Question

An investment earned the following returns over a four-year period: 28 percent, 21 percent, 1 percent, and -36 percent. What is the variance of the returns on this investment?A) 0.0618B) 0.0824C) 0.1400D) 0.1739E) 0.2473

Answer 1

Answer:

A) 0.0618

Explanation:

Variance is given by:

$V = \frac{\sum(Xi - \mu)^2}{n}$

Where 'Xi' is the value for each term 'i' in the sample of size 'n' and μ is the sample mean.

The mean investment return is:

$\mu = \frac{0.28+0.21+0.01-0.36}{4} \\\mu = 0.035$

The variance is:

$V = \frac{\sum(Xi - \mu)^2}{n}\\V = \frac{(0.28- 0.035)^2+(0.21- 0.035)^2+(0.01- 0.035)^2+(-0.36- 0.035)^2}{4}\\V= 0.0618$

The variance of the returns on this investment is A) 0.0618.