The market and Stock J have the following probability distributions: Probability rM rJ 0.3 15% 20% 0.4 9 5 0.3 18 12 a. Calculate the expected rates of return for the market and Stock J. b. Calculate the standard deviations for the market and Stock J.

The answer is provided below

Explanation:

The expected rates of return for the market = 13.5

the expected rates of return for the market and Stock J = 11.6

The standard deviations for the market = 3.85

The standard deviations for Stock J = 6.22

The explanation has been attached.

[tex]The market and Stock J have the following probability distributions: Probability rM rJ 0.3 15% 20% 0[/tex]

A) The expected return for the market is 13.5 and stock is 11.6.

B) The standard deviation of the market is 3.85 and stock is 6.22.

Explanation:

[tex]\text{The formula to find the expected value.} \\\mu =E(X) = \sum xP(x) \\\text{Expceted return from market.} \\\mu_m = E(rates \ of \ return \ on \ market) \\= (15)(0.3)+(9)(0.4)+(18)(0.3) \\= 13.5 \\\text{The expected rate of return from stock J.} \\\mu_j = E(rates \ of \ return \ on \ market) \\= (20)(0.3) + (5)(0.4) + (12)(0.3) \\= 11.6 \\[/tex]

[tex]\\B. \text{The formula for variance.}\\\sigma ^2 = Var(X) \\= \sum x^2 P(x)- \mu^2 \\Standard \ deviation, \sigma = \sqrt{\sigma ^2} \\\text{Vraince from market.} \\\sigma _m ^2 = \left [ (15)^2 (0.3) + (9)^2 (0.4) + (18)^2 (0.3) \right ] - (13.5)^2 \\= 167.1 - 182.25 \\= 14.85 \\[/tex]

[tex]Standard \ deviation = \sqrt{14.85} \\= 3.85357 \\\text{Variance of stock J.} \\\sigma _j ^2 = \left [ (20)^2 (0.3) + (5)^2 (0.4) + (12)^2 (0.3) \right ] - (11.6)^2 \\= 173.2 - 134.56 \\= 38.64 \\Standard \ deviation \ of \ stock \ J = \sqrt{38.64} \\= 6.216108 \\= 6.22[/tex]