Sortino Ratio

The Sortino ratio is a performance measure that relates the return of an investment to the risk of falling short of a chosen target. It divides the average return in excess of the target by the downside deviation, a measure of variability that counts only the periods in which the return was below the target. A higher ratio indicates more return for each unit of harmful volatility.

The ratio is a modification of the Sharpe ratio, which treats all volatility as risk, whether returns are above or below average. It is named after Frank Sortino, who developed and promoted downside-risk measures from the 1980s. The Sortino ratio is widely used to assess hedge funds, trading strategies and other investments whose returns are not symmetric.

The standard calculation is:

where the downside deviation is:

• $R_p$ is the average return of the portfolio over the measurement period.
• $T$ is the target or minimum acceptable return. Common choices are zero, the risk-free rate or a return the investor is required to earn.
• $r_i$ is the return in period $i$, and $n$ is the total number of periods.
• $\min(0, \; r_i - T)$ is the shortfall below the target in that period, or zero if the target was met.

The sum is divided by the total number of periods, not by the number of losing periods. Dividing by the losing periods alone is a common error that overstates the downside deviation of strategies with few losses.

Suppose a strategy has six monthly returns of 3, -2, 4, -1, 2 and 0 percent, and the target is zero. The average return is $6 / 6 = 1$ percent. Only two months fall below the target, with shortfalls of -2 and -1. Their squares sum to $4 + 1 = 5$. Dividing by 6 gives 0.833, and the square root is 0.913 percent. The monthly Sortino ratio is $1 / 0.913 = 1.10$.

For comparison, the ordinary standard deviation of the six returns is 2.37 percent, so the monthly Sharpe ratio with a zero risk-free rate is $1 / 2.37 = 0.42$. The Sortino figure is much higher because the two largest moves, the gains of 3 and 4 percent, add to the standard deviation but not to the downside deviation. A monthly ratio is usually annualized by multiplying by the square root of 12, which here gives about 3.8.

The Sharpe ratio is a complete summary only if returns follow a normal distribution, in which gains and losses are mirror images. Many investments are not like that. A strategy with positive skewness, such as trend following, has occasional large gains that raise its standard deviation and so lower its Sharpe ratio, although investors do not regard large gains as a hazard. The Sortino ratio does not penalize it for them.

The idea has a long history. Harry Markowitz, the originator of modern portfolio theory, discussed semi-variance as an alternative to variance in the 1950s, but variance was easier to compute and became standard. Downside measures also fit the findings of behavioral research that investors feel losses more keenly than equal gains.

The ratio is used to rank funds or strategies as a form of risk-adjusted return, and it is most informative when set beside the Sharpe ratio. A Sortino ratio well above the Sharpe ratio signals that much of the volatility is on the upside. Similar figures signal roughly symmetric returns. There is no universal threshold for a good value, since the result depends on the target, the data frequency and the period covered, and comparisons are valid only when these match.

Analysts typically read the ratio alongside the maximum drawdown, which shows the worst peak-to-trough loss actually suffered, and related measures such as the ratio of return to drawdown.

• Few observations. Downside deviation is estimated from the losing periods only, so it rests on less data than a standard deviation and is less reliable for short track records.
• Hidden tail risk. A strategy that collects small, steady gains and has not yet met its rare large loss, as in selling volatility, can show a very high Sortino ratio until the loss arrives.
• Sensitivity to the target. Changing the target return changes both the numerator and the denominator, and can reorder a ranking.
• Inconsistent definitions. Data providers differ on the target, on the divisor and on annualization, so published figures are not always comparable.
• Leverage and costs. Like other ratios, it says nothing about the capacity of a strategy or the financing needed to reach a desired return.

The ratio also shares the general weakness of statistics drawn from history: it describes the period measured, and a change in market conditions can alter the volatility and the shape of returns.