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Sharpe Ratio

Properties2
descriptionA measure of risk-adjusted return — excess return per unit of volatility — and how it is annualized from daily returns.
tagstrading, finance, quant

2 min read

Sharpe Ratio

Definition

The Sharpe ratio (William F. Sharpe) compares an investment’s return to its risk, expressing the insight that excess returns may reflect volatility rather than skill. It is the portfolio’s excess return over the risk-free rate divided by the standard deviation of that excess return:

Sharpe = (Rp − Rf) / σ(excess return)

where Rp is portfolio return, Rf the risk-free rate, and σ the standard deviation of excess returns. A higher Sharpe means better risk-adjusted performance.

Core Ideas

Annualizing from daily returns

To annualize a Sharpe ratio computed from daily returns:

Sharpe(annual) = √252 × AVG(excess return) / STDEV(excess return)
  • √252 scales daily figures to a year (252 trading days). Use √52 for weekly returns.
  • AVG(excess return) is the mean daily return above the risk-free rate.
  • STDEV(excess return) is the volatility of those daily excess returns.

Unlike the Kelly Criterion, the Sharpe ratio is time-scale dependent — you must annualize consistently to compare.

Relationship to Kelly and volatility

Because μ = Sharpe × σ, Kelly leverage f* = μ/σ² reduces to Sharpe / Volatility. The single-strategy maximum compounded growth rate is g = r + S²/2, tying Sharpe directly to achievable long-term growth.

Use as a screen

In Quantitative Trading, the Sharpe ratio is a first-pass filter: a candidate strategy must clear a minimum Sharpe (alongside acceptable drawdown) before deeper backtesting.

Relationships

Graph View

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