QUESTION 1: INVESTMENTS MIX Consider the following statement to answer You manag
ID: 2773264 • Letter: Q
Question
QUESTION 1: INVESTMENTS MIX
Consider the following statement to answer
You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of27%. The Treasury-bill rate is 7%.
i. One of your clients chooses to invest 70% of a portfolio in your fund and 30% in a T-bill moneymarket fund. What is the expected value and standard deviation of the rate of return on yourclient’s portfolio?(2 marks)
ii. Suppose that your client decides to invest in your portfolio a proportion y of the total investmentbudget so that the overall portfolio will have an expected rate of return of 15%.
iii. a. What is the proportion y? (Hint: Use CAPM formula)
b Further suppose that your risky portfolio includes the following investments in the givenproportions: Stock A (27%), Stock B (33%), and Stock C (40%). What are your client’sinvestment proportions in your three stocks and the T-bill fund?(2 marks)
iv. Now suppose that your client prefers to invest in your fund a proportion ythat maximizes theexpected return on the overall portfolio subject to the constraint that the overall portfolio’sstandard deviation will not exceed 20%.
a What is the investment proportion, y?
b What is the expected rate of return on the overall portfolio?(2 marks)
v. Suppose that your client’s degree of risk aversion is A = 3.5. What proportion, y, of the totalinvestment should you suggest that he invest in your fund?(2 marks)
vi. The market price of a security is $40. Its expected rate of return is 13%. The risk- free rate is 7%and the market risk premium is 8%. What will be the market price of the security if itscovariance with the market portfolio doubles (and all other variables remain unchanged)?Assume that the stock is expected to pay a constant dividend in perpetuity.(2 marks)
Explanation / Answer
Answer :
1. Mean = (0.30 * 7%) + (0.7 * 17%) = 14% per Year
Standard Deviation = 0.70 * 27% = 18.9% per Year
2. Mean Return on Portfolio = Rf + (Rp - Rf)y
= 7% + (17% - 7%)y = 7% + 10%y
If the mean of the portfolio is equal to 15%, then solving for y we will get
15% = 7% + 10%y
y = (15% - 7%) / 10% = y = 0.8
3. (a) Mean Return on Portfolio = Rf + (Rp - Rf)y
= 7% + (17% - 7%)y = 7% + 10%y
If the mean of the portfolio is equal to 15%, then solving for y we will get
15% = 7% + 10%y
y = (15% - 7%) / 10% = y = 0.8
Thus in order to obtain a mean return of 15%, the client must invest 80% of total funds in the risky portfolio and 20% in treasure bills.
(b). Investment proportions of the client's funds:
20% in T bills
0.8 *27% = 21.6% in stock A
0.8 * 33% = 26.4% in stock B
0.8 * 40% = 32.0% in Stock C
4. (a)
Portfolio standard deviation = y * 27%. if client wants a standard deviation of 20% then
y = (20% / 27%) = 0.7407 = 74.07% in the risky portfolio
(b) Mean return = 7% + (17% - 7%)y = 7% + 10% (0.7407) = 7% + 7.407% = 14.407%
5. y = (Rp - Rf) / 0.01A * standard deviation2
y = (17 - 7) /(0.01 * 3.5* 272) = 10 / 25.515 =0.3919
Thus, the client's optimal investment proportions are 39.19% in the risky portfolio and 60.81% in T - bills
6. If the covariance of the security doubles , then so will its beta and its risk premium. The current risk permium is 6% ( 13% - 7%), so the new risk premium would be 12%, and the new discount rate for the security would be 19% (12% + 7%).
If the stock pays a level perpetual dividend , then from the original data that the diviend D must satisfy the equation for a perpetuity:
Price = Dividend / Discount rate
$ 40 = D / 0.13 , D = $ 5.20
At the new discount rate of 19% the stock would be worth only $ 5.20 / 0.19 = $ 27.37. As a consequence , the increase in stock risk has lowered the stock value by ( $ 27.37 - $ 40 ) / $40 = 31.58%