Series 65: 7.3.8 Standard Deviation, Range, And Correlation

Taken from our Series 65 Online Guide

7.3.8  Standard Deviation, Range, and Correlation

Investors use standard deviation (SD) to measure the variability of a security’s returns. For example, if a stock’s price fluctuates greatly over time, its returns will show a high standard deviation, meaning greater risk to the investor. Securities with high standard deviations tend to have higher expected returns (and yields), because the market requires compensation for greater risk.

A security with a higher standard deviation has a greater probability of high or low returns than a security with a lower standard deviation. Thus, a high standard deviation means more risk for the investor.

In the example that follows, even though Securities A and B have the same average return of 4.4%, Security A has a higher standard deviation than Security B. In fact, an investor can expect to see the returns on Security A varying on average by 10.8%, but the returns of Security B should vary less than 1%. This makes Security A a much riskier investment than Security B.

The range of a set of scores (e.g., returns) is the difference between the lowest score and the highest score. In the table, Security A’s returns vary from -10% to 20%, resulting in a range of 30. In contrast, security B’s returns range from 3% to 5%, with a range of only 2. Securities with lower ranges show less variability in their returns, which usually means lower risk.

Year 1

Year 2

Year 3

Year 4

Year 5

Average

SD

Security A

3%

7%

-10%

2%

20%

4.4%

10.8%

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