From the February 2013 issue of Futures Magazine • Subscribe!

Sortino ratio: A better measure of risk

The Sortino ratio, S, is defined as:

 

where

  • R is the average period return;
  • T is the target or required rate of return for the investment strategy under consideration (originally T was known as the minimum acceptable return, or MAR. In his more recent work, MAR is now referred to as the Desired Target Return).
  • TDD is the target downside deviation.

The target downside deviation is defined as the root-mean-square, or RMS, of the deviations of the realized return’s underperformance from the target return where all returns above the target return are treated as underperformance of 0. Mathematically:

Target Downside Deviation = 

where

Xi = ith return
N = total number of returns
T = target return

The equation for TDD is very similar to the definition of standard deviation:

Standard Deviation = 

where

Xi = ith return
N = total number of returns
u = average of all Xi returns. 

The differences are:

  1. In the target downside deviation calculation, the deviations of Xi from the user selectable target return are measured, whereas in the Standard Deviation calculation, the deviations of Xi from the average of all Xi is measured.
  2. In the target downside deviation calculation, all Xi above the target return are set to zero, but these zeros still are included in the summation. The calculation for Standard Deviation has no Min() function.

Standard deviation is a measure of dispersion of data around its mean, both above and below. Target downside deviation is a measure of dispersion of data below some user-selectable target return with all above target returns treated as underperformance of zero. Big difference.

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