Question

Given the following information:

State of Economy	Probability	Rate of Return if State Occurs Stock G	Rate of Return if State Occurs Stock H
Boom	0.3	12%	25%
Normal	0.5	15%	10%
Recession	0.6	6%	-18%

Suppose you hold a portfolio with 60% invested in G and 40% invested in H.

(1) What is the portfolio’s return if each state of the economy occurs, respectively?

(2) What is the portfolio’s expected return?

(3) What is the portfolio’s standard deviation?

Is there a way to do this without excel?

Answer 1

	G		H
	Return	Weight	Return	Weight	Portfolio Return [{R(g)*W(g)}+{R(h)*W(h)}]
Boom	0.12	0.6	0.25	0.4	0.172
Normal	0.15	0.6	0.1	0.4	0.13
Recession	0.06	0.6	-0.18	0.4	-0.036

Note: There seems to be typo error in Probability of Recession. Total of All Probabilities should be 1. Therefore, Probability of Recession is taken as 0.2. In case, there is anything else, kindly comment. Although, the METHOD to solve will remain the same.

Economy	Probabilty	Return	(a) Probability* Return	Return- Expected Return[D]	Probability*D*D
Boom	0.3	0.172	0.0516 = 5.16%	0.0626	0.001175628
Normal	0.5	0.13	0.065 = 6.5%	0.0206	0.00021218
Recession	0.2	-0.036	-0.0072 = -0.72%	-0.1454	0.004228232
		(b) Expected Return = Sum of Probability*Return	0.1094 = 10.94%	Variance =Sum of [D^2]	0.00561604
				(c) Standard Deviation =Variance^1/2	0.074940243 = 7.494%