4.4 Lower Partial Standard Deviation

The Lower Partial Standard Deviation (LPSD) is another measure of downside risk. It is computed in the same way as the standard deviation except that we consider only negative deviations from the mean (or any other benchmark). If you have a sample where  observations are below the mean value, you can compute the LPSD as follows:

for

$X_i<\mu$

Notice that the mean value, [latex]\mu[/latex], is computed using Equation (4). In other words, you need to use your entire sample of [latex]n[/latex] observations to compute the mean value but consider only negative deviations from the mean in computing the LPSD.