How to Calculate Downside Deviation

A high downside deviation represents a greater risk of bad returns.
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When you’re considering an investment, you might have a minimum percentage return in mind that you want it to earn each month or year. Calculating downside deviation can help you identify and steer clear of investments that are unlikely to meet these expectations. This risk measure, expressed as a percentage, reveals the extent to which an investment’s historical returns were lower than your minimum acceptable return, or MAR. A lower percentage suggests less risk of losing money. An investment with a high downside deviation has a habit of cranking out poor returns and might put a dent in your portfolio.

Step 1

Substitute an investment’s information for each of the past six months into the formula (E - B + D)/B, in which B and E represent the price at the beginning and end of each month and D represents the dividends or interest it paid during the month. For example, if a stock’s price was $10 and $11 at the beginning and end of last month, respectively, and it paid no dividends, last month’s formula is ($11 - $10)/$10.

Step 2

Calculate each formula to determine the investment’s monthly returns for each of the past six months. In this example, subtract $10 from $11 and divide by $10 to get 0.1, or a 10 percent return last month. Assume the other monthly returns in decimal form were -0.02, 0.03, 0.05, 0.02 and -0.04.

Step 3

Identify the monthly returns that were less than your MAR, which is the minimum monthly return you require in order to own the investment. In this example, assume you require a 1 percent, or 0.01, monthly MAR. The stock’s monthly returns of -0.02 and -0.04 were less than your MAR.

Step 4

Subtract each return you identified in Step 3 from your MAR. Square each result. In this example, subtract -0.02 from 0.01 to get 0.03. Square 0.03 to get 0.0009. Subtract and square the other result to get 0.0025.

Step 5

Add each squared result. Divide that result by the number of returns you calculated in Step 2. In this example add 0.0009 to 0.0025 to get 0.0034. Divide 0.0034 by 6 to get 0.000567.

Step 6

Calculate the square root of your result. Multiply that result by 100 to calculate the investment’s downside deviation as a percentage. Concluding the example, calculate the square root of 0.000567 to get 0.0238. Multiply 0.0238 by 100 to get a 2.38 percent downside deviation. This investment has a lower tendency of generating returns less than your 1 percent MAR than an investment with, say, a 9 percent downside deviation.

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