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

A) 0.0618

Step-by-step explanation:

Variance is given by:

`V = (\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 = (0.28+0.21+0.01-0.36)/(4) \\\mu = 0.035`

The variance is:

`V = (\sum(Xi - \mu)^2)/(n)\\V = ((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.