Figure 1



The most common risk measure is standard deviation — a statistic measurement of volatility that tells you how tightly the various annual returns are clustered around the average. When the annual returns are tightly bunched together the standard deviation is small and the bell-shaped curve is narrow. When the annual returns are spread apart and the bell curve is relatively flat, it tells you that you have a relatively large standard deviation.

The combination of the average and the standard deviation characterize various bell curve shapes, and those shapes represent the risk and return of the Index Portfolio. Figure 2 shows you graphically what a standard deviation represents.

Figure 2



One standard deviation away from the average in either direction on the horizontal axis (the green area on the graph) accounts for somewhere around 68 percent of the annual returns in the time period. Two standard deviations away from the mean (the green and blue areas) account for roughly 95 percent of the annual returns. And three standard deviations (the green, blue and red areas) account for about 99 percent of the annual returns.

Standard Error
Standard Error

The standard error of the mean indicates the degree of uncertainty in calculating an estimate from a sample, like a series of returns data. A standard error can be calculated from the standard deviation by dividing the standard deviation by a square root of the sample size. So with only 3 years of returns data on the S&P 500, the error in the average return is 2.6 times larger than having 20 years of data.

Risk and Return Tables

Figure 3


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Figure 7

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