What Is the Connection between Expected Return and Standard Deviation?

Expected return and standard deviation are connected in the world of finance because a high standard deviation will lessen the likelihood of the investor actually receiving the expected return. The expected return is measured as an average of returns over a period of years. By contrast, the standard deviation shows the extent to which the returns differed from the expected return over that same period of time. Investors must be aware of expected return and standard deviation when deciding upon their security selections, since they have to choose whether or not to pursue high returns if the risk attached to those returns is correspondingly high.

Using the term expected return in the stock market is a bit of a misnomer, since the prices of stocks are fickle at best and downright unpredictable at worst. Certain investors might be looking for consistency over a period of time. Others might wish to go for the big returns at the expense of exposing themselves to a particularly volatile stock. Tolerance for risk is crucial to how investors view the connection between expected return and standard deviation.

It is important to understand what is meant by expected return and standard deviation before their relationship can be explored. The expected return of a stock is what the return should be based on its returns from past years. By contrast, standard deviation is a measurement of how much that stock has strayed from the expected return over time. As the standard deviation rises, so too does the possibility that the stock will not match the expected return.

To show how expected return and standard deviation are linked, consider the example of two stocks that each have been in existence for three years and each have an expected return of 15 percent. Stock A returned 14 percent, 15 percent, and 16 percent in the three years, while Stock B returned 10 percent, 15 percent, and 20 percent in the same three years. While the average return for both was 15 percent, Stock B deviated from that return much more than Stock A did.

From that example, it can be said that Stock B is much less likely to meet its expected return based on the previous performance. If an investor wants an expected return that will hew closely to 15 percent with little risk, he should choose Stock A. By contrast, an investor with a higher tolerance for risk might wish to choose Stock A and hope that the timing is right for a big deviation in a positive direction. How much risk an investor wishes to incur is the ultimate determiner in how he or she views the relative importance of expected return and standard deviation.