Chapter 3.2, Problem 26P

Expand Your knowledge: Moving Averages 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 had years, giving you a better overall return with less risk. To see what we mean, let's use a 3-year moving average on the Calvert. Social Balanced Fund (a sociallyresponsible fund).

Year	1	2	3	4	S	6	7	8	9	10	11
% Return	1.78	17.79	744	5.95	-4.74	25.85	9.03	18.92	17.49	6.80	-2.38

Source Fund Reports

(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 year 3 and the poor 2 years and average them. To compute a 3-year moving average for year 4, we take the data values for year 4 and the poor 2 years and average them. Verify that the following 3-year moving averages are correct.

Year	3	4	5	6	7	8	9	10	11
3-year moving average	9.01	10.40	2.89	9.02	10.05	17.93	15.15	14.40	7.30

(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) Interpretation 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 he studied in more detail in Chapter 6.