| TABLE 1. The Impact of Volatility on Terminal Wealth | ||||||||
| Period Returns (%) | Arithmetic Average (%) |
Standard Deviation (%) |
Geometric Average (%) |
$1 Invested: Terminal Wealth ($) |
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| 1 | 2 | 3 | 4 | |||||
| Portfolio A | 10 | 10 | 10 | 10 | 10 | 0 | 10 | 1.464 |
| Portfolio B | 25 | -5.0 | 5 | 15 | 10 | 11.2 | 9.4 | 1.434 |
| Calculating the Averages: | ||||||||
| Portfolio A | ||||||||
| Arithmetic Average: [10.0 + 10.0 + 10.0 + 10.0] ÷ 4 = 10.0% | ||||||||
| Geometric Average*: [(1 + 0.10) x (1 + 0.10) x (1 + 0.10) x (1 + 0.10)]1/4 - 1.0 = 0.10 = 10.0% | ||||||||
| Terminal Wealth of $1: $1 x [(1 + 0.10) x (1 + 0.10) x (1 + 0.10) x (1 + 0.10)] = $1.464 | ||||||||
| Portfolio B | ||||||||
| Arithmetic Average: [25.0 + (-5.0) + 5.0 + 15.0] ÷ 4 = 10.0% | ||||||||
| Geometric Average*: [(1 + 0.25) x (1 - 0.05) x (1 + 0.05) x (1 + 0.15)]1/4 - 1.0 = 0.094 = 9.4% | ||||||||
| Terminal Wealth of $1: $1 x [1 + 0.25) x (1 - 0.05) x (1 + 0.05) x (1 + 0.15)] = $1.434 | ||||||||
| * The Geometric Average takes into consideration the compounding effect of the prior period return earning money over the next period. In the equation, ¼ represents the fourth root of the amount in brackets. The fourth root of a number is the amount which, when multiplied by itself four times, results in that number [for example, if N¼ = R, then R x R x R x R = N]. | ||||||||