In 1952, Harry Markowitz wrote his now famous statement asserting that investors should be just as concerned with risk as they are with returns. Markowitz theorized that risk can be estimated with a measure of the past variance of returns from the average return over a time period. This measure, the standard deviation, possesses a noteworthy property. Given a large sample from a normal distribution, approximately two-thirds of the data lies within one standard deviation of the mean. So, if an investment had a very long average annual return of 10% and a standard deviation of 15%, then investors should expect to earn about 10% per year, plus or minus 15%, or an approximate range of -5% (10% minus 15%) to +25% (10% plus 15%) two-thirds of the future years. To expand the range of variance from the average to include 95% of the data or outcomes, the standard deviation must be doubled as shown in the Standard Deviation illustration above. So, the range of outcomes for two standard deviations would be 10% plus or minus 30% or from -20% to +40% for 95% of the outcomes. Three standard deviations include 99% of the outcomes, or 10% plus or minus 45%, which would mean returns should range from -35% to +55% about 99% of the outcomes.
The bell-shaped curve in the diagram shows the distribution of historical outcomes. The black center line on the bell is the mean or average. One standard deviation away from the mean in either direction (green) accounts for about two-thirds of all outcomes; two standard deviations from the mean (green and blue) accounts for about 95% of outcomes; three standard deviations from the mean accounts for about 99% of outcomes.
Prudent investing can only be accomplished when investors estimate the uncertainty of expected returns. This “uncertainty” estimate is based on the standard deviation of long-term past returns. If investors do not understand standard deviation, they cannot claim a prudent analysis has been completed. On the other hand, by operating with a picture of the long-term historical outcomes as set forth in a bell-shaped curve, investors are empowered to invest with a clearer picture of expected risk and return.
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