Sortino ratio

Overview

The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside variance equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. As such, risk-adjusted returns normalize risks across programs.

Definition

The ratio

S

{\displaystyle S}

is calculated as

S =

R − T

D R

{\displaystyle S={\frac {R-T}{DR}}}

, where

R

{\displaystyle R}

is the asset or portfolio average annual total return,

T

{\displaystyle T}

is the target or required rate of return for the investment strategy under consideration (originally called the minimum acceptable return MAR), and

D R

{\displaystyle DR}

is the target semi-deviation (the square root of target semi-variance), termed downside deviation. An intuitive way to view downside risk is the annualized standard deviation of returns below the target. Another is the square root of the probability-weighted squared below-target returns. The squaring of the below-target returns has the effect of penalizing failures at a quadratic rate. This is consistent with observations made on the behavior of individual decision making under uncertainty.

D R =

∫

Usage

The Sortino ratio is used to score a portfolio's risk-adjusted returns relative to an investment target using downside risk. This is analogous to the Sharpe ratio, which scores risk-adjusted returns relative to the risk-free rate using standard deviation. When return distributions are near symmetrical and the target return is close to the distribution median, these two measures will produce similar results. As skewness increases and targets vary from the median, results can be expected to show dramatic differences. From the preceding it therefore follows that these metrics will not produce accurate results for the short term, such as asset-trading. Practitioners who use a lower partial Standard Deviation (LPSD) instead of a standard deviation also tend to use the Sortino ratio instead of the Sharpe ratio.

See also

Modern portfolio theory Omega ratio Post-modern portfolio theory Sharpe ratio Upside potential ratio