How to Size a Strategy From Backtest Results

Sizing a strategy means converting a backtested Sharpe ratio and drawdown into a position size that survives the estimation error in both figures.

Sizing a strategy from backtest results means converting a reported Sharpe ratio, volatility, and drawdown into an actual position size, and doing it in a way that accounts for the fact that every one of those backtested figures carries estimation error that a live strategy will not be forgiven for ignoring. A strategy sized as if its backtest were exact tends to be oversized the moment live volatility or correlation shifts even slightly from the historical sample.

The Kelly criterion gives the position size that maximizes long-run geometric growth, expressed as edge divided by odds for a simple bet, or as expected return divided by variance in the continuous case. Applied directly to a backtested strategy, full Kelly sizing routinely recommends a leverage level that would produce drawdowns exceeding 50 percent, because the formula assumes the input edge and variance are known exactly, and a backtested edge is an estimate, not a certainty. Kelly Criterion Position Sizing in Finance works through the full derivation and the assumptions behind it.

Because the true edge is uncertain, practitioners size to a fraction of full Kelly, commonly one quarter to one half, which sacrifices some long-run growth in exchange for a large reduction in the probability and severity of drawdowns caused by the edge being smaller in reality than the backtest suggested. Half Kelly sizing captures roughly three quarters of full Kelly's growth rate while cutting variance in half, which is why it is the more commonly cited starting point on trading desks.

A more common approach on multi-strategy desks sizes each strategy to a fixed annualized volatility target, such as 10 percent, rather than sizing directly from an edge estimate. This has the practical advantage of making strategies comparable and combinable regardless of how confident the researcher is in the underlying edge estimate, and it automatically reduces position size when a strategy's realized volatility rises, which happens to correlate with periods when backtested relationships are most likely to be breaking down. The position size under this approach is the target volatility divided by the strategy's trailing realized volatility, rescaled continuously as realized volatility…

Any sizing formula that takes a Sharpe ratio as an input should use a discounted figure, not the raw backtested number, because the backtested number was produced by a research process that, even without any bias, involved trying multiple variants before settling on the one reported. A common rule of thumb applies a haircut of one third to one half to a backtested Sharpe ratio before it is used for sizing, and a strategy whose net-of-cost Sharpe ratio, discussed in Transaction Cost Modelling Inside a Backtest, is already close to zero after this haircut should not be sized at all, regardless of how attractive its gross backtest looked.