Glossary

Sharpe Ratio — Definition, Formula, and Why It Can Mislead

The Sharpe ratio is excess return per unit of total volatility. Definition, formula, worked example, and the lookback-window sensitivity that makes it gameable.

By NakedPnL Research·May 7, 2026·4 min read

TL;DR

Sharpe ratio is mean excess return divided by the standard deviation of those excess returns.
It is highly sensitive to the choice of lookback window and to non-normal return distributions.
NakedPnL deliberately does not display Sharpe on profile pages because a visible Sharpe number on a public registry can be optimised against rather than honestly reported.

Definition

The Sharpe ratio, introduced by William F. Sharpe in 1966, is the ratio of a portfolio's mean excess return over the risk-free rate to the standard deviation of those excess returns. It is the most widely cited risk-adjusted-return metric in finance and is intended to capture how much extra return an investor earns per unit of total volatility taken.

Formula

S = (mean(R_p - R_f)) / stdev(R_p - R_f)

where:
  R_p = periodic portfolio return
  R_f = periodic risk-free rate over the same period

Annualisation:
  S_annual = S_periodic * sqrt(periods_per_year)

For daily returns, periods_per_year is conventionally 252 (trading days) or 365 (calendar days for crypto).

Worked example

A trader records daily excess returns over one calendar year with a mean of 0.08% per day and a standard deviation of 1.2% per day. The daily Sharpe is 0.08 / 1.2 = 0.0667. Annualised at 365 trading days for a 24/7 crypto venue, S_annual = 0.0667 × √365 ≈ 1.27. Run the same calculation against a different one-year window — say six months earlier — and the figure can shift by 40 percentage points purely because the volatility denominator is dominated by a handful of outlier days.

Why NakedPnL doesn't display this on profile pages

Sharpe ratio is famously sensitive to the choice of lookback window. Goetzmann, Ingersoll, Spiegel, and Welch documented in their 2007 paper Portfolio Performance Manipulation and Manipulation-Proof Performance Measures that a manager with no skill can engineer a higher reported Sharpe simply by truncating the window or by writing systematic short volatility (selling out-of-the-money options or running negatively-skewed trades) so the visible distribution looks tight until the rare large loss arrives. A Sharpe number prominently displayed on a public registry is precisely the kind of single-figure target that invites this optimisation. NakedPnL therefore restricts public profile metrics to TWR, total PnL, and trade count — figures that are harder to game on an append-only chain. Sharpe and other risk-adjusted measures remain available to allocators who pull the underlying daily-return series via the API and choose their own window deliberately.

Sortino ratio — replaces total volatility with downside deviation
Calmar ratio — replaces volatility with maximum drawdown
Information ratio — Sharpe relative to a benchmark
Volatility (standard deviation of returns)

Frequently asked questions

What is a 'good' Sharpe ratio?

Conventional shorthand is that 1.0 is acceptable, 2.0 is very good, and 3.0 is excellent. These thresholds are folklore and depend on the asset class, the lookback window, and the risk-free rate convention used. They should not be treated as portable across strategies.

Why use standard deviation as the risk measure?

The original Sharpe formulation assumes returns are approximately normal, in which case standard deviation captures all of the relevant risk. Real return distributions are typically fat-tailed and negatively skewed, which is the main critique of Sharpe and the motivation for downside-only measures such as Sortino.

Can the Sharpe ratio be negative?

Yes. If the mean excess return is negative — i.e. the portfolio underperformed the risk-free rate — Sharpe is negative. A more negative Sharpe is, however, not strictly more informative, because the denominator is still scaled by volatility.

References