First, calculate the numerator of the Sortino ratio,
the average period return minus the target return:
Average Annual Return - Target Return:
(17% + 15% + 23% - 5% + 12% + 9% + 13% - 4%)
÷ 8 – 0% = 10%
Next, calculate the Target Downside Deviation:
1. For each data point, calculate the difference
between that data point and the target level. For
data points above the target level, set the difference
to 0%. The result of this step is the underperformance
data set.
17% - 0% = 0%
15% - 0% = 0%
23% - 0% = 0%
-5% - 0% = -5%
12% - 0% = 0%
9% - 0% = 0%
13% - 0% = 0%
-4% - 0% = -4%
2. Next, calculate the square of each value in
the underperformance data set determined in
the first step. Note that percentages need to be
expressed as decimal values before squaring, i.e.
5% = 0.05.
0%^2= 0%
0%^2 = 0%
0%^2 = 0%
-5%^2 = 0.25%
0%^2 = 0%
0%^2 = 0%
0%^2 = 0%
-4%^2 = 0.16%
3. Then, calculate the average of all squared
differences determined in Step 2. Notice that
we do not “throw away” the 0% values.
Average: (0% + 0% + 0% + 0.25% +
0% + 0% + 0% + 0.16%) ÷ 8 = 0.0513%