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CHAPTER 32 – Credit Default SwapsStart with an Interest Rate Swap Plain vanilla: Fixed for Float6 month LIBOR is 280 bpsTwo separate parties enter into 2 interest rate swaps with a bank:Pay 282 for LIBOR (buy LIBOR)Get LIBOR for 278 (sell LIBOR)What happen to CFs if LIBOR goes to 300?What happen to CFs if LIBOR goes to 250?Which side of the IRS hedges a bond’s interest rate risk?Now to CDSProtection Buyer pays a fee to the Protection Seller. If a reference-security “credit event” occursThe protection seller buys the bond from the protection buyer for par value The protection buyer delivers the bondSince the reference security is now worth less than parThe protection seller incurs a loss Equal to par minus the after-credit-event value of the reference securityIf the issuer is in default (a credit event) and the (present value of the) expected recovery rate for the reference security is 40%The market price of the bond will be $40The protection seller would incur a $100 – $40 = $60 loss The protection buyer would receive par value. Or the Protection Seller just pays $60 cashThis contract is a securitized derivative whose value is derived from the credit risk on an underlying reference security: a bond, loan or any other financial asset. If the likelihood of a credit even increasesThe value of the credit derivative increase.“Credit risk” includes three types of risk: Default Risk: the risk that the specific issuer will default Credit Spread Risk: the risk that the credit spread for the entire rating category will increase Downgrade Risk: the risk that an individual issuer will be downgraded Contract International Swap and Derivatives Association (ISDA) Produces the standard contracts upon which most CDS relyReference Entity and Reference ObligationThe ISDA CDS agreement will identify the reference entity and/or the reference obligationThe Reference Entity is the issuer of the debt instrument Also referred to as the reference issuer.Corporation, municipality, a sovereign government. Vail Resorts, Inc., Boulder Valley School District,…The Reference Obligation (aka reference asset) is the particular debt issue for which the credit protection is being sought. Reference Entity is Vail ResortsReference Obligation would be the 6.50% bonds of 2019.Credit EventsAttempt to capture all situations in which the credit quality of the reference entity deterioratesOr which cause the value of the reference obligation to decline.ISDA Credit EventsBankruptcyFailure to PayRestructuringRepudiationMoratoriumObligation AccelerationObligation DefaultCDS on an Asset-Backed Securities CDS (ABS CDS)Focus of cash-paying ability of the collateral - not on bankruptcyPay-As-yoU-Go (PAUG): Capture non-default events that impact the CFs of ABS tranche.Since reference entity is NOT a corporationCorporate credit event is default (or similar) PAUG captures NON-default events that impact the CFs of the specific reference ABS trancheFailure to payReference obligation fails to make a scheduled interest or principal payment.Write-downPrincipal component of the underlying reference obligation is “written down” and deemed irrecoverableDistressed ratings downgrade The underlying reference obligation is downgraded to a rating of Caa2/CCC or lowerPhysical Settlement vs. Cash SettlementPhysical Settlement Protection buyer delivers the reference obligation to the Protection Seller Gets a cash payment equal to parCash Settlement Protection Seller pays the Protection Buyer difference between par and the after-event price of the bond. After-Event Price Determined by an auction Also called a “credit-fixing event”Conducted by ISDA through the interdealer bond marketNo need for an auction for Physical settled CDS, only for Cash settled CDS (Why?)Cheapest-to-Deliver (CDT)A CDS can either be on an Issue or an IssuerIf on an Issuer then it is called a Single-Name CDS If a Single-Name CDS is also physical settled (as opposed to cash settled)Then the protection buyer delivers to the protection seller an amount of face value of bonds of the reference entity specified in the CDSThe protection buyer has the choice of which of the eligible debt instrument issued by the reference entity to deliver WHY?The ISDA swap documentation defines the characteristics for an issue to qualify as a deliverable obligation.The protection seller then pays the protection buyer the face value of the bonds. Since reference entities that are the subject of credit default swaps have many issues outstanding, there will be a number of alternative issues of the reference entity that the protection buyer can deliver to the protection seller. These issues are known as deliverable obligations.The cheapest-to-deliver bond is determined from set of deliverable bonds through the auction process. The Protection Spread (S) Probability of Default (q) and Amount Recovered if Default (1 – R).Spread (S) is the annual premium expressed as a percentage of face value Actually expressed in basis points so 1/10,000 of face value or 1/100 of a percent.0.0050 = 0.50% or 50 bpsProbability of Default (q) is the probability of default in the periodRecover (R) is the value of the reference security after a credit event.Protection Seller pays the Protection Buyer 1 – RApproximate Relationship: S = q × (1 – R)Example: Compute Cost (S)The recovery rate for a bond equals 30%This is either the estimated recovery value or the “after-event price” determined in an auction There is a 0.50% chance of default in any pute the annual cost of credit protection for $10,000,000 of face value of the bonds.The is also called a $10 million Notional AmountFirst compute S (in basis points) S = q × (1 – R) = 0.005(1 – 0.30) = 0.005(0.70) = 0.0035 = 0.35% = 35 bps SpreadDollar cost of protection = 35 bps x Par Value Protected = 0.0035 x $10,000,000 = $35,000Example: Compute Default Probability (q)The recovery rate for a bond equals 45%The annual spread is 100 bpsCompute the probability of default in any year.S = q × (1 – R) q = S/(1 – R) q = S/(1 – R) = 0.0035/(1- 0.45) = 0.0182 = 1.82% Probability of DefaultExample: Compute the Implied Recovery Rate (R)The annual spread is 120 bpsThe probability of default in any year is 2.00%S = q × (1 – R) R = 1 - S/qR = 1 - S/q = 1 - 0.0120/0.02 = 0.40 = 40% Recovery RateStandard North American Contract - SNACSince 2009, CDS follow the SNAC CDS RulesPayments (called coupon payments) are either 100 bps or 500 bps Payments are quarterlyAll CDS payments are made on the same dates (3/20, 6/20, 9/20 and 12/20) The payment amounts are computed using either 100 bps or 500 bps couponsQuarterly CDS payment = Notional × 0.0100 × Actual/360 Quarterly CDS payment = Notional × 0.0500 × Actual/360 What if the reference entity only requires a spread of 90 bps? Since you are required to pay 100 bps And therefore you are required to overpay by 100 – 90 = 10 bpsYou receive an upfront payment equal to the expected present value of the amount you are required to overpay each quarterWhat if the reference entity requires a spread of 120 bps? Since you are required to pay 100 bps And therefore you are able to underpay by 120 – 100 = 20 bpsYou pay an upfront payment equal to the expected present value of the amount you are required to underpay. SNAC is GOOD becauseAll CDS contracts, regardless of the day they are initiated Or the spread at the time of initiation HAVE THE SAME PAYMENTS MADE ON THE SAME DAYSThe only difference is upfront paymentsCalculating SNA paymentsFor a CDS on an Investment Grade bondQuarterly Payment = Notional Amount x 0.0100 x Actual/360For a CDS on an Non-Investment Grade bondQuarterly Payment = Notional Amount x 0.0500 x Actual/360Payment Amount Example:A 5 year, $10 million notional amount, single-name CDS on an investment-grade bond It has a spread of 80 bps.It is initiated on 12/20/2018 and follows the SNAC CDS pute the periodic payments:Payment for 12/20/2018 through 3/20/2019Days in period: December11January 31February 28March 2090Quarterly Payment = Notional Amount x 0.0100 x Actual/360 = $10,000,000 x 0.0100 x 90/360 = $25,000Payment for 3/20/2019 through 6/20/2019Days in period: March11April 30May 31June2092Quarterly Payment = Notional Amount x 0.0100 x Actual/360 = $10,000,000 x 0.0100 x 92/360 = $255,556Go to CDS Payment SpreadsheetNotice Year 2020June 20, 2020 is a SaturdaySo payment date is moved to Monday, June 22Increasing the March to June period by 2 days to from 92 in 2019 to 94 in 2020September 20, 2020 is a Sunday So payment date is moved to Monday, September 21June to September period is 2 days shorter because it starts on June 22But also 1 day longer because it ends on September 21June to September period is net 1 day shorter from 92 in 2019 to 91 days in 2020Overpay or Underpay Example 1:Same CDS:A 5 year, $10 million notional amount, single-name CDS on an investment-grade bond It has a spread of 80 bps.q = 4.00%R = 80% S = 0.04(1 – 0.80) = 0.04(0.20) = 0.0080 = 80 bpsIt is initiated on 12/20/2018 and follows the SNAC CDS pute the periodic OVER or UNDER payments:For now, assume each period has 90 days. In other words, each payment is 30/360Under our simplifying assumption, each payment - given the 100 bps coupon rule - is $25,000But given the risk of the bond, should be paying = $10,000,000 x 0.0080 x 90/360 = $20,000So protection buyer will OVERPAY $25,000 - $20,000 = $5,000 each quarter.Why not just pay the amount you should pay? You can’t. That’s the SNAC rules!We’ll see why this is actually good in a minute.OVERPAY in each period Get money upfrontOverpay or Underpay Payment Example 2:Same CDS:A 5 year, $100 million notional amount, single-name CDS on an investment-grade bond It has a spread of 110 bps.q = 4.00%R = 72.5% S = 0.04(1 – 0.725) = 0.04(0.275) = 0.0110 = 110 bpsIt is initiated on 12/20/2018 and follows the SNAC CDS pute the periodic OVER or UNDER payments:For now, assume each period has 90 days. In other words, each payment is 30/360Under our simplifying assumption, each payment - given the 100 bps coupon rule - is $25,000But given the risk of the bond, should be paying = $100,000,000 x 0.0110 x 90/360 = $27,500So protection buyer will UNDERPAY $25,000 - $27,500 = -$2,500 each quarter.UNDERPAY in each period PAY money upfrontCompute Each Period Overpayment or UnderpaymentAll Investment Grade CDS contracts require payment of 100 bps per yearIf you should be paying 80, you are OVERPAYING by 100 – 80 = 20 bps per yearOr 20 x 0.25 = 5 bps per quarterBut – you only pay this if the bond DOES NOT DEFAULT!q = 4.00% per year 4.00%/4 = 1% per quarter1% chance the bond will default and you won’t make the payment1 – (q/4) = 1 – 1% = 99%99% chance you will make the first paymentEXPECTED 1st PAYMENT = Payment x Prob = 5.00 bps x 0.99 = 4.95 bpsYou only make the 2nd payment if you don’t default in BOTH the 1st AND the 2nd periodSurvival probability: 0.99 x 0.99 = 0.9801(99.00%)2 = 98.01% chance of NOT defaulting in the 1st and the second periodEXPECTED 2nd PAYMENT = Payment x Prob = 5.00 bps x 0.9801 = 4.9005 bpsYou only make the 3rd payment if you don’t default three times:Survival probability: 0.99 x 0.99 x 0.99 = 0.9703(99.00%)3 = 97.03% chance of NOT defaulting in periods 1, 2 or 3 EXPECTED 3rd PAYMENT = Payment x Prob = 5.00 bps x 0.9703 = 4.8515 bpsCompute Present Value of Each Period Overpayment or UnderpaymentExpected 1st Payment = Payment x Prob = 5.00 bps x 0.99 = 4.95 bpsBut that payment happens in 3 months Assume a 2.00% APR discount (so 2.00%/4) = 0.50% in each periodPV of 1st Expected Payment = 4.95 bps/(1 + 0.0050) = 4.9254Expected 2nd Payment = Payment x Prob = 5.00 bps x 0.9801 = 4.9005 bpsBut that payment happens in 6 months or 2 3-month periodsPV of 2nd Expected Payment = 4.9005 bps/(1 + 0.0050)2 = 4.8519Expected 3rd Payment = Payment x Prob = 5.00 bps x 0.9703 = 4.8515 bpsBut that payment happens in 9 months or 3 3-month periodsPV of 3rd Expected Payment = 4.8515 bps/(1 + 0.0050)3 = 4.7794Sum of PV of Expected Overpayments or Underpayments IS the UPFRONT PAYMENTGo to CDS Examples Trading CDSFor a CDS with a notional amount of $10m with q = 4.00%, R = 80%, S = 80 bpsA protection buyer receives $85,715A protection seller pays $85,715For a CDS with a notional amount of $10m with q = 6.00%, R = 80%, S = 120 bpsA protection buyer pays $81,517A protection seller receives $81,517Closing a CDS PositionIf you BOUGHT PROTECTION to OPEN the positionYou SELL PROTECTION to CLOSE the positonCash flow amounts are fixed at 100 bps (or 500 bps) Cash flow dates are set to 3/20, 6/20, 9/20 and 12/20When you agree to Buy ProYou agree to make paymentsWhen you agree to Sell ProYou agree to get the EXACT SAME PAYMENTS ON THE EXACT SAME DATESTherefore the payments offset and you are “flat”The Profit or Loss from the trade comes from difference in the upfront paymentsA Trade – Buy protection when S = 80 and Sell (to go flat) when S = 120Buy protection when S = 80Receive $85,715Sell protection when S = 120Receive $81,517Net proceeds = $85,715 + $81,517 = $167,232Go To CDS Trade ScenariosIndex Credit Default Swap (CDX)It is the sum of 125 cash-settled individual CDS contracts. The protection seller sells protection on an equally-weighted basket of reference entitiesThis basket is determined (by agreement) by IHS Markit. Each 3/20 and 9/20 IHS Markit creates a new index of 125 Investment Grade bonds (CDX-IG). An Investment Grade credit default swap on the CDX-IG has a fixed coupon equal to 100 bpsThe required spread for the CDX is the average of the CDS spreads of the 125 bonds in the index Quarterly payments are computed using a fixed spread (or running spread or coupon rate) of 100 bps. Quarterly CDX payment = Notional × 0.0100 × Actual/360So given the actual spread for the 125 bonds (the average), an upfront payment for the CDX is computed using same method as a single name CDS Credit EventIf a credit event occurs for one of the 125 reference entities in the indexThe protection seller pays the protection buyer the difference between par and the after-event price of the reference security. But unlike a single-name CDS, the CDX does not cease to exist. The one bond that had the event is removed from the index the CDX continues to exist on the rest of the 124 reference entitiesthe notional amount and quarterly payments are reduced by 1/125 to 124/125 = 0.992So a $10,000,000 notional amount becomes $9,920,000See Chapter 32 HW Extra Question #11CDX IG vs CDX HYIG is investment grade125 bonds in the indexRunning Spread (required payment) is 100 bpsHY is High Yield100 bonds in the indexRunning Spread (required payment) is 500 bps ................
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