Case 003Debt fund credit decisionsHard

A debt fund is offered A-rated manufacturing bonds paying 250 basis points over AAA. With an assumed 3.5% three-year default rate and 35% recovery, does the spread pay for the risk, and what else must it pay for?

Wellington ManagementLondon · 2021

The situation

The debt team at Dhruvtara Mutual Fund is offered a basket of three-year bonds from A-rated manufacturing companies at 250 basis points over AAA bonds of the same maturity. The credit analyst assumes, for this exercise, that 3.5% of A-rated issuers default within three years and that holders recover 35% of face value in a default.

These bonds trade rarely; the dealer desk estimates it would give up about 60 basis points a year of yield to be able to sell them as easily as AAA paper. The team also puts about 50 basis points a year on the risk that an issuer is downgraded and the bond's price falls even without a default.

Your task

Does 250 basis points pay for expected loss, what else must it pay for, and would you add the bonds?

Quick check

What is the annual expected loss from defaults, in basis points?

Worked solution

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

30-second answerThe answer to give first

Yes, 250 basis points covers the expected loss of about 76 with room to spare, but that is only one of its jobs. After a 60 basis point liquidity premium and 50 for downgrade risk, about 64 basis points is true reward. That is thin: if defaults ran at 6.5% instead of 3.5%, the reward would vanish. Add the bonds only in small, spread-out positions inside a mandate that allows them.

Step 1What is the extra yield actually paying you for?

A friend offers you 14% on a loan when the bank pays 7%. The extra 7% is not free money; part of it pays for the chance you are not repaid, part for the fact that you cannot get your money out early, and part for the worry if your friend's job looks shaky. A credit spread is the same: it must pay for expected default losses, for illiquidity and for the risk of a price fall before any default, and only what is left over is reward. Interviewers ask this to hear whether you break the spread into those jobs, which is the concept the question is fishing for.

Step 2How big is the expected loss?

Spread the three-year default rate across the years, then take off the recovery. 3.5% over three years is about 1.17% a year, and each default costs 65% of face value, so the expected loss is about 76 basis points a year. This is the expected lossProbability of default times the share of the money lost in a default. It is the average cost of defaults, not the worst case., the average cost of defaults across many bonds. It uses a simple straight-line split of the three-year rate, which is close enough for an interview; a precise model compounds the yearly default chance and lands within a basis point or two.

The relationship

EL = \frac{3.5\%}{3} \times (1 - 35\%) \approx 1.17\% \times 0.65 \approx 0.76\% = 76\text{ bp}

3.5%	assumed share of A-rated issuers defaulting within three years
35%	assumed recovery on face value after a default
EL	expected loss a year from defaults

What it says in wordsThe average yearly cost of defaults is the yearly default chance times the share of face value lost.

Of the 250 basis point spread, about 76 pays for expected defaults, 60 for illiquidity and 50 for downgrade risk, leaving about 64 basis points as the true reward for holding the bonds.

Step 3How wrong can the default assumption be before the trade stops paying?

Run the one sensitivity that matters. Keep the 110 basis points for liquidity and downgrade risk fixed and ask what default rate eats the rest. The reward disappears if three-year defaults run at 6.5% instead of 3.5%, less than double the assumption, and the whole spread is gone at 11.5%. Default rates on lower-rated bonds are not stable; they cluster in bad years. A cushion that survives less than a doubling is modest, and you should say that plainly.

At the assumed 3.5% three-year default rate the bonds keep 174 basis points after expected loss, enough to cover liquidity and downgrade risk; that cover runs out at 6.5% and the whole spread is gone at 11.5%.

Step 4Why do position size and mandate decide the answer?

Expected loss is an average across many bonds, but a fund owns a handful. If the fund put 5% of its assets in these bonds, the extra yield adds about 12.5 basis points a year to the fund, while one issuer holding 2% of the fund defaulting at 35% recovery costs about 130 basis points of NAV in a day. One default wipes out roughly 10 years of the whole sleeve's extra carry. So the view is: add, but in several issuers at 1% or less each. The mandate comes first: SEBI's scheme categories set minimum shares of high-rated paper for some debt funds, so check the scheme's category rules and confirm the current figures before any A-rated bond goes in.

Where candidates lose it

The usual loss is comparing 250 basis points with the raw 3.5% default rate, or with the annual default chance, and forgetting the recovery. Either mistake gives a wrong expected loss and a confident wrong answer.

The second is stopping once the spread beats expected loss. The interviewer wants to hear that illiquidity and downgrade risk also have to be paid for, and that the leftover is thin.

What the interviewer asks next

Recovery falls to 20%. What is the expected loss now?
How would you estimate the liquidity premium from market data?
Would you rather own these bonds in a credit risk fund or a corporate bond fund, and why?
What happens to this trade if the fund faces heavy redemptions?

Asked at Wellington Management, Generalist, London, 2021 (Wall Street Oasis): I was asked how to determine whether to invest or not on a particular class of corporate bonds

Company names and figures are illustrative.