Case 078Duration and rates positioningCore
After a 150 basis point hiking cycle, a short duration fund yields 7.8% against 6.1% a year ago, with a duration of 2.5. What one-year return should an investor expect if rates stay flat, fall 50 or rise 50, and why is the starting yield the best single guide?
1The situation
Yamunotri Mutual Fund's short duration fund holds high-quality bonds with a portfolio yield to maturity of 7.8% and a modified duration of 2.5 years. A year ago, before the central bank raised its policy rate by a total of 150 basis points, the same fund yielded 6.1%. Investors who bought then have had a poor year and are asking whether short-term debt funds are worth holding.
Treat any rate change as happening at once and across the curve, ignore convexity, and quote returns before the fund's expense ratio.
2Your task
What one-year return does the fund give if yields stay flat, fall 50 basis points or rise 50, what did last year's investor get, and why does the starting yield matter more than the rate call?
Quick check
Yields rise another 50 basis points immediately. Roughly what does the fund return over the next year?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
About 7.8% if yields stay flat, about 9.0% if they fall 50 basis points and about 6.6% if they rise 50. With a duration of 2.5, a 50 basis point move changes the price by only 1.25 points, while the fund earns 7.8% of carry. Yields would have to rise over 3 percentage points in the year for the fund to lose money. Last year's investor started at 6.1% and took the whole 150 basis point rise, ending near 2.4%.
Step 1What two pieces make up a bond fund's one-year return?
Carry and price. A rented flat pays you rent every month whatever happens to property prices, and its resale value moves on top of that. A bond fund earns its yield as carry, about 7.8% a year here, and its price moves by roughly duration times the change in yields, in the opposite direction. Modified durationThe approximate percentage change in a bond price for a one percentage point change in its yield. A duration of 2.5 means about a 2.5% price change. of 2.5 means a 1 percentage point rise in yields costs about 2.5% of price.
| y | starting yield to maturity, 7.8% |
| D | modified duration, 2.5 |
| Δy | change in yields, in percentage points, assumed at once |
Step 2What does each scenario give?
Run the three cases. Flat: 7.8%. Down 50 basis points: 7.8 plus 1.25, 9.05%. Up 50: 7.8 minus 1.25, 6.55%. The spread between the best and worst case is 2.5 points, and all three sit within 1.25 points of the starting yield. The rate call you would spend a morning arguing about moves the answer less than the yield you can read off the factsheet today.
Step 3Why did last year's investor do so badly, and what changed?
The 6.1% investor had half the cushion and took the full shock. Carry of 6.1% less a price loss of 2.5 x 1.5 = 3.75 points left about 2.35% for the year, if the whole rise had come at the start; in practice hikes arrive in steps and the fund reinvests at rising yields, so the real figure would be a little better. The same calculation gives each investor a breakeven: the yield rise that wipes out one year of carry. At 6.1% it was 2.44 percentage points; at 7.8% it is 3.12 percentage points, a rise nobody would call likely in a single year.
| Investor | Starting yield | Yield change | Price effect | One-year return | Rise that wipes out a year |
|---|---|---|---|---|---|
| Bought a year ago | 6.1% | +1.50 | -3.75 | 2.35% | 2.44 pts |
| Buys today, rates flat | 7.8% | 0 | 0.00 | 7.80% | 3.12 pts |
| Buys today, rates up 50 | 7.8% | +0.50 | -1.25 | 6.55% | 3.12 pts |
Close with the limit and the view. The approximation ignores expenses, convexity and changes in credit spreads, and a fund's yield to maturity is only reached if the bonds are held and do not default. Over a horizon close to the fund's duration, higher yields also mean higher reinvestment income, so rate moves largely wash out and the return converges on the starting yield. That is why the starting yield is the best single guide for a short duration fund, and why the time after a hiking cycle, not before it, is when the arithmetic is most forgiving.
Where candidates lose it
The usual error is treating last year's return as a guide to next year's. The 2.35% was the price of the hiking cycle; the same event lifted the starting yield from 6.1% to 7.8%, which is what drives the next year.
The second is forgetting to scale by duration. Candidates hear rates rise 50 and imagine a loss, when a 2.5 duration fund loses only 1.25 points of price against 7.8 points of carry.
What the interviewer asks next
- The fund's expense ratio is 0.4%. What does the investor actually receive in each scenario?
- How would the three scenarios look for a gilt fund with a duration of 8?
- What happens to the answer if credit spreads widen 50 basis points while government yields fall 50?
Company names and figures are illustrative.