# Geometric Mean Return Tips

CFA® exam: review / Geometric Mean Return

$R_G=\sqrt[T]{(1+R_1)\times(1+R_2)\times...\times(1+R_T)}-1$

## 3 things to remember when calculating geometric mean return

1. Remember to use the root (because we calculate a mean) and apply the right number of periods, e.g.:
• If we have 3 interest rates, we have to take the cube root (the one-third power).
• If we have 3 prices, we have to take the square root (because we have 2 rates of return: between Time 1 and Time 2 AND between Time 2 and Time 3).
2. Remember to subtract 1 after taking the root.
3. Remember that the number of shares doesn't matter.

### Geometric mean return – NO dividends, prices given

If a company doesn’t pay dividends and you have to compute the geometric mean return over multiple periods, just divide the last price by the first price and take the appropriate root. The prices between the first and last periods are not important at all. Have a look at this example:

Example:

You are given 4 prices of a stock from the first to the last one: P1, P2, P3, P4. When computing the geometric mean, prices P2 and P3 are not important because:

$(1+R_G)^3=\frac{P2}{P1}\times\frac{P3}{P2}\times\frac{P4}{P3}=\frac{P4}{P1}$

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