Drawdowns and position sizing

Definition

Track the running peak of equity, $M_t = \max_{s \le t} E_s$. The drawdown at time $t$ is

$$D_t = \frac{M_t - E_t}{M_t}$$

and the maximum drawdown is the largest $D_t$ over the sample. The drawdown duration is how long equity spends below a prior peak.

The asymmetry of losses

After losing a fraction $d$, you need a gain of

$$\frac{1}{1 - d} - 1$$

to get back to even. A 10% loss needs 11%; a 25% loss needs 33%; a 50% loss needs 100%; a 90% loss needs 900%. Deep drawdowns are not just painful, they are mathematically expensive. Explore it in the drawdown calculator.

How long does recovery take?

If a strategy compounds at $g$ per year, recovering from drawdown $d$ takes about

$$T \approx \frac{-\ln(1 - d)}{g}$$

years. At $g = 15\%$, a 30% drawdown costs roughly 2.4 years of compounding just to stand still.

Expected maximum drawdown

For a strategy with annualised Sharpe $SR$ and volatility $\sigma$, max drawdown grows with the length of the sample, and is larger the lower the Sharpe. Simulating ten years of a 20%-vol strategy, the median maximum drawdown is about $1.5\sigma$ (30%) at Sharpe 1 and about $2\sigma$ (40%) at Sharpe 0.5 — and one path in four does noticeably worse. A 40% drawdown in a Sharpe-0.5 strategy is the expected outcome, not proof the strategy is broken.

Sizing per trade

The most common practical rule: risk a fixed fraction of equity on each trade, measured from entry to stop.

$$\text{position size} = \frac{\text{equity} \times \text{risk fraction}}{|\text{entry} - \text{stop}|}$$

With 1% risk per trade, ten consecutive losers cost about 9.6% (compounded), not 10%, and you are still in the game. With 10% risk, the same streak costs 65%.

Volatility-scaled sizing

Using ATR (average true range) as the stop distance — a stop at, say, $2 \times \text{ATR}$ — makes position size inversely proportional to volatility. Each trade then carries a similar amount of risk regardless of the regime. This is what many vault specs mean by “ATR position sizing”.