Calculating the Geometric Average Return
Calculate the geometric average return for the large company stocks for the last four years in Table 1.1 , 2003–2006.
First, convert percentages to decimal returns, add one, and then calculate their product.
|
Year |
Large Company Stocks |
Product |
|
2003 |
28.68 |
1.2868 |
|
2004 |
10.88 |
X1.1088 |
|
2005 |
4.91 |
X1.0491 |
|
2006 |
15.79 |
X1.1579 |
|
1.7332 |
Notice that the number 1.7332 is what our investment is worth after five years if we started with a one dollar investment. The geometric average return is then calculated as Geometric average return = 1.73321/4 1 = .1474, or 14.74% Thus the geometric average return is about 14.74 percent in this example. In contrast, in Example 1.4, the average arithmetic return was calculated as 15.07 percent. Here is a tip: If you are using a financial calculator, you can put $1 in as the present value, $1.7332 as the future value, and 4 as the number of periods. Then, solve for the unknown rate. You should get the same answer we did.