Question

Universal Corporation is planning to invest in a security that has several possible rates of return. Given the probability distribution of returns in the popup​ window, expected rate of return on the​ investment? Also compute the standard deviation of the returns. What do the resulting numbers​ represent?

PROBABILITY   RETURN
0.20 -5%
0.30 0%
0.40 5%
0.10 20%

Answer 1

Expected rate of return = Sum of product of return and probability

Expected return, ER:

• ER = 0.2 * (-5%) + 0.3 * 0% + 0.4 * 5% + 0.1 * 20%
• ER = -0.01 + 0 + 0.02 + 0.02
• ER = 0.03 = 3%

Expected return = 3%

Standard deviation is the measure of variability of returns from its mean. It is computed as the square root of sum of squared differences.

Standard deviation,s:

• s = SQRT [ Sum of (R - ER)^2 * p ] where p = probability and ER = expected return
• s = SQRT [(-0.05 - 0.03)^2 * 0.2 + ( 0 - 0.03)^2 * 0.3 + (0.05 - 0.03)^2 * 0.4 + (0.20 - 0.03)^2 * 0.1]
• s = SQRT[ 0.0064 * 0.2 + 0.0009 * 0.3 + 0.004 * 0.4 + 0.0289 * 0.1]
• s = SQRT [0.00128 + 0.00027 + 0.00016 + 0.00289]
• s = SQRT [0.0046]
• s = 0.067823

standard deviation of the returns = 6.78%

With expected return of 3% and standard deviation of 6.78%, it can be interpreted as the returns are very volatile and vary so much from the mean, and is thus a risky investment.