Question

You have a portfolio worth $100,000 consisting of two stocks, A and B. You invested $30,000 in stock A and the remainder in Stock B. Consider the following information:

Type your answers in the appropriate section showing all steps of your work

State of the Economy	Probability Of State	Return on A	Return on B
Growth	0.25	15%	8%
Normal	0.50	5%	20%
Recession	0.25	-10%	25%

               

Expected return 3.75% ??                                              

Standard deviation ??               6.26%

a) What is the expected return for Stock B?

b) What is the standard deviation for Stock A?

c) What is the expected return for the portfolio of these two securities?

Hint: Use the weighted average of the stock’s individual standard deviation as that is all you have.

d) Are there benefits to forming a portfolio of these two securities? Explain in words.

f) Suppose the Beta of stock B = 1.8. You have determined the return on Government of Canada T-Bills = 3% and the return on the market portfolio = 12%. Is stock B correctly priced? Show your work and state whether you would recommend buying or selling Stock B and why.

Answer 1

(a): Expected return for stock B = (0.25*8%) + (0.50*20%)+(0.25*25%)

= 18.25%

(b): Standard deviation for stock A = [0.25*(15% - 3.75%)^2 + 0.50*(5%-3.75%)^2 + 0.25*(-10%-3.75%)^2]^0.5

= 8.93%

(c): Weight of A = 30,000/100,000 = 30% and of B = (100,000-30,000)/100,000 = 70%

So expected return of portfolio = 30% of 3.75% + 70% of 18.25%

= 13.90%

(d): The benefits of forming a portfolio is that the standard deviation of the portfolio declines. This means that in case of forming a portfolio the overall level of standard deviation will fall and hence the risk level will fall a lower level of standard deviation shows lower level of volatility and more stability with regards to the returns.

(f): Rate of return of B = risk free rate + beta*market premium

= 3% + 1.8*(12%-3%)

= 19.2%

This is more than the expected return of 18.25% that was computed in "a". Hence we can say that stock B is not currently priced. As 19.2% > 18.25% one should buy the stock as its expected returns are lower than actual returns.