Question

Problem 6-06
Expected Returns: Discrete Distribution

The market and Stock J have the following probability distributions:

Probability	rM	rJ
0.3	15%	21%
0.4	8	3
0.3	18	13

Calculate the expected rate of return for the market. Round your answer to two decimal places.
%

Calculate the expected rate of return for Stock J. Round your answer to two decimal places.
%

Calculate the standard deviation for the market. Do not round intermediate calculations. Round your answer to two decimal places.
%

Calculate the standard deviation for Stock J. Do not round intermediate calculations. Round your answer to two decimal places.
%

Answer 1

a) Expected return on market = probability weighted rate of return.

E(rM) = 0.3 * 15% + 0.4 * 8% + 0.3 * 18%

E(rM) = 4.5% + 3.2% + 5.4% = 13.1%

b) Expected return on Stock J

E(rJ) = 0.3 * 21% + 0.4 * 3% + 0.3 * 13%

E(rJ) = 6.3% + 1.2% + 3.9% = 11.4%

c) Standard deviation of return for Market. Standard deviation is square root of sum of probability weighted squared deviations from expected value.

Std deviation² = 0.3 * (15% - 13.1%)² + 0.4 * (8% - 13.1%)² + 0.3 * (18% - 13.1%)²

Std deviation² = 0.000108 + 0.001040 + 0.000720 = 0.001869

Std deviation = 4.32%

d) Standard deviation of return for Stock J. Standard deviation is square root of sum of probability weighted squared deviations from expected value.

Std deviation² = 0.3 * (21% - 11.4%)² + 0.4 * (3% - 11.4%)² + 0.3 * (13% - 11.4%)²

Std deviation² = 0.002765 + 0.002822 + 0.0000768 = 0.005664

Std deviation = 7.53%