Credit Default Swaps Notes

Announcements

• Project due April 28; email group members ASAP with subject line: FINA 475 001: ……).
• Final Exam: Thursday, May 1, 4:00 PM online via Blackboard; upload work to Assignments - Final Exam Work.
• Class Participation and Extra Credit:
  • 8 In-Class Assignments with ≥ 80% =⇒ 100% + Eligible for 2.5% Extra Credit (e.g., Final Score: 78 (C+) → 80.5 (B)).
  • 60% − 80% =⇒ 70%.
  • 25% − 50% =⇒ 50%.
  • < 25% =⇒ 0%.
• Homework 3: Optional, redeem for 5% grade increase in any Midterm (Max 100 pts); Example: 80 x 1.05 = 84.

Basic Concepts

• Credit Derivative → a Derivative instrument where the Underlying is some measure of Credit Quality.
  • Total Return Swaps.
  • Credit Spread Options.
  • Credit-linked Notes.
  • Credit Default Swaps.
• Credit Default Swaps (CDS) → more popular and most liquid.
  • Basic idea: One party makes payments to the other and receives in return the promise of compensation IF a third party defaults.
  • In any derivative, the payoff is based on (derived from) the performance of an underlying instrument, rate, or asset etc.
  • In CDS, the underlying is credit quality.

Concepts Contd.

• CDS provides compensation = Expected Loss when a credit event occurs.
• Credit events → Bankruptcy, Failure to pay, and Restructuring etc.
• CDS may also used by investors to:
  • Leverage their portfolios.
  • Access maturity exposures not available otherwise.
  • Access credit risk while limiting interest rate risk.
  • Improve the liquidity of their portfolios given the illiquidity in the corporate bond market.
• Two parties to the Swap: Protection Buyer and Protection Seller.
  • Protection buyer (fee) −→ Protection Seller.
  • In case of credit even, Protection buyer ←− Protection Seller (Payment).
• Somewhat similar to put options.
• A CDS does not eliminate credit risk, only minimizes it, specifically min(Loss | Default).

Types of CDS

• Single-name CDS → CDS on one specific borrower.
  • Borrower is called the reference entity, and the contract specifies a reference obligation.
• Index CDS → a portfolio of single-name CDS.
  • Take positions in the credit risk of a combination of companies.
  • Similar to taking a position via an ETF, or a portfolio.
• Tranche CDS → Covers a combination of borrowers, but only up to pre-specified levels of losses.
  • For example, Senior unsecured tranches of borrowers.
  • Or tranches in Assets Backed Securities.
  • Payoff → determined by the Cheapest-to-Deliver obligation.
  • Debt instrument that can be purchased at the lowest cost but has same seniority as the reference.

CDS Settlement

• Physical Settlement (Current standard).
  • Protection buyer has 30 days to select the security to be delivered.
  • Protection buyer delivers the defaulted bonds, receives the notional amount in CDS contract.
  • Protection seller seeks to recover losses from the defaulted bond.
• Cash settlement.
  • Protection buyer sells the defaulted bond in the open market.
  • Protection seller pays the remaining balance of the notional amount.
  • Benefit → Protection seller is not exposed to additional default risk.

Physical Settlement vs Cash Settlement

Physical Settlement

• Default Occurs.
• Buyer delivers the bond.
• Seller pays face value.
• Settlement Complete.

Cash Settlement

• Default Occurs.
• Bond is Valued (Face - Market Value).
• Seller pays difference.
• Settlement Complete.

Cheapest-to-Deliver (CTD) Bond?

• Imagine you have a contract (like a Credit Default Swap) that lets you deliver any one bond to settle it.
• The Cheapest-to-Deliver (CTD) Bond is the bond:
  • That meets the contract requirements (eligible bond).
  • Costs you the least to acquire or deliver.
• It’s like paying your debt with the smallest legal coin you have!

Sample Problem

• Assume that a Hightower Corp. has several debt issues trading in the market.
• With a downturn in business the company has filed for bankruptcy (i.e. Credit Event).
• What is the cheapest-to-deliver obligation for a CDS contract where the reference bond is a Five-year Senior Unsecured bond?
  • A. Subordinated unsecured bond trading at 20% of par.
  • B. 5-year Senior unsecured bond trading at 50% of par.
  • C. 2-year Senior unsecured bond trading at 45% of par.
• Answer: C (cheapest to deliver).

Main Players - Buyers and Sellers

• Banks trading division.
• Banks loan portfolios.
• Hedge funds.
• Corporations.
• Insurance and Reinsurance companies.

Features of CDS

• International Swaps and Derivatives Association (ISDA) → unofficial governing body.
• Each CDS contract → Notional amount.
• Total notional amount of CDS can ≥ or ≤ total debt outstanding of the reference entity.
• Protection buyer does not have to be an actual bond holder of the firm.
• Anyone that believes that there will be a change in the credit quality of the reference entity.
• Expiration / Maturity date → coverage is provided up to that date.
• The buyer of a CDS pays a periodic premium to the seller, called the CDS Spread, usually a spread over the reference rate.
• Value of CDS contract could change over the life as the reference entity’s credit quality changes.

Credit Events

• Credit Event → anything that defines a ”Default” by the reference entity.
• A Credit Even triggers the payment from Protection Seller → Protection Buyer.
• Event must be Unambiguous: Did it occur, or did it not?
• Bankruptcy → defined by law. Legal procedure, creditors claims are deferred.
• Failure to pay → borrower does not make scheduled payment, even after grace period.
• Restructuring → number of possible events:
  • Reduction or deferral of principal or interest.
  • Change in seniority of debt.
  • Change in currency of payment.
  • Debt to equity swap etc.

Sample CDS Contract

• Bond Issuer → Groupon Inc. (Reference Entity).
• Reference Security → 3.5% Senior secured note, Due Oct 15, 2028.
• Term of CDS → 5 years.
• Notional value → $1 million.
• Premium → 65 basis points (annual), paid quarterly.
• Credit Events → Bankruptcy, Liquidation, Technical Default, Missed/Non-timely payment, Rating downgrade > 2 notches.
• Protection Buyer → Pay a premium of $\frac{65}{4} = 16.25$ basis points every quarter, until maturity or credit event.
• If Credit Event occurs → Protection seller makes the buyer good for losses; in case of Credit Event → seller pays $1mn, receive the securities.

Example

• A French company files for bankruptcy =⇒ Credit Event has occured.
• Debt structure:
  • Bond A → Senior unsecured. Trades at 30% par.
  • Bond B → Senior unsecured. Trades at 40% par.
• Investor X → Bond A (€10mn) and €10mn CDS.
• Investor Y → Bond B (€10mn) and €10mn CDS.
• Q1. What is the recovery rate for both CDS contracts?
• Q2. Would Investors X and Y prefer to cash settle or physically settle their CDS contract? Or are they indifferent?

Example - Solution

• A French company files for bankruptcy =⇒ Credit Event has occured.
• Debt structure:
  • Bond A → Senior unsecured. Trades at 30% par.
  • Bond B → Senior unsecured. Trades at 40% par.
• Investor X → Bond A (€10mn) and €10mn CDS.
• Investor Y → Bond B (€10mn) and €10mn CDS.
• Q1. What is the recovery rate for both CDS contracts?
• Q2. Would Investors X and Y prefer to cash settle or physically settle their CDS contract? Or are they indifferent?
• Bond A is the cheapest-to-deliver obligation, trading at 30% of par, so the recovery rate for both CDS contracts is 30%.
• Investor X → no preference between settlement methods:
  • Sell bonds for €3mn (30% recovery rate) + €7mn, Or Give bonds to CDS seller and get €10mn (from CDS).
• Investor Y → prefer physical settlement:
  • Sell Bond B for €4mn, Buy Bond A for €3mn, give to CDS Seller, receive €10mn (total €11 mn).

Index CDS

• So far focus on single-name CDS. But, there are also Index CDS.
• Index CDS is not in itself a traded instrument any more than a stock index is a traded product.
• Index CDS → generate a payoff based on any default that occurs on any entity covered by the index.
• Uses:
  • Take positions on the credit risk of the sectors covered by the indexes.
  • Protect bond portfolios that are similar to the components of the indexes.

Basics of CDS Pricing

• CDS Spread → premium paid by the protection buyer to the seller.
• $CDS Spread ≈ (1 - Recovery Rate) * P(Default)$
• Eg. If RR=60%, P(D)=2% =⇒ CDS Spread = 0.4 * 2% = 0.8% (80 bps).
• Assuming a $100 notional contract value, time period 1 year, the CDS contract fair value = $0.80.
• Note: P(Default) → Conditional probability over time.
• Example: A 2-year, 5%, $1,000 par bond with cash payments of $50 in 1 year and $1050 in 2 years.
• P(Default) in Year 1=2%, Year 2=4% =⇒ 2-year P(Default) = 1 − (P(Survival1) ∗ P(Survival2)).

Basics of CDS Pricing (Continued)

• CDS Spread → premium paid by the protection buyer to the seller.
• $CDS Spread ≈ (1 - Recovery Rate) * P(Default)$
• Eg. If RR=60%, P(D)=2% =⇒ CDS Spread = 0.4 * 2% = 0.8% (80 bps).
• Assuming a $100 notional contract value, time period 1 year, the CDS contract fair value = $0.80.
• Note: P(Default) → Conditional probability over time.
• Example: A 2-year, 5%, $1,000 par bond with cash payments of $50 in 1 year and $1050 in 2 years.
• P(Default) in Year 1=2%, Year 2=4% =⇒ 2-year P(Default) = 1 − (P(Survival1) ∗ P(Survival2)) = (1 − (0.98 ∗ 0.96)) = 1 − 0.9408 = 0.0592 or 5.92%,
• Also known as the hazard rate.
• Use this probability in pricing the CDS.

Applications of CDS

• CDS → Transfer credit risk.
• Broadly, derivatives serve two general purposes:
  • Trade on the underlying - less capital, derivatives market more efficient.
  • Valuation difference between the derivative and the underlying - take of-setting positions and earn a profit.
• Managing Credit Exposure - increase or decrease credit exposure.
• Lender to buy protection to reduce its credit exposure to a borrower.
• Seller CDS Dealer → profit from market making. Effective risk management essential, sophisticated credit risk modeling.
• Speculators: Investor with no exposure to the reference entity can also purchase credit protection. (Naked credit default swap).

Sample Problem #1

• Barclays purchased a $10 mn, 6-year senior unsecured bond issued by Flag Inc. in Jan 2021.
• Subsequently, the CIO of Barclays recommends the investment team to buy a $10mn protection on the bonds.
• In Jan 2022, Flag Inc. fails to make a scheduled interest payment on the outstanding subordinated unsecured bonds.
• Flag Inc., however does not file for bankruptcy.
• For Barclays has a Credit Event occurred?

Sample Problem #1 Contd.

• A fixed-income analyst is asked to collect data on the company current debt issues:
  • Bond 1: 2-year senior unsecured bond, selling at 40% par.
  • Bond 2: 5-year senior unsecured bond, selling at 50% par.
  • Bond 3: 5-year subordinated unsecured bond, selling at 20% par.
• Assuming a credit event has occurred, should Barclays cash-settle or physically settle?

Solution

• Barclays should physically settle.
• Cash Settlement:
  • Barclays owns Bond 2 ($5mn worth).
  • Sell Bond 2 for $5mn, get balance $5mn from CDS seller.
  • Total = $10m.
• Physically settle:
  • Sell Bond 2 for $5 mn.
  • Buy equivalent amount of Bond 1 for $4 mn.
  • Give Bond 1 to CDS seller, get $10mn.
  • Total $11 mn.

Sample Problem #2

• Table gives the hazard rates (P(Default)) for the next five years for bonds issued by Orion Inc.
• What is the probability that Orion will default on its bonds during the first three years?

Sample Problem #2 - Solution

• Table gives the hazard rates (P(Default)) for the next five years for bonds issued by Orion Inc.
• What is the probability that Orion will default on its bonds during the first three years?

• $PSurvival,1 = 1 − 0.22 = 99.78\%$
• $PSurvival,2 = 1 − 0.35 = 99.65\%$
• $PSurvival,3 = 1 − 0.50 = 99.50\%$
• $=⇒ PDefault,3 = (1 − (0.9978 ∗ 0.9965 ∗ 0.9950)) = 1.07\%$

Example - Using CDS for Trading

• Elon Musk did a Leveraged Buyout (LBO) of Twitter Inc.
• LBO → buy a company using a combination of equity and debt, but the acquirer is not borrowing money, the target company does.
• Deal terms:
  • $33.5bn Equity.
  • $13.5bn in Debt.
• Equity-CDS trade in anticipation of such a deal.

Example - Using CDS for Trading (Continued)

• Elon Musk did a Leveraged Buyout (LBO) of Twitter Inc.
• LBO → buy a company using a combination of equity and debt, but the acquirer is not borrowing money, the target company does.
• Deal terms:
  • $33.5bn Equity.
  • $13.5bn in Debt.
• Equity-CDS trade in anticipation of such a deal.
  • Buy the stock + Buy CDS.
  • At deal closing, Stock Price (↑).
  • After deal closing, P(Default) increases =⇒ CDS price ↑.

Conceptual #2

• Sigma Partners believes that Delta Corporation may make an unsolicited bid at a premium to the market price for all of the publicly traded shares of Blueberry.
• Blueberry’s market capitalization and capital structure are comparable to Delta’s i.e. both firms have high leverage ratios.
• To complete the transaction Delta will issue new equity along with 5- and 10-year senior unsecured debt.
• New debt issuance will increase Delta’s debt ratio even more.
• A profitable trade involving Delta and Blueberry would be:
  • A. Short Blueberry but 10-year CDS on Delta.
  • B. Long Blueberry buy 5-year CDS on Delta.
  • C. Long Delta shares and buy 5-year CDS on Delta.

Conceptual #2 - Solution

• Sigma Partners believes that Delta Corporation may make an unsolicited bid at a premium to the market price for all of the publicly traded shares of Blueberry.
• Blueberry’s market capitalization and capital structure are comparable to Delta’s i.e. both firms have high leverage ratios.
• To complete the transaction Delta will issue new equity along with 5- and 10-year senior unsecured debt.
• New debt issuance will increase Delta’s debt ratio even more.
• A profitable trade involving Delta and Blueberry would be:
  • A. Short Blueberry but 10-year CDS on Delta.
  • B. Long Blueberry buy 5-year CDS on Delta.
  • C. Long Delta shares and buy 5-year CDS on Delta.
• Answer: B

Sample Problem #4

• You bought protection on the subordinated unsecured debt of Flimsy Inc. At the time of purchase the P(Default) and Recovery Rates are given in the table below.
• Your notional principal was $10 mn. At the time of purchase, Flimsy had a rating of AA.
• What would be your profit loss from the CDS position if the rating of Flimsy’s debt changed to AAA, CCC?

Solution

• $CDS Spread (AA) = (1 − 0.9) ∗ 0.025 = 0.0025 = 0.25\%$
• Cost of CDS $ = 0.0025 ∗ 10, 000, 000 = $25, 000.
• $CDS Spread (AA→AAA) = (1 − 0.99) ∗ 0.005 = 0.00005 = 0.005\%$
• Profit/Loss = ∆Spread * $10m = (0.00005 − 0.0025) ∗ 10, 000, 000 = −$24, 500.
• $CDS Spread (AA→CCC) = (1 − 0.5) ∗ 0.2235 = 0.1118 = 11.18\%$
• Profit/Loss = ∆Spread * $10m = (0.1118 − 0.0025) ∗ 10, 000, 000 = $1, 092, 500.

In-Class Exercise

• You bought a 5-year annual-pay $10 mn notional value CDS on a 5-year, 1% annual bond with Par value of $1000.
• Bond has a Recovery Rate= 80%, P(Default) = 6.00% and is currently trading at $985.
• At the end of year 3 the P(Default) increases to 6.5% and subsequently the YTM on the bond also increases by 50 bps.
  1. If you decide to sell the CDS what was your profit/ loss?
  2. If you sell both the CDS and the bond what was your profit/loss?
  3. Do you anticipate the Federal Reserve will increase/decrease rates in their next meeting? By how much?

Solution

• $CDS Spread = (1 - Recovery Rate) * P(Default) = (1 − 0.80) ∗ 6\%$
• =⇒ Cost of CDS = 1.2% * 10mn = $120,000.
• $New CDS Spread = (1 − 0.80) ∗ 6.5\%$
• New value of CDS = 1.3% * 10mn =$130,000 =⇒ Gain on CDS = 130,000 - 120,000 = $10,000.
• For the Bond: Price = $985.
• PV = −985, N = 5, PMT = 10, FV = 1000 =⇒ I /Y = 1.31%.
• Price in 3 years i.e. 2 years to maturity.
• N = 2, I /Y = 1.31, PMT = 10, FV = 1000 =⇒ PV = 993.91.
• Gain on Bond = 993.91 - 985 = $8.91 per 1000 par value =⇒ Gain on $10mn portfolio = $(8.91/1000) ∗ 10, 000, 000 = 88, 100$
• Total Gain = 10,000 + 81,100 = $98,100.