the reference entity to the protection seller, in an amount equal to the notional amount of the CDS. The protection seller then pays the protection buyer the face amount of the debt Allen Resources, Inc

5 Study Session 17 Cash settlement - seller pays buyer the difference between the notional amount of the CDS protection and the post-credit-event value of the debt. This method is becoming more common, especially since there is often more notional amount in CDS issued than there is of par value of the debt it covers. 5. CDS spread - the premium paid by the protection buyer to the protection seller for the credit protection. Expressed as a rate per year (e.g., spread over LIBOR) but paid quarterly, it equals the IRR which equates the expected premium amounts with the expected losses. Alternatively, some CDS are now priced in such a way that the premium paid is transferred to the seller through two mechanisms: first, a periodic coupon payment (the standard is 1% of notional for investment grade, 5% for below-investment grade), and second, an up-front, lump-sum payment (which can be negative, if the CDS spread is lower than the 1% or 5%, as applicable). 6. Term of contract - the CDS has a limited life, usually a few years, though it can be longer. Also, contracts can be ended early, in effect, by taking an opposite position in a new CDS. Credit Events and Settlement Learning Objective: Explain credit events and their effect on settling CDS contracts. Credit Events The ISDA s Determinations Committee (DC) decides whether a particular corporate event qualifies as a credit event. The most common cause is the filing of bankruptcy (either for reorganization or liquidation). Failure to pay interest and/or principal, even in the absence of a bankruptcy filing, would also qualify as a credit event (as noted above). Restructuring of debt outside of bankruptcy (e.g., changing seniority of issues) is not deemed to qualify as a credit event in the United States, because bankruptcy typically must come first. The ISDA DC may also get involved if, in the event of a merger, divestiture, etc., ambiguity arises regarding responsibility for certain debt issues. They will determine whether a succession event has occurred, and if so, the CDS contract cay be modified by the committee (if necessary) to fairly assign responsibility for debt. Settling CDS CDS settlement begins with ISDA DC making a determination that a credit event has occurred. As with many derivatives, CDS settlement may take the form of physical settlement (CDS protection buyer delivers the debt instrument in exchange for the notional amount of coverage) or an equivalent cash payment. As with many derivatives, physical settlement is less common Study Guide for the Level II 2015 CFA Exam - Reading Highlights

6 Credit Default Swaps Keep in mind that even if a credit event occurs, all may not be lost with respect to the value of the debt instrument. There is typically some residual value that is recovered (e.g., 40%). Since a CDS seller should not have to pay back more than was lost to the protection buyer, we find the following holds true: CDS payout amount = CDS payout ratio Notional amount where: CDS payout ratio = 1 Recovery rate % Note that the recovery rate may not be known for some time; an auction of cheapest-to-deliver debt may be held to estimate it. However, if a CDS allows for either cash or physical settlement, a CDS buyer may find cash settlement preferable if they hold a defaulted bond that is worth more than the cheapest-todeliver bond for the CDS protection. Example - CDS Settlement Options Brown Truck Delivery has defaulted on its senior unsecured debt. Popeil Finance owns $5 million of Bond Series X as well as $4 million in CDS protection. Bond X is now trading at 25% of par. Snowden Securities owns $10 million of Bond Series Y, also senior unsecured debt, which is trading at 30% of par. Snowden has $9 million in CDS protection on Bond Y. Calculate the potential CDS payout amounts to Popeil and Snowden. Solution For Popeil, the payout ratio will be 75%, so a cash settlement would be for $3 million (75% of $4 million). Popeil could also then sell the bond for its residual value of $1.25 million, leaving a total amount of proceeds of $4.25 million (a loss of $0.75 million, or 15%). By pursuing physical settlement, Popeil would only net the face amount of CDS coverage, $4 million. Similarly, Snowden could obtain proceeds of $9 million through physical settlement. However, by electing a cash settlement and noting that the CTD bond is Series X, Snowden could deliver a cheaper bond than the one it is holding. The payout ratio will be 75%, so 75% of $9 million is $6.75 million. Snowden could then sell the Series Y bond for $3 million (30% of $10 million) and end up with $9.75 million, a loss of only 2.5%. In this example, Snowden s recovery was higher because it held a more valuable bond than the CTD bond, and because it purchased proportionately higher CDS protection (90% of its exposure versus the Popeil s 80%) Allen Resources, Inc

7 Study Session Pricing CDS Learning Objective: Describe the pricing of CDS contracts. CDS pricing is complicated because the underlying (credit quality) has subjective elements and potentially vague meanings. Extensive credit modeling is typically employed. The core of CDS pricing is determining a probability of default. Default is usually defined as the failure to pay interest and/or principal in full and on time. Because the contract can only be triggered once (like life insurance), the probability of default is analogous to a hazard rate - the probability of occurrence of an event, given than it has not yet occurred. Probability trees may be constructed reflecting a default/no-default bifurcation at each node, and probability-weighted financial outcomes determined at each endpoint. These figures may be added together (and discounted for present value) to determine the expected cost of the CDS, which is its net price before profit loading. Example - CDS Pricing, 2 Stage To keep things simple, we will consider a two-stage model to illustrate the process. The model can be made much more complex, but the fundamental principles can be illustrated here. Alexander Jovian issues a 2-year, annual-pay, high yield note with a 9% coupon, $1,000 par value, sold at par. The probability of default in the first year is 5% and 8% in the second year. If default occurs at any time, recovery is expected to be 30%. Find the probability Alexander Jovian will default during the 2-year period. Also, calculate the loss (given default) and the expected loss. Solution To determine the overall probability of default, it is necessary to realize that the probability of ever defaulting is equal to one minus the probability of surviving the entire exposure period without defaulting. Logically, if you don t survive the entire exposure period without defaulting, you must have defaulted at some point. The probability of surviving the first year is 95% ( ). The probability of surviving the second year, given survival of the first, is 92% ( ). Assuming independence, the joint probability of survival is = 87.4%. Therefore, the probability of default (at any time) is = 12.6%. The loss given default is 70% of the $90 first-year coupon, if default is in the first year. That is $63. If default occurs in the second year, the loss is 70% of $1,090, or $763. But note, a firstyear default implies a default on all subsequent payments as well. So a loss in the first year is actually a loss of $63 + $763 = $826. Study Guide for the Level II 2015 CFA Exam - Reading Highlights

8 Credit Default Swaps The expected loss is given by: Expected loss = Loss given default Probability of default Note that we don t use the overall probability of default here. The expected loss is dependent on when default occurs, so we write: Expected loss = (5% $826) + (95% 8% $763) = $ Note that the second term incorporates the probability of surviving the first year, then defaulting. The final step in this process would be to incorporate a discount rate to these expected losses, and discount them back to the effective date of the CDS. This would then give us the value of the protection part (called a leg) of the CDS contract. For example, at a 5% annual discount rate, we would have: PV[E(Loss)] = [5% ($63 / $763 / )] + [95% 8% $763 / ] = $ $52.60 = $90.20 The other part of the CDS contract is the premium leg. The premium takes into account the present value of the payments made under the contract. Since this is a high yield bond, assume 5% of the notional amount is payable annually at the beginning of each pay period. If default occurs, premium stops. Therefore, the present value of expected premium will be: PV[E(Premium)] = $50 + (95% $50 / 1.05) = $95.24 Notice that the first payment is not discounted, because it occurs at the beginning of the period. Also, note that this amount is larger than the present value of expected loss. In such cases, there is an up-front payment as well to equalize these amounts. Upfront payment = PV(Protection leg) PV(Premium leg) = $90.20 $95.24 = -$5.04 This implies the protection seller would have to pay the protection buyer $5.04 per $1,000 at the outset, and then collect the CDS premium as planned. (Actually, the $5.04 would probably be offset against the first $50 in premium and the amount would be further adjusted for the profit of the CDS seller, which is outside the scope of this material.) Pricing with the Credit Curve A credit spread is the incremental rate over a benchmark rate (such as LIBOR) which represents (approximately) the expected loss, due to default, from holding a risky debt instrument instead of a risk-free one. The cost of CDS protection is often quoted as a spread to a benchmark because doing so puts bonds of different risk on the same footing. For instance, an investment-grade bond with a coupon equal to its yield to maturity may sell at the same price as 2014 Allen Resources, Inc

9 Study Session 17 a below-investment-grade bond that also sells at par due to having a high coupon. However, their risks are not similar, even though their prices are. Their credit spreads will differ markedly. The credit curve is a set of credit spreads across a range of time-to-maturities. Usually, the credit curve slopes upward, indicating that the probability of default for the particular issuer rises over time. A negative slope indicates serious short-term risks compared to long-term risks. Another approach to CDS pricing involves using credit spreads to infer the cost of the protection leg. From this point of view, and, using the term coupons to refer to the premium payments from the CDS buyer to the CDS seller, we find the following can be used as an estimate: Also: Upfront premium required PV(Credit spread) PV(Fixed coupons) Upfront premium (Credit spread Fixed coupon) Duration of CDS Like bonds, quoted prices of CDS are often expressed as per 100 of par value, so when accounting for any upfront premium, we find: CDS price = 100 Upfront premium % Example - Pricing CDS with Credit Spreads (1 of 2) Suppose an investment-grade issuer has a 125 basis point, 10-year credit spread, and a duration of CDS equal to seven years. If the premium for investment-grade CDS is 1%, estimate the upfront premium due. Solution Therefore: Upfront premium (Credit spread Fixed coupon) Duration of CDS Upfront premium ( ) 7 = 1.75% This is the amount applied to the notional amount. The CDS price will be = per 100. Example - Pricing CDS with Credit Spreads (2 of 2) Suppose you have a 10-year, high-yield bond with a CDS of duration 6 for which the upfront premium is -2.50%. Assume the premium (fixed coupon) for the CDS is 5%. Find the credit spread Study Guide for the Level II 2015 CFA Exam - Reading Highlights

10 Credit Default Swaps Solution Upfront premium (Credit spread Fixed coupon) Duration of CDS (CS ) 6 = Solving for CS, the credit spread, we obtain approximately 458 basis points. Note that the negative sign on the upfront premium means that the CDS seller is paying the CDS buyer the upfront premium. The idea that the seller pays the buyer at the outset may sound odd, but keep in mind, the CDS coupon from the buyer to the seller is 500 basis points, every year. So long as the spread is less than the CDS coupon, the CDS seller will be paying the upfront premium to the buyer. This should be evident by looking at the equation above. Changes in Spreads Over time, spreads may rise or fall with deteriorating or improving credit quality, respectively. When spreads change, the buyer of CDS protection will have a gain or loss in their CDS position. It is relatively easy to estimate these gains (realized upon closing out the CDS position). Example - Changing Spreads Change in CDS price Change in spread Duration Notional Mannzeal Securities has purchased CDS protection on a bond. The CDS has a duration of 3, a notional amount of $1,000,000, and a credit spread on the underlying of 250 bp. If the credit spread falls to 200 bp, what is the change in value of the CDS position? Solution Closing a Position Change in CDS price Change in spread Duration Notional $1,000,000 = -$15,000 Closing a position in a CDS contract can be done a number of ways. A common way to close a position prior to maturity is to enter into a CDS contract that exactly offsets the existing position (or does so when combined with an additional cash settlement). Upon default, of course, the CDS buyer may close their position by exercising the CDS protection. If default never occurs, and the contract is not otherwise closed during its life, it will expire upon maturity, with the CDS buyer having paid for the protection but never using it Allen Resources, Inc

11 Study Session 17 Managing Credit Exposure Learning Objective: Explain how credit exposure can be modified with CDS, including attempts to capitalize on expectations of changes in the credit curve. A buyer of credit protection, such as a lender, is exposed to credit risk and may wish to hedge their position. Alternatively, a speculator may hope to gain from a pessimistic credit outlook on a particular issuer (or a group of issuers, such as with an index CDS) by buying CDS protection. A seller of credit protection (e.g., a CDS dealer making a market in credit derivatives) is willing to assume the credit risk of an underlying asset in exchange for a premium. A speculator may hope to gain from an optimistic credit outlook on an issuer or group of issuers by selling CDS protection. Risks for Buyers and Sellers of CDS The buyer and seller of credit protection take short and long positions, respectively, in the credit risk of the reference entity. Bondholders also take a long position in the credit risk of the reference entity, but they do so directly and their investment requires greater capital commitment. If the CDS protection buyer already owns debt of the reference entity, entering into a CDS protection agreement as a buyer will reduce their exposure to the financial consequences of a negative credit event for the reference entity. The protection buyer does not eliminate all risk, however. The buyer takes on: Risk that both the reference entity and counterparty (protection seller) default - a double default, leaving no protection. Risk that the counterparty defaults and a replacement protection seller must be found (potentially at a less advantageous price, if credit quality of the underlying has declined). Basis risk - the risk that the amount of protection secured does not match the exposure of the hedged asset. Also, note that the buyer of CDS protection will be unable to financially benefit from a positive credit event. The protection seller takes on risk as well: The seller of CDS protection takes a long position in the credit risk of the reference entity. This is financially comparable to having loaned the notional amount to the reference entity itself. However, most CDS need not be funded. In other words, the protection seller is exposed to the risk up to the notional amount, without having to actually have lent the cash. The opportunity for highly leveraged returns should be apparent Study Guide for the Level II 2015 CFA Exam - Reading Highlights

12 Credit Default Swaps The seller also has counterparty risk to the buyer, to the extent that the buyer s default will lead to loss of premium for the CDS. However, like insurance, protection would likely cease should the buyer stop paying premiums. Anticipating Changes in the Credit Curve Recall that it is not required that a prospective CDS buyer have existing credit risk exposure. A buyer may simply be speculating on changes in the level or shape of the credit curve for a particular issuer or a group of issuers. Naked CDS When an unrelated party with no credit exposure to an issuer nevertheless purchases CDS protection on that risk, such a contract is called a naked CDS. It is, in effect, a bet that credit quality will deteriorate and the naked CDS buyer will be able to capitalize on the troubles of the issuer or sector. There is controversy over this, in that CDS are like credit insurance, and a typical requirement for insurance contracts is that the policyowner have insurable interest. In life insurance this is obvious - it is bad public policy to allow unrelated third parties to profit from the death of an insured. The insured should be worth more alive than dead; you don t want to provide a financial incentive for murder. However, it is argued, it is not obvious what a buyer of a naked CDS could do to cause credit deterioration of a debt issuer. Also, there already are other financial instruments (e.g., puts, short sales) which allow their holders to profit from negative financial events. By permitting the purchase of naked CDS, the CDS market gains liquidity as well as more informational depth - that is, market participants will be rewarded for having a correct view. It also counters the systematic demand bias that would characterize a long-only market. One rebuttal to this line of reasoning is that debt underwriters who can lay off credit risk via CDS lose incentive to carefully underwrite the debt. Consequently, they could find themselves in a position to profit from a negative credit situation which their negligence helped to cause. Another rejoinder is that with traditional insurance, insurers must set aside reserves for future claims using actuarial valuation techniques. No such reserve requirement is in place for naked CDS or synthetic CDOs, which increases the risk of insolvency. Naked CDS are prohibited on European sovereign debt. Long-Short Trade A long-short trade involves two CDS, one short (on credit quality, i.e., a purchase of CDS protection) and one long. For example, if an analyst predicts rising interest rates, they may wish to buy CDS protection on issuers in the homebuilding sector (whose business typically slows when interest rates rise, because fewer people buy homes), but go long the credit quality of insurers, whose products can often be priced lower in a higher interest rate environment Allen Resources, Inc

13 Study Session 17 Alternatively, in anticipation of strong economic growth and an accompanying shift away from discount stores to higher-priced stores, one could go short (buy CDS protection) on Target while going long (selling CDS protection) on Nordstrom. Both retailers may see their spreads fall in an economic expansion, but spreads for Nordstrom may fall further, resulting in an overall profitable strategy. Curve Trade A curve trade involves buying CDS in one part of the maturity spectrum and selling in another, in anticipation of credit curve shifts. For example, if an analyst believed that short-term economic growth would be helped by an imminent government stimulus program, they might go long on short-term credit risks and short long-term credit risks, anticipating a steepening of the curve. Note, like bonds, longer-term maturities on CDS are more volatile than shorter-term CDS. Synthetic CDO CDS may be used to create synthetic collateralized debt obligations (CDOs), so that speculative bets may be taken on the credit performance of underlying reference entities (usually a pool or index of issuers). The experience of the CDS may be split into tranches, like a CDO. However, the underlying debt is not purchased, unlike with a CDO. This allows for low cost and high leverage (with no capital requirements, there is no theoretical limit to the total amount of notional bets outstanding). The synthetic CDO market has shrunk considerably since the 2008 financial crisis. CDS and Market Inefficiencies Learning Objective: Explain how CDS may be used to attempt to profit from discrepancies in valuation of correlated instruments in different markets. CDS afford the opportunity to participate in arbitrage-like trades through price convergence of similar financial instruments in different markets. Trading to take advantage of converging price differences (or spreads) between a security and its related derivative is referred to as a basis trade. The general trading rule to remember for arbitrage (and arbitrage-like situations such as basis trades) is to buy the cheaper security while simultaneously selling the more expensive security. The higher the correlation between the securities, the more sure the arbitrage profit should be (although pricing discrepancies tend to be smaller the more highly correlated the securities are - that is why leverage is frequently used - to magnify the small returns). This strategy can be employed for single-entities as well as indexes, although clearly, correlations should be stronger for single entities Study Guide for the Level II 2015 CFA Exam - Reading Highlights

14 Credit Default Swaps Example Suppose Bilever, Inc., has a 5-year bond with a yield of 6%. The benchmark rate is 2%, and CDS protection on the bond is 5%. Describe three strategies to profit from the discrepancy in credit spreads. Solution The credit spread of the bond is 6% 2% = 4%. It may be that the bond is overpriced, or that the CDS cost is too high, or both. One could sell the bond short, and hope for a price fall. Alternatively, one could sell CDS protection and hope that the CDS spread falls. Finally, one could undertake a basis trade, and profit from price movement of both (assuming eventual convergence) Allen Resources, Inc. All rights reserved. Warning: Copyright violations will be prosecuted. Any use of these materials without the express written consent of the publisher is a violation of federal and/or international copyright laws Allen Resources, Inc