Question

1.

a.

A portfolio is invested 15 percent in Stock G, 65 percent in Stock J, and 20 percent in Stock K. The expected returns on these stocks are 10 percent, 20 percent, and 25 percent, respectively. What is the portfolio's expected return?

• 20.28%

• 19.50%

• 18.52%

• 20.48%

• 14.67%

b.

Consider the following information:

  

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B	Stock C
Boom	0.64	0.09	0.31	0.05
Bust	0.36	0.05	0.05	-0.05

  

Requirement 1:

What is the expected return on an equally weighted portfolio of these three stocks? (Do not round your intermediate calculations.)

(Click to select)   10.61%   10.71%   6.67%   9.69%   10.20%

  

Requirement 2:

What is the variance of a portfolio invested 30 percent each in A and B and 40 percent in C? (Do not round your intermediate calculations.)

0.004088   0.006947   0.003699    0.003894   0.005098

Answer 1

Answers : -

a) Option b = 19.50 %

b) Option e = 10.20%

c) Option d = 0.003894

Explanations :-

a)

	Expected Return of Portfolio
State of Economy	Probability(P)	Return(R)	Expected Return(P × R)
Stock G	0.15	0.10	0.015
Stock J	0.65	0.20	0.13
Stock K	0.20	0.25	0.05
Expected Return = Total (P × R)	0.1950 (19.5%)

.

b)

expected return on an equally weighted portfolio
	Probability(P)	Return(R) of A	Expected Return(P × R) of stock A	Return(R) of B	Expected Return(P × R) of stock B	Return(R) of c	P×R of stock C
Bhoom	0.64	0.09	0.0576	0.31	0.1984	0.05	0.032
Bust	0.36	0.05	0.018	0.05	0.018	- 0.05	-0.018
			0.0756		0.2164		0.014

As per the question Return of stock are equally distributed between the 3 stock , so the probability of every stock return is

   = 1/3    = 0.333333 or 33.3333%

Stock	Probability(P)	Return(R)	Expected Return(P × R
Stock A	0.3333	0.0756	0.02519748
Stock B	0.3333	0.2164	0.07213621
Stock C	0.3333	0.014	0.00466662
Expected return on an equally weigted portfolio ( Total (P ×R))

.

c)

calculate the expected returns for the portfolio in the boom and bust states.

• ( 0.30 x 0.09) + ( 0.30 x 0.31) + (0.40 x 0.05) = 14%
• (0.30 x 0.05) + (0.30 x 0.05) + (0.40 x -0.05) = 1%

calculate the total portfolio expected return  

(0.64 x 14%) + (0.36 x 1%) = 9.32%

calculate deviation of boom and bust portfolios expected return.

14% - 9.32% = 4.68%

1% - 9.32% = -8.32%

square the deviation of the boom and bust portfolios

4.68%² = 0.00219024

-8.32%² = 0.0069224

multiply each square deviation by its respective probabilitty

• 0.00219024 x 0.64 = 0.0014017536
• 0.0069224x 0.36 = 0.002492064

sum of products for variance

• portfolio variance =0.0014017536 + 0.002492064= 0.0038938176 =0.003894