Question

Compute the geometric mean for the following data on growth factors of an investment for 10 years.
1.10, 0.50, 0.70, 1.21, 1.25, 1.12, 1.16, 1.11, 1.13, 1.22
a. 1.0148
b. 1.1475
c. 1.0221
d. 1.0363

Answer 1

The geometric mean for the above set of data given is: 1.1475 (Option B). See the explanation below.

What is Geometric Mean?

The geometric mean can be defined as the average rate of return of a set of values obtained by multiplying the terms together.

Geometric mean is best suited for series with serial correlation, which is notably true for investment portfolios.

What is the computation justifying the above answer?

The formula for geometric mean is given as:

$\left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots x_{n}}}$

Hence,

The geometric Mean =

1.0147506490423

$\approx$ 1.1475


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