Maximum drawdown worked month by month on one fund's NAV: the running peak, the trough, the recovery, and how sampling frequency and leverage change the number.
Maximum drawdown is the largest percentage fall in a fund's NAV from a running peak to a later trough: for each month, divide NAV by the highest NAV reached so far, subtract one, and take the most negative result. On an illustrative 36-month series for a credit fund, NAV falls from 106.48 in month 13 to 97.20 in month 17, a maximum drawdown of 8.71 per cent, which takes a 9.55 per cent gain and eleven months to recover.
Worked in full in Financial Risk Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An open-ended credit fund with a NAV per unit of 100.00 at launch and 36 monthly returns, all illustrative. The first year is steady, with one small loss in month 6; months 14 to 17 lose 1.2, 2.6, 3.4 and 1.8 per cent in a row as spreads widen; the rest is a recovery.
| Months | Returns |
|---|---|
| 1 to 12 | 0.6, 0.5, 0.7, 0.4, 0.6, −0.3, 0.5, 0.8, 0.4, 0.6, 0.5, 0.7 |
| 13 to 24 | 0.3, −1.2, −2.6, −3.4, −1.8, 1.1, 0.9, 1.4, 0.8, 1.0, 0.7, 0.9 |
| 25 to 36 | 0.6, 0.8, 0.5, 0.7, 0.6, 0.4, 0.5, 0.6, 0.3, 0.7, 0.5, 0.6 |
NAVt = NAVt−1 × (1 + rt); Peakt = max(NAV0, …, NAVt)
Drawdownt = NAVt / Peakt − 1; MDD = min over t of Drawdownt
Excel, NAV in B2:B38: =MAX($B$2:B2) in C2 for the peak, =B2/C2-1 in D2 for the drawdown, both filled down, then =MIN(D2:D38).
| Month | Return | NAV | Running peak | Drawdown |
|---|---|---|---|---|
| 13 | 0.3% | 106.48 | 106.48 | 0.00% |
| 14 | −1.2% | 105.20 | 106.48 | −1.20% |
| 15 | −2.6% | 102.47 | 106.48 | −3.77% |
| 16 | −3.4% | 98.98 | 106.48 | −7.04% |
| 17 | −1.8% | 97.20 | 106.48 | −8.71% |
| 18 | 1.1% | 98.27 | 106.48 | −7.71% |
| 20 | 1.4% | 100.54 | 106.48 | −5.58% |
| 22 | 1.0% | 102.36 | 106.48 | −3.87% |
| 24 | 0.9% | 104.01 | 106.48 | −2.32% |
| 27 | 0.5% | 106.00 | 106.48 | −0.46% |
| 28 | 0.7% | 106.74 | 106.74 | 0.00% |
The peak is month 13 at 106.48, the trough month 17 at 97.20, and the NAV first exceeds the old peak in month 28. Peak to trough took four months; trough to recovery took eleven. A drawdown is reported with three numbers, depth, length and recovery time, and the third is usually the one investors feel.
MDD = 97.20 / 106.48 − 1 = −8.71%
Gain needed to recover = 1 / (1 − 8.71%) − 1 = 9.55%
Calmar ratio = annualised return / |MDD| = 3.63% / 8.71% = 0.42
Over the 36 months the fund returns 11.30 per cent, 3.63 per cent a year, to a final NAV of 111.30. The drawdown erased more than the whole first year's gain, and an investor who subscribed at the month-13 peak waited fifteen months to be back to par.
| Case | Max drawdown | Annual return | Calmar | Gain to recover |
|---|---|---|---|---|
| Monthly NAV, unlevered | −8.71% | 3.63% | 0.42 | 9.55% |
| Quarterly NAV, unlevered | −7.43% | 3.63% | ||
| Annual NAV, unlevered | −2.03% | 3.63% | ||
| Monthly, 1.5x | −12.86% | 5.45% | 0.42 | 14.76% |
| Monthly, 2.0x | −16.87% | 7.26% | 0.43 | 20.30% |
| Monthly, 3.0x | −24.50% | 10.86% | 0.44 | 32.44% |
Sampling hides drawdowns. On quarter-end NAVs the peak is month 12 at 106.16 and the lowest point month 18 at 98.27, a drawdown of 7.43 per cent; the month-17 trough never appears. On year-end NAVs the episode almost vanishes, at 2.03 per cent. A fund that reports quarterly can never show a larger maximum drawdown than the same fund marked monthly, and usually shows a smaller one; daily data can only show as much or more. Valuing assets with a lag hides drawdowns in the same way, as unsmoothing appraisal-based returns shows. Compare drawdowns only at the same frequency.
Leverage scales the drawdown almost in proportion and the recovery more than in proportion: at 3.0x a 24.50 per cent fall needs 32.44 per cent to recover. The Calmar ratio hardly moves, which is why it is a poor guide to whether a levered fund's investors, or its lenders, can live through the episode.
Maximum drawdown is backward-looking and rests on one episode, so it is a poor estimator of the next one. Use it beside a forward measure of the tail such as expected shortfall, and beside the question it cannot answer: how much of the book could be sold while the NAV was falling.
The measures the book uses for what breaks a fund, including the share of the book that can be sold inside a week, are in the free workbook for this case.
It depends on the return the fund earns, which is why the Calmar ratio divides one by the other. The fund here returns 3.63 per cent a year with a maximum drawdown of 8.71 per cent, a Calmar ratio of 0.42. Levered twice it returns 7.26 per cent with a drawdown of 16.87 per cent: the ratio barely moves while the drawdown nearly doubles.
Put NAV in column B from B2. In C2 enter =MAX($B$2:B2) and fill down for the running peak; in D2 enter =B2/C2-1 for the drawdown; then =MIN(D:D) returns the maximum drawdown. On the series here that returns -8.71 per cent in month 17, measured from the month-13 peak of 106.48.
One divided by one minus the drawdown, less one. An 8.71 per cent fall needs 9.55 per cent to get back to the peak; a 24.50 per cent fall, the same series at three times leverage, needs 32.44 per cent. The asymmetry grows with the size of the fall.
This article is one calculation from Financial Risk Management. 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.
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