Question

Over the past 4 years an investment returned 0.1 -0.12 -0.08 and 0.13, what is the standard deviation of returns?
a. 8.96 percent.
b. 16.05 percent.
c. 17.92 percent.
d. 18.09 percent.
e. 20.03 percent.

Answer 1

Answer:

The answer is below

Explanation:

Standard Deviation is a measure used to represent the volatility or risk in an instrument. The higher the SD, the higher will be the fluctuations in the returns and vice versa Given that:

the past 4 years an investment returned 0.1 -0.12 -0.08 and 0.13

$Arithmetic\ mean=\frac{\Sigma x_i}{n}= \frac{0.1+(-0.12)+(-0.08)+0.13}{4} =0.0075$

The standard deviation (σ) is:

$\sigma=\sqrt{ \frac{\Sigma(x_i-mean)2}{n-1} }=\sqrt{\frac{(0.1-0.0075)^2+(-0.12-0.0075)^2+(-0.08-0.0075)^2+(0.13-0.0075)^2}{3} } \\\\\sigma=12.58\%$