The geometric average annual return for a large capitalisation share portfolio is 12% for ten years and 5% per year for the next five years. The geometric average annual return for the entire 15-year period is
A)9.11%.
B)9.95%.
C)9.62%.
D)10.23%.

Question

Quizplus · Accepted Answer

The geometric average annual return over the entire period can be calculated using the formula for the geometric mean of the returns for each sub-period. This is done by multiplying the growth factors of each period together and then taking the nth root, where n is the total number of years. The growth factor for each period is 1 plus the annual return (expressed as a decimal). For the first 10 years, the growth factor is 1.12, and for the next 5 years, it is 1.05. The calculation is as follows:$$ \text{Geometric Average} = \left( (1.12)^{10} \times (1.05)^{5} \right)^{\frac{1}{15}} - 1 $$$$ \text{Geometric Average} = \left( 3.106 \times 1.276 \right)^{\frac{1}{15}} - 1 $$$$ \text{Geometric Average} = (3.963)^{\frac{1}{15}} - 1 $$$$ \text{Geometric Average} \approx 1.0962 - 1 $$$$ \text{Geometric Average} \approx 0.0962 $$$$ \text{Geometric Average} \approx 9.62\% $$

The Geometric Average Annual Return for a Large Capitalisation Share