How to Calculate Downside Deviation

Investors are constantly searching for a better way to measure and quantify risk. Subsequently, portfolio managers are often measured on their ability to generate returns in excess of the market (alpha). Standard deviation is a tool investment managers use to help quantify the risk or "deviation" from expected returns. Standard deviation measures the degree of variability (volatility) from the average return (mean). Higher deviation points to higher volatility. Similar to standard deviation, downside deviation looks at variation around an average return; however, it focuses only on those returns thatfall below the minimum acceptable return.


Step 1

Define MAR. This is a number of your choosing. It signifies the minimum amount of return you will accept on a particular investment. Let's use 5 percent for this example.

Step 2

Subtract MAR from the return for each period. If you are looking at annual returns over five years, subtract MAR (5 percent) from each return for each year. You will have five values.

Step 3

Reset the value to 0 if the return is positive. Let's say the first year return is 10 percent. Subtracting MAR, or 5 percent, from 10 percent equals 5 percent. This is a positive value, so change it to 0. If year two returns are 4 percent, then the difference is going to be -1 percent. Record this number; do not change it.


Step 4

Square the differences and add them together. The first year squared is 0; however, the second year squared is 1. Square all five years and take the sum of all squares.

Step 5

Divide by the periods and take the square root. In our example we have five years or five periods. Take the sum in Step 4 and divide by 5. Finally take the square root of this number. This is the downside deviation.


Sortino's ratio uses downside deviation for another measure of portfolio risk. The calculation is variation on Sharpe's ratio, which is more widely used.