Case 092Duration and rates positioningHard
A floating rate fund (quarterly resets, spread duration 2.5, rate duration 0.3) and a short duration fund (duration 2.4) both yield 7.4%. If rates rise 100 basis points and credit spreads widen 50, what does each lose, and which risk did the floater investor keep?
1The situation
Akshayvat Mutual Fund runs two debt funds that currently yield the same 7.4%. Its floating rate fund holds corporate bonds whose coupons reset every quarter off a money market benchmark plus a fixed spread; its rate duration is about 0.3 years, the average time to the next reset, while its spread duration is 2.5 years, the average life of the bonds. Its short duration fund holds fixed-coupon corporate bonds with a duration of 2.4 years to both rates and spreads.
A distributor has been selling the floater as the fund that is immune to rising rates. Test that in a stress where policy rates and benchmark yields rise 100 basis points at once and credit spreads widen 50 basis points, with no defaults. Treat the price change as duration times the yield change and ignore convexity. Floating rate funds must hold a minimum share of floating-rate assets under the category rules; confirm the current figure.
2Your task
What does each fund lose on the day of the shock, roughly where does each end the year, and which risk did the floater's investor keep?
Quick check
Rates rise 100 basis points and spreads widen 50 at once. What is the floater's immediate loss?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
The floater loses about 1.55 points on the day, the short duration fund about 3.60, and the floater's investor kept the credit spread risk in full. The floater's loss is 0.30 from rates and 1.25 from spreads; the short duration fund's is 2.40 and 1.20. Over a year the floater recovers its rate loss at the first reset and its coupon steps up, ending near 6.9% if spreads stay wide, while the short duration fund ends near 5.3%. A floater removes rate risk; it does not remove the issuer.
Step 1What are the two durations, and why does a floater have both?
A bond's yield has two parts: the benchmark rate and the spread the market charges for the issuer's credit. A floating rate bond resets the first part every quarter and fixes the second for its whole life. A shop tenant on a rent that tracks an index every quarter is protected from inflation in rents, but if the shop's own street goes downhill, the lease still runs for three years. Rate durationPrice sensitivity to a change in benchmark interest rates. For a floater it is roughly the time to the next coupon reset, because the coupon catches up with the market then. measures the first exposure; spread durationPrice sensitivity to a change in the credit spread over the benchmark. For a floater it is close to the remaining life of the bond, because the spread does not reset. measures the second, and a floater resets only the first. That is why the two numbers are 0.3 and 2.5 for the same fund.
Step 2What does each fund lose on the day?
Multiply each duration by its own shock. Floater: rates, 0.3 x 1.00 = 0.30 points; spreads, 2.5 x 0.50 = 1.25 points; total 1.55 points, of which 81% is the spread. Short duration: rates, 2.4 x 1.00 = 2.40; spreads, 2.4 x 0.50 = 1.20; total 3.60 points. On the spread leg the floater actually loses slightly more, because its bonds are a little longer. The distributor's claim is true of exactly one of the two shocks.
| D_rate | rate duration: 0.3 for the floater, 2.4 for the short duration fund |
| Δr | change in benchmark rates, +1.00 point |
| D_spread | spread duration: 2.5 and 2.4 |
| Δs | change in credit spreads, +0.50 point |
Step 3Which risk did the floater's investor keep?
Run the shocks one at a time. A pure rate rise of 100 basis points costs the floater 0.30 points and the short duration fund 2.40; a pure spread widening of 50 costs them 1.25 and 1.20, almost the same. The floater's investor swapped rate risk for nothing and kept credit risk whole. That matters because the two shocks tend to arrive together: tightening cycles squeeze weaker borrowers, and spreads widen most when rates are rising fastest. The investor who bought the floater to sleep through a hiking cycle still owns the same issuers as the short duration fund, and will feel the same credit scare.
Step 4Where does each fund end the year?
The day-one loss is not the year. The floater's 0.30 rate loss disappears at the first reset, when its coupons step up by the full 100 basis points for the remaining three quarters; if spreads stay wide, it ends the year near 6.9%: 7.4 of carry, less 1.25 of spread loss, plus about 0.75 of higher coupon. The short duration fund keeps its lower prices but its bonds pull back towards par as they shorten, recovering roughly a year's worth of the loss over the year, so it ends near 5.3%. These are approximations that ignore the roll-down and reinvestment, but the ranking is robust: in a year of rising rates the floater wins, and in a year of widening spreads both lose the same.
| Points of NAV | Floater | Short duration |
|---|---|---|
| Rate loss on the day, 100 bp | -0.30 | -2.40 |
| Spread loss on the day, 50 bp | -1.25 | -1.20 |
| Total on the day | -1.55 | -3.60 |
| Approximate one-year return, spreads stay wide | 6.9% | 5.3% |
Close with the limit and the view. In India many floating rate funds hold fixed-coupon bonds and swap them to floating with interest rate swaps, which adds basis risk between the swap benchmark and the bonds, and the category rule on minimum floating-rate holdings shapes how pure the fund can be; confirm the current figure. The view for the distributor: sell the floater as a fund that is protected from rate rises, never as one without credit risk, and tell the investor that its credit quality, not its reset frequency, decides what it does in a credit scare.
Where candidates lose it
Candidates say the floater is immune because its coupons reset, and give a loss near zero. The reset covers the benchmark; the spread over it is fixed for the bond's life, so a 50 basis point widening costs 2.5 x 0.5 = 1.25 points, most of the floater's loss.
The second miss is quoting one duration for a floater. The question hands you two because the fund has two exposures, and the whole answer is in treating them separately.
What the interviewer asks next
- Rates fall 100 basis points instead. What does each fund do, and which investor regrets his choice?
- The floater's bonds are swapped from fixed coupons. What new risk does that add?
- How would a credit event in one 4% holding affect each fund's NAV, and does the reset help at all?
- Why might a floater's spread duration be longer than a short duration fund's duration?
Company names and figures are illustrative.
