Case 019Credit derivatives and counterparty riskHard

A company's CDS trades at 450 bp with a 40% recovery assumption, and one-year puts struck at Rs 80 on its Rs 200 stock cost Rs 6. For one year of protection against default, which is cheaper: CDS or deep out-of-the-money puts?

The situation

A desk holds Rs 100 crore of loans and bonds to Kumbharli Metals, a leveraged steel processor, and wants one year of protection against a default. Two markets offer it. Kumbharli's five-year CDS trades at 450 basis points running, quoted with the market's standard 40% recovery assumption; treat the credit curve as flat, so a year of protection also costs about 450 basis points. The stock trades at Rs 200, and one-year listed puts struck at Rs 80 cost Rs 6.

Assume that in a default the stock goes to zero. Ignore discounting, bid-offer and margin for the first pass.

Your task

What default probability does each market imply, what does it cost to cover the loss on Rs 100 crore with each, and which would you use, after looking at what each pays when things do not go as assumed?

Quick check

Before computing: how does the price of default protection compare between the two markets?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

On these numbers the two cost the same: the CDS implies a default intensity of 4.5% over 60%, 7.5% a year, and the put costs Rs 6 per Rs 80 of default payout, also 7.5%; covering Rs 60 crore of loss costs Rs 4.5 crore either way. The puts also pay Rs 15 crore if the stock falls to 60 without a default; the CDS pays the actual loss if recovery is worse than 40%. For a bondholder the CDS fits better; the puts win if the worry is stress short of default.

Step 1What does each market charge for default?

Two insurers quote for the same house: one charges Rs 4,500 a year for a Rs 60,000 payout, the other Rs 6,000 for an Rs 80,000 payout. You compare them per rupee of cover, and both charge 7.5 paise. A CDS at 450 basis points pays 60% of notional if the company defaults, so its price per rupee of payout is 4.5 over 60, a default intensity of 7.5% a year; the 80 put pays Rs 80 if the stock goes to zero and costs Rs 6, which is also 7.5 paise per rupee of payout. The CDS figure is the hazard rateThe default intensity implied by a CDS spread: roughly the spread divided by the loss given default. Over a year it gives a default probability of one minus e to the minus hazard rate., and over one year it gives a default probability of 1 minus e to the minus 0.075, 7.23%.

The relationship
λ≈s1−R=4.5%60%=7.5%PK=680=7.5%PD1y=1−e−0.075=7.23%\lambda \approx \frac{s}{1 - R} = \frac{4.5\%}{60\%} = 7.5\% \qquad \frac{P}{K} = \frac{6}{80} = 7.5\% \qquad PD_{1y} = 1 - e^{-0.075} = 7.23\%
sthe CDS spread, 450 basis points a year
Rthe recovery assumption, 40%
P, Kthe put price, Rs 6, and its payout if the stock goes to zero, Rs 80
What it says in wordsThe CDS spread divided by the loss given default, and the put price divided by its default payout, both come to 7.5%: the two markets are charging the same for a rupee paid on default.
Two markets, one price: both charge about 7.5% a year per rupee paid on defaultCDS at 450 bp, 40% recoveryPays 60% of notional on defaultCosts 4.5% of notional a yearCost per rupee of payout: 4.5 / 607.5%per year, per rupee of default payoutone-year default probability 7.23%One-year 80 put at Rs 6Pays Rs 80 if the stock goes to zeroCosts Rs 6 todayCost per rupee of payout: 6 / 807.5%per year, per rupee of default payoutand it also pays if the stock is stressedBoth ignore discounting; the CDS figure treats the credit curve as flat.
The CDS charges 4.5% a year for a 60% payout and the put charges Rs 6 for an Rs 80 payout, so both price a rupee of default payout at 7.5 paise, a one-year default probability of about 7.2% on the CDS side.
Step 2What does it cost to cover Rs 100 crore, and what does each pay?

The loss on default is 60% of Rs 100 crore, Rs 60 crore. CDS on Rs 100 crore of notional costs 4.5% a year, Rs 4.5 crore; to get Rs 60 crore from puts paying Rs 80 each the desk needs 75 lakh puts, which at Rs 6 cost Rs 4.5 crore. The cost is identical. So the decision cannot be made on price; it has to be made on the outcomes the two hedges treat differently, and there are three.

Outcome in one yearLoss on exposureCDS paysPuts payBetter hedge
Healthy, stock 220000neither; both cost 4.5
Stressed, survives, stock 600015puts
Default, recovery 40%606060equal
Default, recovery 20%808060CDS
In Rs crore: both hedges cost Rs 4.5 crore; the puts pay Rs 15 crore in a stressed survival where the CDS pays nothing, and the CDS pays Rs 80 crore when recovery is 20% while the puts stay at Rs 60 crore.
Same Rs 4.5 crore cost, different payouts: what each hedge pays in four outcomes20406080Rs crore00Healthystock 220015Stressedsurvives, stock 60606060Defaultrecovery 40%808060Defaultrecovery 20%loss on the exposureCDS on Rs 100 crore pays75 lakh puts pay
For the same Rs 4.5 crore, the 75 lakh puts pay Rs 15 crore if the stock falls to 60 without a default, the CDS pays Rs 80 crore if recovery turns out at 20%, and the two pay the same Rs 60 crore in a default at the assumed 40% recovery.
Step 3Which would you use, and what would change your mind?

Read the table as a judgement. The puts carry a payout the CDS does not, Rs 15 crore in a stressed survival, at the same price, so per rupee of pure default cover the puts are actually the cheaper of the two; but the CDS pays the true loss whatever the recovery, which is what a holder of the bonds needs. For this desk, holding Rs 100 crore of the company's debt, the CDS is the cleaner hedge, and the puts are the better buy only if the worry is a sharp fall in the equity without a default. Three practical checks would change the answer. 75 lakh deep out-of-the-money puts is Rs 150 crore of stock equivalent, which may be more than the listed open interest; the CDS on a name like this may trade only by appointment; and the one-year CDS point may be well away from 450 if the curve is inverted, as it often is for a stressed name.

Say the limits. The stock-to-zero assumption is a simplification: equity in a default is usually near zero but not always, which reduces the put payout. Discounting is ignored, which flatters the put slightly because its premium is paid up front. The CDS settles on an auction price that may differ from where the desk's own bonds trade, a basis risk the table hides. And the hedge is one year; if the company survives the year, the CDS can be extended at whatever spread then prevails, while the puts have to be bought again at a new price.

Where candidates lose it

Candidates compare Rs 6 with the Rs 200 stock price and call the puts cheap at 3%, or compare 450 basis points with 100% of notional. Neither is a price of default; the comparison has to be per rupee paid on default, and on that basis the two are the same.

The second loss is stopping at the equal price and calling it a draw. The interviewer is asking which hedge fits the exposure: the stressed survival and the recovery risk point in opposite directions, and the answer depends on whether the desk owns the bonds or just fears the name.

What the interviewer asks next

  • The stock is expected to be worth Rs 10, not zero, in a default. What happens to the put-implied price of default?
  • The one-year CDS trades at 600 bp while the five-year is at 450. Which hedge would you pick now?
  • How would you combine the two to cover both a stressed survival and a low recovery?
  • Why might a hedge fund buy the puts and sell the CDS on the same name, and what is it betting on?

Company names and figures are illustrative.