Mini Chapter One
Credit Default Swaps
As we kickstart this subject let’s begin with the most liquid product in this space, the Credit Default Swap.
What is a CDS contract?
A credit default swap as the name suggests is a derivative contract that facilitates the swapping/exchange of credit risk in an underlying reference entity between two counterparties.
- The arrangement involves the seller of the credit risk (CDS/protection buyer) to make a nominal fee for an exchange of a contingent payment triggered in the event of default on the reference entity obligations.
- One can think of the CDS payment made by the buyer as an insurance premium paid to hedge against the losses on default by the reference entity.
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- In the event of a default that – could occur due to failure to pay the underlying or other reference obligations, repudiation, moratorium or conditions defined in the CDS contract – the settlement could happen either physically or in cash. In case of the less frequent physical settlement the CDS seller receives the ‘cheapest to deliver’ of the reference obligation from the buyer and in turn pays par value for it. The more popular cash settlement mechanism replicates the same economics wherein the CDS seller pays par minus recovery value to the buyer in the event of default.
- Underlying documentation – ISDA master documentation as is standard for other financial derivatives is also used for CDS contracts.
Benefits of trading Credit Default Swaps
- The significance of this derivative to the credit world is its ability to isolate and trade in and out the credit risk of an underlying investment from other market risks.
- Furthermore the sensitivity around selling/transferring issuer credit risk are much better managed as the CDS contract has no issuer involvement (as opposed to transferring a loan which gets recorded in the issuers’ books), alongside helping with better price discovery.
- Those with higher funding costs who would normally not buy a lower yielding bond (effectively selling credit protection without any compensation/negative carry) could use CDS to take exposure synthetically to higher grade credits.
- Connecting the Dots
In effect CDS would behave like a synthetic long bond position funded via fixed rate repo (to maturity) removing the interest rate risk inherent in a cash bond trade to isolate the credit risk.
- Conversely banks with lower funding costs can fund their own purchase of cash bonds and benefit from a spread higher than that implied by the CDS. This would be a function of the bank’s funding cost and a potential basis between the CDS and bond spread (negative basis) as covered later.
- CDS also helps hedge credit risks on bond positions holding back the compulsion of having to physically sell the bond in times of stress. Adverse taxation and accounting treatments (that get triggered at the time of sale) can be avoided in the same vein.
Valuation/Pricing of a CDS
Intuition behind pricing the credit protection (CDS) on a certain reference entity/asset is to think about the compensation on it at the time of default (Par minus Recovery Value) and the Probability of that Default. These are the two key inputs for any CDS pricing model, also used to arrive at the present value of an investment that has both risk free and (credit) risky cash flows. For bonds in general:
- Current Price of an asset = Present Value of [Cash flows x (1- Probability of Default) + Cash flows x Recovery value x Probability of default)]. Given that the risky cash flows have already been assigned a probability of default and a recovery rate, much like risk free cash flows they should also be discounted at the risk free rate.
- Hence from the above, given current market prices one can back out the probability of default for different recovery value scenarios.
- The present value of a 1 year zero coupon bond can therefore be computed as:
where Pd is the Probability of Default, RV is the recovery value, e-rt is the risk free discount factor. When Pd = 0, it becomes a risk-free bond.
- Connecting the Dots
Drawing a parallel with the options world – probability of default for a CDS is akin to an asset’s implied volatility, while recovery value can be thought of as the strike. This is because a more volatile credit would intuitively have a higher probability of default and triggering the CDS in the event of default would be like exercising the option to receive par minus recovery value.
- Market credit spread on a bond is effectively the additional compensation a buyer demands over the risk-free rate assuming a certain default probability and a finite recovery value. Simply put – if 100 dollars are lent as 1 dollar each to 100 individuals with a 5% probability of default i.e. 5 individuals do not return the money at all (recovery value = zero), one would expect the remaining 95 to pay up ~$ 1.0526 each (5.26% additional over risk free rate) to make whole the $100 principal lent. In other words, for a 5% probability of default with no recovery value the breakeven spread to be charged on the risk free rate would be higher than the probability of default. Any non-zero Recovery Value would bring down this spread below Pd but it would still be above zero as long as the recovery (in the event of default) is less than par. In the practical world of finance this is the thinking behind credit risk related compensation sought by lenders.
- The intuition above can be explained by simply enhancing the discount rate of a risky bond by its credit spread i.e.:
- PV of a 1y Zero coupon Risky Bond with
- The intuition above can be explained by simply enhancing the discount rate of a risky bond by its credit spread i.e.:
note that the discount factor (function of the risk-free rate) here is assumed to be multiplicatively enhanced by the credit spread’s’.
- This should now equate to the Zero coupon PV notation above but using annual compounding to keep it uniform:
- For a bond with zero Recovery Value then
- While for a bond with RV not equal to zero we can approximate Credit Spread or Credit default swap spread:
- This notation even though an approximation (as we have not accounted for compounding and convexity here) cements the concept of linking the probability of default with the credit spread. Just like higher interest rates imply lower discount factors, higher credit spreads would have the same effect as they increase the discount rate/lower discount factors.
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- Market pricing of the additional compensation (over the risk-free rate) to be charged on risky bonds/loans/reference obligation should adjust for any ‘guaranteed’ principal or interest components as it would be backed out of a joint probability of default of the guarantor and issuer/obligor.
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- Trivia
Brady Bonds are a relatable reference that come to mind to think about how ‘below market rate’ coupons could pose as a restructuring solution for the defaulted debt during the Latin American crisis. Given the illiquidity of emerging market dollar debt back in the 80s the intention was to convert the existing (defaulted) debt on the balance sheets of the lenders (with an unavoidable haircut of course) to a more tradable instrument. The tradability/enhanced liquidity of the debt was made possible by guaranteeing and or collateralising the principal/interest component of the debt. The quality of collateral was usually as good as a Zero Coupon 30y US treasury bond that was purchased by the debt country and the country’s own foreign reserves. Interest payments too were sometimes collateralised by a much better-rated (than the issuing country) debt, which meaningfully brought down the joint default probability of the restructured debt. This in turn afforded a below market coupon to the Latin American bonds.