Question

Given the following information,

Economy	Probability of Economy	Stock A	Stock B
Recession	0.5	-2%	0%
Neutral	0.2	0%	1%
Boom	?	20%	5%

a) What are the expected returns for stock A and B, respectively?

b) What is the standard deviation/risk for stock A? List the formula and input the number, no calculation needed.

c) What is the portfolio return given that you have $10,000 and allocate $3,000 in stock A and the rest in stock B? List the formula and input the number, no calculation needed.

d) The principle of diversification states that as the number of stocks under the portfolio increases, the portfolio risk more likely A) increases or B) decreases?

Answer 1

Ans:- Probability of Boom will be 1 - Recession - Neutral = 1 - 0.5 - 0.2 = 0.3.

  The expected return is calculated by ( ∑ Respective Probability * Respective Return).

Standard deviation is nothing but the square root of variance and it is calculated by

the square root of ∑ Deviation ^2 * Probability.

Ans:- (c) Portfolio return if $3000 is invested in stock A and the rest i.e $7000 in stock B will be given by

Expected return of A * $3000 + Expected return of B * $7000 = 0.05 * $3000 + 0.017 * $7000 = $269.

Ans:- (d) The Principal of diversification states that as the number of stocks under the portfolio increases, the portfolio risk more likely to decrease because the risk is diversified. option B is the right answer.