Question

Your investment has a 40% chance of earning a 15% rate of return, a 50% chance of earning a 10% rate of return, and a 10% chance of losing 3%. What is the standard deviation of this investment

Answer 1

Answer:

5.139%

Explanation:

P(Xi) = Probability of event Xi

E(X) = Expected value of X

The expected value of this investment is the weighted average of the possible returns:

$E(X) = 0.40*0.15+0.50*0.10+0.10*(-0.03)\\E(X) = 0.107$

The standard deviation of this investment is:

$S=\sqrt{\sum P(X_i)(X_i-E(X))^2}\\S=\sqrt{0.40*(0.15-0.107)^2+0.50*(0.10-0.107)^2+0.10*(-0.03-0.107)^2} \\S=0.05139=5.139\%$

This investment has a standard deviation of 5.139%.