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038

Case 038Interest rate derivativesHard

Tikona Credit Fund buys a five-year 9.2% bond of Mahuli Infra at 101 and swaps it to floating with a par asset swap. The five-year swap rate is 7.0% and the annuity factor 4.1. What is the asset swap spread, and what is the fund still exposed to?

1The situation

Tikona Credit Fund likes the credit of Mahuli Infra, a toll-road operator, but does not want a view on interest rates. Mahuli's five-year bond pays a fixed 9.2% coupon annually and trades at 101 per 100 of face value. The fund wants Rs 100 crore of face.

A dealer offers a par asset swap: Tikona pays par, Rs 100 crore, for the bond and a swap in one package; it passes the bond's fixed coupons to the dealer and receives the floating benchmark rate plus a spread, every year for five years. The five-year swap rate is 7.0% and the annuity factor, the present value of one rupee a year for five years at swap rates, is 4.1. Assume the bond is bought on a coupon date, so there is no accrued interest.

2Your task

Compute the asset swap spread, explain each part of it, and say what risk Tikona still carries once the swap is on.

Quick check

The bond pays 9.2% and the swap rate is 7.0%. Once the 1-point premium over par is allowed for, the asset swap spread is about:

Worked solution

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

30-second answerThe answer to give first

The asset swap spread is about 196 bp over floating: 220 bp of excess coupon less 24.4 bp a year to repay the point above par. That is Rs 1.96 crore a year on Rs 100 crore. The swap removes the interest rate risk, so what remains is almost pure Mahuli credit risk: if Mahuli defaults, Tikona keeps paying fixed on a swap with no bond behind it, and loses par less recovery. It also carries the dealer's credit on the swap.

Step 1What is a par asset swap doing?

Take a fixed-rate bond and ask what it would pay if it were a floating-rate loan. Think of renting out a flat on a fixed five-year lease when you would rather have rent that tracks the market: you agree with someone else to hand them the fixed rent and receive a market-linked rent plus a margin. In a par asset swap the fund pays par for the bond, gives the bond's fixed 9.2% coupons to the dealer, and receives floating plus a spread, so the spread is the bond's credit premium restated over floating. Because the fixed coupons in and out cancel, rate moves no longer change what Tikona earns. The word par matters: Tikona pays Rs 100 crore even though the bond costs Rs 101 crore, and the dealer funds the difference.

Par asset swap: the fund keeps floating plus spread, and Mahuli's creditTikona Credit Fundholds the bondpays par, Rs 100 croreMahuli Infra bond5 years, 9.2% fixedmarket price 101Swap dealerfunds the 1 pointabove par at the start9.2% couponpays 9.2% fixedfloating + 196 bpWhat Tikona is left withfloating + 196 bp a year, if Mahuli paysFixed coupons in and out cancel;the rate risk is swapped away.If Mahuli defaults, the swapcarries on and the bond does not.
In the par asset swap Tikona pays Rs 100 crore for the package, passes Mahuli's 9.2% coupon to the dealer and receives floating plus about 196 bp, so the rate risk cancels and what remains is Mahuli's credit, which the swap does not cover if Mahuli defaults.
Step 2How is the spread worked out?

Set it up as a fair exchange for the dealer. Each year the dealer receives 9.2% and pays floating plus a spread s. A five-year swap at 7.0% says fixed 7.0% is worth the same as floating, so the dealer is ahead by 9.2 less 7.0, 2.2% a year, less s. At the start the dealer is behind by 1 point, the premium it funded. Fairness means 2.2% less s, times the annuity factor of 4.1, equals 1 point, so s is 2.2% less 1 divided by 4.1, which is 2.2% less 0.244%, or 1.956%, about 196 bp. The annuity factor converts a lump sum today into an equal amount each year, which is why the 1 point becomes 24.4 bp rather than 20 bp: discounting means a rupee today buys more than a fifth of a rupee a year for five years.

The relationship
s=(c−Sw)−P−100A=(9.2%−7.0%)−14.1=2.200%−0.244%=1.956%s = (c - S_w) - \frac{P - 100}{A} = (9.2\% - 7.0\%) - \frac{1}{4.1} = 2.200\% - 0.244\% = 1.956\%
sasset swap spread over the floating rate
cbond coupon, 9.2%
S_wfive-year swap rate, 7.0%
Pbond price per 100, 101
Aannuity factor at swap rates, 4.1
What it says in wordsThe spread is the bond's excess coupon over the swap rate, less the premium over par spread across the life of the swap.
From excess coupon to asset swap spread, basis points a year50100150200220Coupon less swap9.2% - 7.0%-24.4Premium paid1 point / 4.1195.6Asset swap spreadover floatingSpread2.2% - 1/4.1= 1.956%The point above par ispaid back through asmaller spread each year.
Starting from 220 bp of coupon over the swap rate and taking off 24.4 bp a year to repay the point paid above par leaves an asset swap spread of 195.6 bp over floating.
Step 3What is Tikona still exposed to?

Start with what it is not exposed to: a rise in rates no longer hurts, because Tikona earns floating plus 196 bp and floating rises with rates. What remains is Mahuli's credit, and the swap makes a default slightly more awkward, not less: the bond stops paying, but the swap does not stop, so Tikona must either keep paying 9.2% fixed with nothing coming in or close the swap at its market value. If rates have fallen since the start, that close-out costs money on top of the bond loss; if they have risen, it pays some back. On Rs 100 crore with an assumed recovery of 40%, the bond loss is Rs 60 crore of par, and Tikona paid par, not 101, which is one of the reasons funds prefer the par structure. Two more risks sit behind it: the dealer's own credit on the swap, which collateral reduces, and the day-count and payment-date mismatch between the bond and the swap, small but real.

Close with what the 196 bp is for. It is the market's price of five years of Mahuli credit risk, stated over floating, and the fund should compare it with Mahuli's five-year credit default swap spread: if the asset swap pays more than the CDS costs, buying the bond, swapping it and buying protection would lock in the difference, a gap traders call the basisThe difference between a CDS spread and a bond asset swap spread on the same issuer and maturity. Funding costs and delivery options keep it from being zero.. State the limitation: the annuity factor of 4.1 is taken as given, and on a real trade the dealer computes it from the swap curve and the exact payment dates, which can move the spread by a basis point or two.

Where candidates lose it

The common loss is answering 220 bp, coupon less swap rate, and forgetting that the fund paid 101 for a bond that repays 100. That premium is a cost and it has to come out of the spread, spread over the life of the deal, not as a full point in one year.

The second is saying the swap removes the fund's risk. It removes rate risk. The credit risk of Mahuli is untouched and the swap adds a close-out problem on default, which is the part of the answer that tells the interviewer the candidate understands why the spread exists.

What the interviewer asks next

  • The bond trades at 98 instead of 101. What is the asset swap spread, and why does it rise?
  • Mahuli's five-year CDS is 170 bp. What trade does that suggest, and what could stop it working?
  • How does a market value asset swap differ from a par asset swap, and which leaves the fund with less counterparty exposure at the start?
  • Rates fall 100 bp and then Mahuli defaults. Walk through what Tikona loses on the bond and on the swap.
← Case 037Six months ago a fund agreed to buy 10,000 shares of Kabini Cables at Rs 520 in one year. The stock is now Rs 560, six months remain and the rate is 7% continuous. What is the forward worth today, and to whom?Case 039 →Purna Finance bought a 3x6 FRA at 7.00% on Rs 50 crore. At fixing the three-month rate is 7.60%. How much is settled, when, and who pays whom?

Company names and figures are illustrative.

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