Maximum drawdown: the largest loss from a peak
The maximum drawdown is the largest percentage decline of a portfolio from a peak to the subsequent trough. It answers the question every investor asks: how much would I have lost on paper in the worst case, and how long did it take for the money to come back?
How to calculate drawdown
For each day (or month), the highest value reached so far is tracked. The drawdown is the distance of the current value from this peak, and the maximum drawdown is the deepest of these values. Important: the calculation uses the value path including reinvested distributions, not individual returns.
Drawdown(t) = Value(t) / running peak − 1; maximum drawdown = lowest drawdownAt the interim value of 110, the portfolio is still 110 / 120 − 1 = −8.33% below its peak. It has risen again, but it is still “underwater”. Only at 130 is the drawdown over. For many investors, this time below the last peak is the real strain.
Figures as in the example above: 90 / 120 − 1 = −25%. The drawdown is only over once the value regains the old peak.
Why losses weigh more than gains
After a loss, you need a larger gain to get back to where you were. In the example above, the portfolio needs +33.3% from 90 to reach 120 again.
Required gain = 1 / (1 − loss) − 1| Loss | Gain required to regain the old peak |
|---|---|
| −10% | +11.1% |
| −20% | +25.0% |
| −33.3% | +50.0% |
| −50% | +100.0% |
| −75% | +300.0% |
Required gain = 1 / (1 − loss) − 1. Up to about −10% the two lines are close together; after that, the required gain grows faster and faster.
This asymmetry is pure mathematics, but it works together with psychology: losses hurt more than equally large gains please. Kahneman and Tversky (1979) described this in prospect theory. If you sell in a deep drawdown, you turn a paper loss into a permanent one. This is the most common way in which volatility turns into real damage.
Duration and recovery time
Duration matters just as much as depth: how long was the portfolio below its peak? A distinction is made between the time to the trough and the recovery time afterwards. Broad equity indices have needed several years after major crises. The MSCI World in euros lost around half its value in the 2007 to 2009 financial crisis. An “underwater chart” shows the drawdown over time and makes such phases visible. For your own planning, the total time from the old peak to the new one often matters more than the depth: five years without progress test your patience more than a short, sharp crash.
A single number for depth and duration combined is the Ulcer Index of Martin and McCann (1989): the square root of the mean of the squared drawdowns. Long, deep periods underwater push it up, short dips barely move it.
Ulcer Index = √(mean of the squared drawdowns in %)For advanced readers: how deep will the next drawdown be?
The maximum drawdown depends on the length of the period: the longer you observe, the deeper it turns out on average. Magdon-Ismail et al. (2004) derived its distribution for a Brownian motion, the simplest model for prices. With positive drift, the expected maximum drawdown grows only slowly (logarithmically) with time; without drift, it grows with the square root of time, and with negative drift, linearly. More important than the formulas is the insight:
“the largest drop from a peak to a trough”This definition sounds trivial, but the value is an extreme statistic of a single price history. A ten-year backtest without a major crisis can show a maximum drawdown of 15%, even though the same strategy would have lost 40% in a different decade. Monte Carlo simulations and long series give a better picture than a single number; see Monte Carlo simulation.
Chekhlov et al. (2005) generalise the maximum drawdown to the conditional drawdown at risk: the average of the worst drawdowns. It contains the maximum drawdown and the average drawdown as limiting cases and can be used as a constraint in portfolio optimisation, similar to the conditional VaR for individual periods.
Actively limiting drawdowns
Grossman and Zhou (1993) showed how an investor must invest who never wants to lose more than a fixed share of their previous peak: the amount in risky assets is proportional to the cushion between wealth and the floor. If the portfolio falls, the cushion shrinks, and with it the equity allocation.
Drawdown with a savings plan and with withdrawals
The maximum drawdown describes an amount invested once. If money keeps flowing in or out, your portfolio experiences the decline quite differently. If you keep saving regularly during a crash, you buy at low prices and are back in profit sooner than the index.
The reverse applies in the withdrawal phase: if you sell regularly during a crisis to live on the money, you sell many units at low prices. These units are missing in the recovery. That is why the same drawdown can make a withdrawal plan fail if it comes at the beginning, and barely matter if it comes late. How to deal with this (a buffer in bonds or cash, flexible withdrawals) is described in the articles Sequence risk and Withdrawal rate.
How much drawdown can you bear?
Before choosing a portfolio, an honest calculation is worthwhile: which loss could you cope with financially, and which emotionally? Financially, what matters is when you need the money. If you want to buy a flat in three years, you can hardly afford a 40% decline without enough time to recover. Emotionally, what matters is whether you would sell during a crash. A portfolio with a slightly lower expected return that you hold through a crisis is better than a riskier one that you sell at the bottom.
- Take the maximum drawdown of a long backtest as the lower bound, not the upper bound, of the possible loss.
- Convert the percentage into euros: −45% of €200,000 is €90,000. That is a different number in your head from “−45%”.
- Check the duration: could you stand five years underwater without changing your strategy?
Putting drawdown into perspective
- A one-off event: the maximum drawdown depends on a single crisis in the test period. A short backtest without a crisis underestimates it.
- Monthly instead of daily data smooth the trough; with daily values it usually turns out deeper.
- With withdrawals, a drawdown becomes more severe, because you sell units cheaply during the crisis. This is sequence risk.
- Relation to return: the Calmar ratio relates CAGR to maximum drawdown; further measures such as the Ulcer Index and the Pain Index are covered under risk metrics.
- Currency: a drawdown in dollars is not the same as in euros. For euro investors, the path in euros is what counts.
As a rough guide: broad stock markets fell by 30 to over 50% in the major crises, and mixed portfolios by much less. When choosing your equity allocation, ask yourself whether you would sit out a decline of this size, and check that beforehand rather than in the middle of the crisis.
How Portfolio Lab calculates
Portfolio Lab builds a value path from the period returns (start = 1) and tracks the highest value reached so far; the starting value counts as the first peak. The drawdown is value divided by peak minus 1, and the maximum drawdown is its minimum. The Backtest shows the path as an underwater chart, together with a table of the ten largest declines with peak, trough, recovery and duration. With monthly data, it counts whole calendar months; with daily data, days divided by 30.44; a decline that has not yet recovered is shown as “not yet”. The Calmar ratio is the CAGR divided by the absolute value of the maximum drawdown over the whole period. More in the metrics methodology.
Frequently asked questions
What is a normal drawdown for equities?
Broad stock markets fell by 30 to over 50% in the major crises. A portfolio of 60% equities and 40% bonds usually fell much less, but not always: in 2022 both fell at the same time.
Is a drawdown a real loss?
Only if you sell. As long as you stay invested, it is a paper loss that can recover. But that is not guaranteed.
How is drawdown related to volatility?
Higher volatility usually leads to deeper drawdowns, but not necessarily. Abrupt crashes can also hit investments with low volatility.
How long does it take to recover after a crash?
That varies a lot: a few months after short crashes, several years after major crises. A savings plan shortens the time until you are back in profit, because you buy more at low prices.
What does an underwater chart show?
The drawdown over time: a line at 0% as long as the portfolio is at a new high, and a trough for every phase below it. The width and depth of the troughs show duration and extent.
Can drawdowns be avoided?
Only partly, and never for free. Bonds, gold or trend following can cushion crashes, but they cost return in good years. Rules that sell when prices fall protect against long bear markets, but often miss the fast recovery that follows.
Literature
- Chekhlov, Alexei; Uryasev, Stanislav; Zabarankin, Michael (2005): Drawdown Measure in Portfolio Optimization. International Journal of Theoretical and Applied Finance 08 (01), pp. 13–58. doi:10.1142/s0219024905002767
- Grossman, Sanford J.; Zhou, Zhongquan (1993): Optimal Investment Strategies for Controlling Drawdowns. Mathematical Finance 3 (3), pp. 241–276. doi:10.1111/j.1467-9965.1993.tb00044.x
- Kahneman, Daniel; Tversky, Amos (1979): Prospect Theory: An Analysis of Decision under Risk. Econometrica 47 (2). doi:10.2307/1914185
- Magdon-Ismail, Malik; Atiya, Amir F.; Pratap, Amrit; Abu-Mostafa, Yaser S. (2004): On the maximum drawdown of a Brownian motion. Journal of Applied Probability 41 (1), pp. 147–161. doi:10.1239/jap/1077134674
- Martin, Peter G.; McCann, Byron B. (1989): The Investor's Guide to Fidelity Funds. Wiley.
This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.