3rd letter to friends of Brunei (Standard Deviation)

In investment planning, the actual return can exceed or less than expected return (or average return). Such variability is known as risk. One of the most important measurements of risk is “standard deviation” (or σ).

The formula for σ is √ [sum of (actual return – average return) 2 / (number of data – 1)]

Let me illustrate using the following data:

Year 1, 2, 3, 4, 5

Return 40%, 25%, -20%, -30%, 30%

The average return of above data is = [0.4+ 0.25 + - 0.2 + - 0.3 + 0.3] / 5 = 0.09 (or 9%)

The sum of (actual return – average return) 2 is

(0.4 – 0.09)2 + (0.25 – 0.09)2 + (-0.2 – 0.09)2 + (-0.3 – 0.09)2 + (0.3 – 0.09)2 = 0.402

Number of data – 1 = 5 -1 = 4

Therefore, σ = √ [0.402 / 4] = 0.31 (or 31%)