Lower partial standard deviation and Sortino ratio

We discussed this concept already. However, for completeness, in this chapter we mention it again. One issue with using standard deviation of returns as a risk measure is that the positive deviation is also viewed as bad. The second issue is that the deviation is from the average instead of a fixed benchmark, such as a risk-free rate. To overcome these shortcomings, Sortino (1983) suggests the lower partial standard deviation, which is defined as the average of squared deviation from the risk-free rate conditional on negative excess returns, as shown in the following formula:

Because we need the risk-free rate in this equation, we could generate a Fama-French dataset that includes the risk-free rate as one of their time series. First, download their daily factors from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. Then, unzip it and delete the non-data part at the end of the text file. Assume the final text file...