Question

2. Stock X has a beta of 1.5 and cost of capital of 15% estimated by CAPM. If we want to estimate X's return volatility based on its past returns, which distribution should we follow sample distribution or population distribution? b. Suppose there is another stock Y whose beta is 0.7 and estimated cost of capital of 10%. What is the expected market return and risk-free rate by assumption? c. Take 15% as expected return of X and 10% as expected return of Y. Suppose their volatility are each 5% and 4% and return correlation is 0.4. What is the expected return and volatility (i.e. standard deviation) of a portfolio that holds 50% of X and 50% of Y? d. Draw the efficient frontier line for a portfolio that holds X and Y, and mark three allocations on the line: 100% invested in X, 100% invested in Y, and 50% in Y that you have calculated in part (c). Remind that the line represents the volatility (horizontal axis) and return (vertical axis) for each possible allocation.

Answer 1

a. We should follow Sample Distribution.

b. Expt. Return= Rf+Beta(Rm-Rf)

For stock x

15%= Rf+1.5(Rm-Rf)

15%= Rf+1.5Rm-1.5Rf

15%= 1.5Rm-0.5Rf......(1)

For stock Y

10%= Rf+0.7(Rm-Rf)

10% = Rf+0.7Rm-0.7Rf

10% = 0.7Rm+0.3Rf........(2)

Multiply equation (1) by 3 and equation (2) by 5 and add (1) into (2)

50% = 3.5Rm+1.5Rf

45%= 4.5Rm-1.5Rf

95%= 8Rm

Rm= 11.875%.

Put Rm= 11.875% in equation (1)

15%= 1.5(11.875%)-0.5Rf

15%= 17.8125-0.5Rf

Rf = 5.625.

c.

C D E Stock y Portfolio Stock x 15.00% 10% 4% 12.50% 3.77% 5% Expected return Standard deviation Covariance correlation 0.0008 0.4 26

Formulas used :-

Covariance=D25*D23*E23

Portfolio return=(0.5*$D$22)+(0.5*$E$22)

portfolio standard deviation=((0.5^2*$D$23^2)+(0.5^2*$E$23^2)+(2*$D$24*0.5*0.5))^(1/2)

d.

Expected Return 1 0.5 0 volatility 5.00% 3.77% 4 .00% 0.5 1 15.00% 12.50% 10.00% Expected Return 20.00% 15.00% 10.00% 5.00% 0.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00%
​​​​​​I hope my efforts will be fruitful to you....?