There are two recovery dates, not one. The first depends on the loss and the new yield; the second is the fund's duration, almost to the decimal.
A bond fund has two recovery dates after a rate rise. It wins back its starting NAV in roughly the loss divided by the new yield, and it catches up with the path it would have followed without the rise after about its Macaulay duration. For an illustrative fund with a modified duration of 6.00 hit by a 2 point rise, that is 2.03 years to regain the NAV and 6.22 years to break even against the no-rise path.
Worked in full in The Credit Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Investors who watched a bond fund fall ask one question: when do I get my money back? The honest answer separates two things the question mixes up. Getting back to the starting figure on the statement is one milestone. Being as well off as if rates had never moved is another, and it takes three times as long.
| Input | Value |
|---|---|
| Starting NAV | 100.0 |
| Yield before the rise, and coupon on the holdings | 4.0% |
| Maturity kept constant by rolling the holdings, years | 7 |
| Macaulay duration before the rise | 6.24 |
| Modified duration before the rise | 6.00 |
| Rate rise, one-off and parallel, points | 2.0 |
| Yield after the rise | 6.0% |
The fund keeps its maturity at 7 years by selling bonds as they age and buying new ones at the current yield, which is roughly how index-tracking bond funds keep their maturity profile stable. With a flat curve and no further moves, a fund like that earns exactly its yield each year after the shock. Expenses are ignored; a real fund recovers more slowly by its expense ratio.
Duration estimate: 6.00 × 2.0 points = 12.0% loss
Exact repricing of a 4.0% coupon, 7-year bond at 6.0%: NAV 88.84, a loss of 11.16%
The duration estimate overstates the fall because of convexity, covered in how to calculate modified duration. In Excel the exact price is =PV(6%,7,-4,-100), which returns 88.84.
Years to recover = ln(starting NAV ÷ NAV after the rise) ÷ ln(1 + new yield) = ln(100.0 ÷ 88.84) ÷ ln(1.06) = 2.03
The rule of thumb, loss divided by new yield, gives 1.86. The higher yield is what does the work: the same rise that caused the loss lifts the fund's income from 4.0 to 6.0 per cent.
Break-even horizon = ln(100.0 ÷ 88.84) ÷ ln(1.06 ÷ 1.04) = 6.22 years
Without the rise the fund compounds at 4.0 per cent from 100.0; with it, at 6.0 per cent from 88.84. The two paths cross after 6.22 years, almost exactly the Macaulay duration of 6.24. This is the textbook meaning of duration: the holding period over which price risk and reinvestment risk cancel.
| Year | With the rise | Without the rise | Difference |
|---|---|---|---|
| 0 | 88.84 | 100.00 | -11.16 |
| 1 | 94.17 | 104.00 | -9.83 |
| 2 | 99.82 | 108.16 | -8.34 |
| 3 | 105.80 | 112.49 | -6.68 |
| 5 | 118.88 | 121.67 | -2.78 |
| 6 | 126.01 | 126.53 | -0.52 |
| 7 | 133.58 | 131.59 | 1.98 |
At the end of year 2 the fund is a whisker short of 100.0; a few days later it is back. By year 7 the investor who sat through the rise is 1.98 ahead of the one for whom rates never moved, because every year after the shock earned 6.0 per cent instead of 4.0.
| Fund maturity, years | Modified duration | Loss | Years to regain NAV | Break-even horizon, years |
|---|---|---|---|---|
| 2 | 1.89 | 3.67% | 0.64 | 1.96 |
| 4 | 3.63 | 6.93% | 1.23 | 3.77 |
| 7 | 6.00 | 11.16% | 2.03 | 6.22 |
| 15 | 11.12 | 19.42% | 3.71 | 11.34 |
| 25 | 15.62 | 25.57% | 5.07 | 15.50 |
| Rise, points | New yield | Loss | Years to regain NAV | Break-even horizon, years |
|---|---|---|---|---|
| 1 | 5% | 5.79% | 1.22 | 6.23 |
| 2 | 6% | 11.16% | 2.03 | 6.22 |
| 3 | 7% | 16.17% | 2.61 | 6.20 |
The size of the rise changes how deep the hole is and how long it takes to climb out of it, but barely moves the break-even horizon. That is set by duration. A bigger shock is a bigger loss and a bigger yield to repay it with, and the two almost cancel.
The arithmetic assumes the rise happens once and then stops. Rates that keep climbing restart the clock with each move, and a fund that also takes credit losses, a high-yield or loan fund, needs those losses netted from the yield before either date is computed.
Believing that individual bonds avoid the problem. A bond held to maturity shows no loss on the statement only because nobody marks it; its market value falls just as far if its duration is the same, and its owner earns the old 4.0 per cent coupon until it matures instead of 6.0. What a bond ladder or a single bond adds is a date when par comes back. The fund has no such date, but on total return it is not behind. The second mistake is quoting the fund's modified duration as the break-even horizon: Macaulay duration is the right figure, about modified duration times one plus the yield.
Divide the loss by the new yield for the first recovery date; read the fund's duration for the second. Here, 2.03 years and 6.22 years. The Credit Investor works yield, default, recovery and duration from the cash flows for bonds, loan funds, BDCs and private credit funds, and the free workbooks for the book's case compute duration and convexity for its bonds line by line.
Because getting the NAV back only requires the higher yield to earn back the price loss, roughly loss divided by new yield. In the illustrative case an 11.16 per cent loss at a 6.0 per cent yield takes 2.03 years. Matching the wealth the investor would have had without the rise takes longer, 6.22 years, about the fund's Macaulay duration.
Not in total return terms. A held bond shows no loss only because it is not marked to market; its market value falls just as far if its duration is the same. The fund reinvests at the higher yield and, in the illustrative case, is 1.98 ahead of the no-rise path by year 7. The difference is that the fund never matures, so there is no date at which par is guaranteed.
Longer to regain the NAV, but not to break even against the no-rise path. In the illustrative 7-year fund a 1 point rise is recovered in 1.22 years and a 3 point rise in 2.61, while the break-even horizon stays near 6.2 years in all three cases, because it is set by duration, not by the size of the shock.
This article is one calculation from The Credit Investor. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: credit, private credit and distressed debt → · All 1614 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.