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091

Case 091Fixed income and creditHard

A company's five-year CDS trades at 300 bps while its bond trades 360 bps over the swap curve. How do you construct the basis trade, what does it carry, and what can make it lose?

1The situation

Anshukam Credit looks at an invented infrastructure issuer, Ketaki Infra. Its five-year bond, swapped into floating rate, pays 360 basis points over the swap curve and trades at 98. Five-year credit default swapA contract in which the protection buyer pays a yearly premium and, if the issuer defaults, receives par in exchange for the defaulted bond. protection on the same issuer costs 300 basis points a year.

Anshukam can fund the bond in repo at the swap rate plus 25 basis points with a 15% haircut. The portfolio manager asks for the trade, its carry on Rs 100 crore, and everything that could turn the apparent free carry into a loss. Use a swap rate of 7% and 40% recovery for any valuation.

2Your task

Construct the trade, compute its carry and return on capital, and list and size what can make it lose.

Quick check

The bond pays 360 over swaps and protection costs 300. Which package earns the 60 basis points?

Worked solution

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

30-second answerThe answer to give first

Buy the bond and buy five-year protection: the package earns 360 minus 300, a basis of 60 basis points, and about 35 after funding at swaps plus 25, Rs 35 lakh a year on Rs 100 crore. On 15% haircut capital that is 2.3% a year. It loses if funding costs rise, if the basis widens, worth about Rs 4.95 crore on a 140 basis point move, if the protection seller fails, or if the bond is not deliverable.

Step 1What is the basis, and how do you trade it?

Think of buying a car and a comprehensive insurance policy on it, then renting the car out. If the rent exceeds the insurance premium, you earn the difference and a crash is the insurer's problem. The bond pays 360 over swaps for bearing Ketaki's default risk; protection on that same risk costs 300, so the market prices one risk two ways, 60 basis points apart. The basis is the CDS premium minus the bond spread, -60 here, a negative basis. The trade buys the cheap risk and pays for protection: own the bond, swapped to floating, and buy protection on the same notional. If Ketaki defaults, Anshukam delivers the bond and receives par, and because the bond was bought at 98, that adds Rs 200 lakh.

Long the bond, long protection: the basis of -60 is the carry, before fundingAnshukamlong bond + protectionRs 100 croreBond, asset-swappedpays swap + 360 bpsProtection seller (CDS)receives 300 bps a yearRepo lenderreceives swap + 25 bpsOn a credit eventdeliver bond, receive par+360-300-25par if defaultnet carry +35 bps a year
Anshukam owns the asset-swapped bond earning swap plus 360, buys protection for 300 and funds in repo at swap plus 25, so the package carries 35 basis points a year and swaps a defaulted bond for par.
Step 2What does it carry, and on how much capital?

Add the legs: +360 from the bond, -300 for protection, -25 for funding over swaps, so 35 basis points a year. On Rs 100 crore that is Rs 35 lakh a year, and because the repo lender keeps a 15% haircut, Anshukam's own capital is Rs 15 crore, a return of 2.3% a year over its funding cost. Small numbers like these are why basis desks run large notionals with borrowed money, and why the risks below matter far more than the carry.

The relationship
carry=sbond−sCDS−sfund=360−300−25=35 bpsΔV≈Δbasis×RPV01×N\text{carry} = s_{\text{bond}} - s_{\text{CDS}} - s_{\text{fund}} = 360 - 300 - 25 = 35 \text{ bps} \qquad \Delta V \approx \Delta\text{basis}\times \text{RPV01}\times N
s bondbond spread over swaps, 360 bps
s CDSprotection premium, 300 bps
s fundrepo funding over swaps, 25 bps
RPV01present value of 1 bp a year for five years, allowing for default, about 3.5
What it says in wordsThe carry is what the bond pays minus what protection and funding cost; the mark-to-market loss if the basis widens is the widening times the risky duration times the notional.
Step 3What can make it lose?

Take them in order of how they actually hurt basis desks. Funding first: the trade needs repo every day for five years, and if the funding spread rises to 100 basis points the carry becomes Rs -40 lakh a year, while a higher haircut forces Anshukam to post capital or cut the position at the worst time. Second, mark-to-market: the basis can widen before it closes. With a risky duration of about 3.54, a move from -60 to -200 costs 1.4% x 3.54 x Rs 100 crore, about Rs 4.95 crore, 14 years of carry and a third of the capital. Both tend to happen together, in a credit crisis, when everyone with the same trade sells bonds to meet funding calls.

The carry is small; the ways it can lose are notNormal year: carry+35Funding squeeze: repo + 100-40Basis widens -60 to -200-495Rs lakh. Mark-to-market = 140 bps x risky duration 3.54 x Rs 100 crore.
Anshukam's package carries Rs 35 lakh a year, turns to Rs -40 lakh if repo funding rises to 100 basis points, and loses about Rs 495 lakh on paper if the basis widens from -60 to -200, about 14 years of carry.

Then the contract itself. The protection seller may fail in the same crisis that makes the protection valuable, so the CDS counterparty and its collateral terms matter. The bond must be deliverable under the CDS terms: a bond that is subordinated, or issued by a subsidiary the contract does not reference, may leave Anshukam owning a defaulted bond with protection on a different one. A restructuring that the contract does not count as a credit event can cut the bond's value without triggering the CDS. And the interest-rate swap inside the asset swap survives a default and must be closed at market. A negative basis looks like free carry, but it is paid for bearing funding, counterparty and documentation risk.

Step 4So is it a trade?

It can be, on terms. Size it so that a widening to -200 and a funding squeeze together do not force a sale: here that means term repo for as long as possible, a position the capital can carry through a 140 basis point mark-down, and a protection seller with daily collateral. Check the deliverability of the exact bond against the CDS reference obligation before trading. The limitation: the -60 basis exists partly because the market prices exactly these risks, so the trade earns a fee for bearing them rather than exploiting an error.

Where candidates lose it

The common loss is calling the negative basis an arbitrage. The package removes most default risk but keeps funding, mark-to-market and counterparty risk, and those are the risks that blow up together in a credit crisis.

The second is computing carry as 60 basis points and forgetting the funding spread and the haircut. The trade is financed, and its return on capital depends entirely on terms the repo lender can change.

What the interviewer asks next

  • What changes if the bond trades at 108 rather than 98?
  • How would a positive basis of +40 be traded, and what makes that harder?
  • Why might the basis widen in a credit crisis even though default risk is hedged?
  • How would you choose the CDS notional if the bond is above par?
← Case 090Sthiram's two assets have expected returns of 8% and 8.5%, volatilities of 15% and 16%, and correlation 0.9. Show how a half-point change in one expected return swings the mean-variance weights, and propose a fix.Case 092 →Kadvari's signal uses each day's closing price to trigger a trade executed at that same close. Re-run with execution at the next open and the annual return falls from 15% to 4%. Where did the 11 points go, and how do you fix the timing?

Company names and figures are illustrative.

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