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:

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:

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.