Maximum Drawdown Calculation With Example

A maximum drawdown calculation identifies the worst decline an investment has suffered from its highest point to its lowest point afterward, expressed as a percentage loss. If a portfolio peaks at $100,000, then falls to $75,000 before recovering, the maximum drawdown is 25%. Calculating it requires scanning the entire return history to find the biggest peak-to-trough drop, then comparing it to other risk metrics like volatility or the Sharpe ratio to assess whether returns justify the pain.

Defining Maximum Drawdown

Maximum drawdown is the largest percentage drop a portfolio experiences from a peak value to a trough value at any later date. It answers: “What is the worst loss an investor who bought at the absolute worst time would have suffered?”

Formally:

$$\text{Max Drawdown} = \frac{\text{Trough Value} - \text{Peak Value}}{\text{Peak Value}} \times 100%$$

The result is negative. A maximum drawdown of −35% means that at some point, the portfolio fell 35% from its prior high.

This metric is psychologically important. While volatility captures the typical swing (standard deviation of returns), maximum drawdown captures the worst realistic swing. Investors often care more about the deepest pain they might endure than about abstract statistical measures.

Worked Example: Calculating Maximum Drawdown

Consider a portfolio with monthly ending values over 12 months:

Step 1: Track the running peak. As the portfolio rises, the peak updates. Once it falls, the peak stays put until a new high is set.

Step 2: At each date, calculate the drawdown from the peak: (Current Value − Peak) / Peak.

Step 3: Find the minimum (most negative) drawdown.

In this example:

• Month 3 is a new peak at $108,000.
• Months 4–6 fall, with Month 6 reaching the trough: $95,000.
• Drawdown at Month 6 = ($95,000 − $108,000) / $108,000 = −12.0%.
• Month 9 recovers above the prior peak to $110,000, establishing a new peak.
• Month 10–11 dip slightly (−3.6% and −5.5% from the $110,000 peak).
• Month 12 hits $112,000, a new all-time high.

Maximum drawdown = −12.0%, occurring at Month 6 (the trough from the Month 3 peak).

Key Insights from This Example

Recovery time: The portfolio took 3 months to recover from the trough ($95,000 in Month 6) back above the prior peak ($108,000), not reaching a new peak until Month 9. Investors who bought at the Month 3 peak and held until Month 9 experienced a −12% peak-to-trough loss and a 6-month drawdown duration.

Not the same as loss: The portfolio did not lose −12% over the year; it ended up 12% higher ($100k → $112k). But the maximum drawdown reveals the path was bumpy, and a worst-case buyer would have suffered real losses.

Subsequent peaks are irrelevant: Month 12’s peak at $112,000 does not change the maximum drawdown calculation; it is computed from past highs only.

Maximum Drawdown vs. Average Drawdown

Average drawdown is the arithmetic mean of all the declines (in our example, the average of the 6 months of negative drawdown %). It is more forgiving than maximum drawdown but less commonly used in practice.

Maximum drawdown is stricter: it focuses on the single worst episode. This makes it useful for portfolio managers and investors wanting to understand the worst-case scenario they might face.

Maximum Drawdown vs. Volatility

Volatility (standard deviation) describes typical swings around the mean return. A portfolio with 15% annual volatility might see 90% of monthly returns fall within ±1.3%. But volatility does not tell you about the absolute worst decline.

A portfolio could have low volatility (stable monthly returns) but still suffer a large maximum drawdown if the returns are consistently negative over a stretch. Conversely, a high-volatility portfolio with frequent large ups and downs might have a smaller maximum drawdown if the ups are large enough to erase the downs quickly.

Example: Two portfolios, both with 15% annual volatility:

• Portfolio A: steady gains of 1.2% per month → max drawdown near 0%.
• Portfolio B: alternating ±10% returns → max drawdown of ~10% (worst case: down 10% from a peak, then recovering).

Volatility alone does not differentiate them, but maximum drawdown does.

The Calmar Ratio

One way to use maximum drawdown is the Calmar ratio (or drawdown ratio):

$$\text{Calmar Ratio} = \frac{\text{Average Annual Return}}{\text{Maximum Drawdown (absolute value)}}$$

A portfolio with 12% annual return and −20% maximum drawdown has a Calmar ratio of 12/20 = 0.60. Higher ratios indicate better risk-adjusted returns; the portfolio earned more per unit of drawdown endured.

The Calmar ratio complements the Sharpe ratio, which divides return by volatility. Some strategies (e.g., long volatility, trend-following) may have high Sharpe ratios but poor Calmar ratios because they suffer occasional deep drawdowns. Conversely, a slow, steady strategy might have a lower Sharpe ratio but an excellent Calmar ratio.

Limitations and Practical Notes

Historical bias: Maximum drawdown is computed from past data. There is no guarantee a future drawdown will not exceed the historical maximum, especially for longer lookback windows.

Path dependence: Maximum drawdown only reports the size of the decline, not the speed. A 20% drawdown over 2 months is more psychologically taxing than a 20% drawdown spread over 12 months, but both show −20%.

Not forward-looking: Like all historical metrics, maximum drawdown describes what happened, not what will happen. A strategy that had a modest 10% maximum drawdown in a bull market may face a 40% drawdown in the next bear market.

Length of data: A 1-year maximum drawdown may not capture a once-in-a-decade crash. Longer histories reveal worse declines. Risk managers often examine drawdowns over 10–20 years or stress-test against historical extreme scenarios.

Sequence risk: Maximum drawdown captures one type of risk—the loss from peak to trough at any point. It does not address sequence risk (the order of returns) or tail risk (rare catastrophic events) directly.

See also