How does one go about calculating the downside deviation? Their solution seems to make no sense, because somewhere in the text they mention that the calculation of the downside deviation involves using negative returns (basically you have a loss of about half your data), yet they divide by 12-1, indicating that the sample size includes all the returns (both positive and negative).

Also they don’t provide hurdle rate in the problem, yet the solution for the sortino ratio assumes that the hurdle is 5%.

>Their solution seems to make no sense, because somewhere in the text they mention that the calculation of the downside deviation involves using negative returns (basically you have a loss of about half your data), yet they divide by 12-1, indicating that the sample size includes all the returns (both positive and negative).

The sample does include all returns, but when the returns are above the hurdle rate they equal zero for the computation. See the chart on page 84, specifically the (HF Return - Hurdle Rate)^2 column.