the approximate geometric average is thus 123 040401 2 1028 which is quite close to 665618
Geometric versus Arithmetic Average Returns: 1926–2006
|
Series |
Geometric Mean |
Arithmetic Mean |
Standard Deviation |
|
Large company stocks |
10.40% |
12.30% |
20.10% |
|
Small company stocks |
12.7 |
17.4 |
32.7 |
|
Long term corporate bonds |
5.9 |
6.2 |
8.5 |
|
Long term government bonds |
5.4 |
5.8 |
9.2 |
|
Intermediate term government bonds |
5.3 |
5.4 |
5.7 |
|
U.S. Treasury bills |
3.7 |
3.8 |
3.1 |
|
Inflation |
3 |
3.1 |
4.3 |
are expressed in decimals (as opposed to percentages), the geometric average return is approximately equal to the arithmetic average return minus half the variance. For example, looking at the large company stocks, the arithmetic average is .123 and the standard deviation is .201, implying that the variance is .040401. The approximate geometric average is thus .123 .040401/2 = .1028, which is quite close to the actual value.