You do not need a lot of money to invest in a mutual fund. However, if you decide to put some money into an investment, you are usually advised to leave it in for (at least) several years. Why? Because good years tend to cancel out bad years, giving you a better overall return with less risk. To see what we mean, let€™s use a 3-year moving average for the Calvert Social Balanced Fund (a socially responsible fund).

(a) Use a calculator with mean and standard deviation keys to verify that the mean annual return for all 11 years is approximately 9.45%, with standard deviation 9.57%.
b) To compute a 3-year moving average for 1992, we take the data values for 1992 and the prior two years and average them. To compute a 3-year moving average for 1993, we take the data values for 1993 and the prior two years and average them. Verify that the following 3-year moving averages are correct:

(c) Use a calculator with mean and standard-deviation keys to verify that for the 3-year moving average, the mean is 10.68%, with sample standard deviation 4.53%.
(d) Compare the results of parts (a) and (c). Suppose we take the point of view that risk is measured by standard deviation. Is the risk (standard deviation) of the 3-year moving average considerably smaller? This is an example of a general phenomenon that will be studied in more detail in Chapter 7.

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Year % Return 1.78 17.79 746 5.95-4.74 25.85 9.03 18.92 1749 6.80-2.38 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 1992 1993 1994 1995 1996 1997 1998 1999 2000 Year 3-year moving average 9.01 10.40 2.89 9.02 10.05 17.93 15.15 14.40 7.30