Cost-Adjusted Sharpe Ratio

The Sharpe ratio is the standard yardstick for risk-adjusted return, and it's almost always first computed on a strategy's gross returns — the returns from trading at the mid-price with no friction. That number describes a strategy that doesn't exist. The cost-adjusted Sharpe ratio recomputes the same formula using net-of-cost returns instead, and because costs subtract from return without reducing volatility (in fact costs can sometimes add volatility through slippage variance), the cost-adjusted Sharpe is essentially always lower than the gross Sharpe — sometimes dramatically so.

The formula, and where cost enters it

The Sharpe ratio is:

$$S = \frac{\bar{r} - r_f}{\sigma_r} ,$$

where $\bar{r}$ is average return, $r_f$ is the risk-free rate, and $\sigma_r$ is the standard deviation of returns. In plain English: how much excess return the strategy earns per unit of volatility it takes on. The cost-adjusted version simply replaces $\bar{r}$ with the net-of-cost average return $\bar{r}_{net} = \bar{r} - \bar{c}$, where $\bar{c}$ is average cost per period:

$$S_{net} = \frac{\bar{r} - \bar{c} - r_f}{\sigma_{r,net}} .$$

In plain English: subtract realistic trading costs from the numerator before dividing by volatility — since costs are a near-certain drag rather than a source of upside variance, this pulls the ratio down without a corresponding benefit to the denominator, and for a high-turnover strategy that drag can be the majority of the gross Sharpe.

Why turnover determines how much the ratio falls

A low-turnover strategy pays costs rarely, so $\bar{c}$ is small relative to $\bar{r}$, and $S_{net}$ stays close to the gross Sharpe. A high-turnover strategy pays costs on every rebalance, so even a modest per-trade cost accumulates into a large $\bar{c}$, and $S_{net}$ can fall far below gross — sometimes to near zero or negative even when the gross Sharpe looked excellent. This is exactly why comparing two strategies on gross Sharpe alone can rank them backwards: a lower-turnover strategy with a modest gross Sharpe can have a higher cost-adjusted Sharpe than a high-turnover strategy with an impressive-looking gross number.

Worked example: two strategies, reversed ranking

Strategy A: gross Sharpe 2.5, average annual return 20%, volatility 8%, turnover produces average annual cost drag of 12%. Net average return: $20\% - 12\% = 8\%$. Assuming volatility is roughly unchanged, $S_{net,A} \approx \frac{8\%}{8\%} = 1.0$.

Strategy B: gross Sharpe 1.5, average annual return 12%, volatility 8%, lower turnover producing cost drag of only 2%. Net average return: $12\% - 2\% = 10\%$. $S_{net,B} \approx \frac{10\%}{8\%} = 1.25$.

Gross Sharpe ranks A above B (2.5 vs 1.5). Cost-adjusted Sharpe ranks B above A (1.25 vs 1.0). The strategy that looked far superior on paper is actually the worse choice once realistic trading costs are applied, purely because its higher turnover eats a much larger share of its gross edge.

What this means in practice

Any strategy comparison, allocation decision, or capital commitment should be made on cost-adjusted Sharpe, not gross. Reporting only the gross number — a depressingly common practice in strategy pitches — flatters exactly the strategies that should be scrutinized hardest: high-turnover, thin-edge approaches whose real risk-adjusted performance depends almost entirely on cost assumptions that are easy to understate.