What is the Sharpe ratio?

The Sharpe ratio measures how much return an investment delivered for each unit of risk it took. It compares the return above the risk-free rate — the extra reward for investing at all — with the volatility needed to earn it. Two portfolios with the same return are not equally good if one got there with twice the swings; the Sharpe ratio shows the difference in a single number.

It was introduced by the economist William F. Sharpe in 1966 and is the most widely used measure of risk-adjusted return.

The formula

S = \frac{R_p - R_f}{\sigma_p}

where

$R_p$ is the annualized return of the portfolio,
$R_f$ is the risk-free rate over the same period, such as short-term government or money market rates,
$\sigma_p$ is the annualized volatility (standard deviation) of the portfolio's returns.

A simple illustration

	Portfolio A	Portfolio B
Annual return	9%	7%
Volatility	20%	10%
Risk-free rate	2%	2%

S_A = \frac{9\% - 2\%}{20\%} = 0.35 \qquad S_B = \frac{7\% - 2\%}{10\%} = 0.50

Portfolio A earned more, but B earned more per unit of risk. Scaled up to the same 20% volatility, B's trade-off between risk and return would have delivered 12% — three points more than A.

How to read it

Below zero: the portfolio earned less than the risk-free rate; the risk was not rewarded at all.
Around 0.3 to 0.5: typical of broad stock markets over long periods.
Above 1: excellent if sustained over many years. It is rare for long-only portfolios, and a reason to check whether the measurement period was short or unusually favourable.

The Sharpe ratio is most useful for comparing portfolios or funds over the same period, because the market environment affects all of them. A ratio of 1.5 over a single strong year says little.

Limits

Upside and downside count the same. A portfolio that occasionally jumps upward is penalized as if it had fallen. The Sortino ratio corrects for this.
Volatility is taken as the whole risk. Strategies with rare but severe losses, such as selling options, can show a high Sharpe ratio right up to the crash.
It depends on the risk-free rate. When interest rates change a lot, as they did in 2022, Sharpe ratios from different periods are not comparable.
Short periods mislead. Returns and volatility estimated from one or two years are noisy, and the ratio can change a lot from one year to the next.

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