Sortino ratio

Sortino ratio is a risk-adjusted return measure that evaluates the return of an investment relative to its downside risk. Unlike the Sharpe ratio, which uses total volatility, the Sortino ratio focuses on returns below a specified target or minimum acceptable return.

Calculation

The Sortino ratio is commonly calculated as:

$Sortino Ratio = \frac{R_{p} - R_{t}}{σ_{d}}$

where:

$R_{p}$ = portfolio or investment return;
$R_{t}$ = target or minimum acceptable return;
$σ_{d}$ = downside deviation.

Downside deviation

Downside deviation measures the dispersion of returns that fall below the target return.

A simplified calculation is:

$σ_{d} = \sqrt{\frac{1}{n} \sum_{t = 1}^{n} min (R_{t} - R_{p, t}, 0)^{2}}$

where:

$R_{p, t}$ = portfolio return during period $t$ ;
$R_{t}$ = target or minimum acceptable return;
$n$ = number of observations.

An equivalent formulation using the negative part operator is:

$σ_{d} = \sqrt{\frac{1}{n} \sum_{t = 1}^{n} {[min (0, R_{p, t} - R_{t})]}^{2}}$

Example

Suppose an investment has a return of 12% and the target return is 4%. If its annualized downside deviation is 8%:

$Sortino Ratio = \frac{12 % - 4 %}{8 %} = 1$

The Sortino ratio is therefore 1.

Interpretation

A higher Sortino ratio generally indicates that an investment generated greater return relative to the downside risk undertaken.

A lower Sortino ratio indicates less return relative to downside risk.

A negative Sortino ratio indicates that the investment's return was below the specified target or minimum acceptable return.

The interpretation depends on the selected target return, measurement period, and methodology used to calculate downside deviation.

Sortino ratio and Sharpe ratio

The Sharpe ratio uses total volatility as its measure of risk:

$Sharpe Ratio = \frac{R_{p} - R_{f}}{σ (R_{p})}$

The Sortino ratio instead uses downside deviation:

$Sortino Ratio = \frac{R_{p} - R_{t}}{σ_{d}}$

where:

$R_{f}$ = risk-free rate;
$R_{t}$ = target or minimum acceptable return;
$σ (R_{p})$ = standard deviation of portfolio returns;
$σ_{d}$ = downside deviation.

The key distinction is that the Sharpe ratio treats both positive and negative deviations from the average return as volatility, whereas the Sortino ratio focuses on unfavorable deviations below the target return.

Target return

The target return, also called the minimum acceptable return (MAR), is the return below which investment performance is considered undesirable for the purpose of the calculation.

The target can be:

the risk-free rate;
an investor-defined minimum return;
an inflation-adjusted return;
a benchmark-related target;
another specified performance threshold.

The choice of target can materially affect the resulting Sortino ratio.

Portfolio management

The Sortino ratio can be used in portfolio management to compare investments according to their returns relative to downside risk.

It can be considered alongside:

Limitations

The Sortino ratio has several limitations, including:

sensitivity to the selected target return;
sensitivity to the measurement period;
dependence on the calculation methodology for downside deviation;
reliance on historical return data;
potential instability when observations of downside returns are limited.

Different calculation conventions can therefore produce different Sortino ratios for the same investment.

Importance

The Sortino ratio provides a risk-adjusted measure that distinguishes between harmful downside volatility and potentially favorable upside volatility. It is particularly useful when investors are primarily concerned with returns falling below a defined target rather than with variability in both directions.

Calculation

Downside deviation

Example

Interpretation

Sortino ratio and Sharpe ratio

Target return

Portfolio management

Limitations

Importance

See also