Maximum Drawdown (MDD)

Maximum drawdown (MDD) is the largest fall in the value of an investment, portfolio or trading strategy from a peak to a subsequent low, before a new peak is reached. It is expressed as a percentage of the peak value. If a fund grew to 150, fell to 90 and later recovered, its maximum drawdown over that stretch was 40 percent.

The measure answers a question investors ask directly: how bad did it get? Unlike volatility, which treats rises and falls alike and averages over the whole period, maximum drawdown looks only at losses and only at the worst episode. It is a standard figure in the reporting of hedge fund and trading-strategy performance and in the evaluation of a backtest.

The drawdown at any time is the percentage by which the current value sits below the highest value reached so far. Maximum drawdown is the largest such figure over the period:

• $V_t$ is the value of the portfolio at time $t$.
• $\text{Peak}_t$ is the highest value the portfolio has reached at any time up to $t$.
• $\max_{t}$ means the largest value of the expression over all times in the period.

Suppose a portfolio's month-end values are 100, 120, 150, 110, 90, 130 and 160. The running peak is 150 from the third month until the last. The drawdown in the fourth month is $(150 - 110) / 150 = 26.7$ percent and in the fifth month $(150 - 90) / 150 = 40$ percent. In the sixth it is 13.3 percent, and in the seventh the portfolio sets a new peak. The maximum drawdown is 40 percent. The figure is often written with a minus sign, as -40 percent.

A loss needs a larger percentage gain to undo it, because the gain is earned on a smaller base. The gain required to recover from a drawdown $D$, written as a decimal, is:

A 20 percent drawdown needs a 25 percent gain to get back to the peak. A 40 percent drawdown needs $1 / 0.6 - 1 = 66.7$ percent, and a 50 percent drawdown needs 100 percent. This asymmetry is why deep drawdowns are so damaging to long-run compounding, and why the time spent below the previous peak, called the drawdown duration or time under water, is reported alongside the depth.

Maximum drawdown is the denominator of several measures of risk-adjusted return. The Calmar ratio divides the annualised return by the maximum drawdown, usually over the past three years. A strategy that earned 12 percent a year with a maximum drawdown of 24 percent has a Calmar ratio of 0.5. Such ratios complement the Sharpe ratio and the Sortino ratio, which are based on the variability of returns.

The measure also has practical uses. Investors in funds often set a drawdown level at which they will withdraw, and trading firms set drawdown limits at which a strategy or a trader is stopped. Allocators use it to judge how much leverage a strategy can bear: a strategy with a 10 percent historical maximum drawdown, run at three times leverage, should be expected to lose at least 30 percent at some point. Methods of sizing bets such as the Kelly criterion are frequently scaled back because the drawdowns they imply are larger than investors will tolerate.

Broad equity markets have suffered very large drawdowns. The S&P 500 fell about 57 percent from its closing high in October 2007 to its low in March 2009, during the 2008 financial crisis, and did not regain the earlier level until 2013. Strategies can have drawdowns unrelated to the market: a momentum crash is a sudden deep drawdown in a strategy that had previously looked steady.

Maximum drawdown is a single observation, the one worst episode in the sample, and so it is a noisy statistic. Two strategies with the same underlying risk can show quite different figures by chance. It also grows with the length of the record: the longer a strategy is observed, the more opportunity it has to hit a bad run, so a five-year track record cannot be compared directly with a twenty-year one. The frequency of measurement matters too, since month-end values miss falls that occurred and reversed within a month.

A backtested maximum drawdown is usually an underestimate of what will be experienced. Parameters chosen to look good in the past tend to avoid past losses in particular, and the future worst case is likely to exceed the historical one. Analysts therefore supplement the historical figure with Monte Carlo simulation, reshuffling or resampling returns to produce a distribution of possible drawdowns, and with measures such as value at risk. Finally, the figure says nothing about how often smaller drawdowns occur, which the average drawdown and related indices try to capture.