You plan to invest in the Kish Hedge Fund, which has total capital of $500 million invested in five stocks: Stock Investment Stock's Beta Coefficient A. $160 million 0.6, B. 120 million 1.4, C. 80 million 2.0, D. 80 million 1.0, E. 60 million 1.9. Kish's beta coefficient can be found as a weighted average of its stocks' betas. The risk-free rate is 3%, and you believe the following probability distribution for future market returns is realistic:
Probability Market Return: 0.1 -30%, 0.2 0%, 0.4 12%, 0.2 30%, 0.1 48%.
a. What is the equation for the Security Market Line (SML)? (Hint: First determine the expected market return.)
I. ri = 3.2% + (9.6%)bi
II. ri = 3.2% + (8.3%)bi
III. ri = 3.0% + (9.6%)bi
IV. ri = 4.4% + (11.0%)bi
V. ri = 3.0% + (8.3%)bi.
b. Calculate Kish's required rate of return. Do not round intermediate calculations. Round your answer to two decimal places. %
c. Suppose Rick Kish, the president, receives a proposal from a company seeking new capital. The amount needed to take a position in the stock is $50 million, it has an expected return of 17%, and its estimated beta is 1.4. Should Kish invest in the new company? The new stock [select-should not, should] be purchased. At what expected rate of return should Kish be indifferent to purchasing the stock? Round your answer to two decimal places. %
1)
Calculation of Expected market return (lets say Rm)
Probabilty (P) | 0.1 | 0.2 | 0.4 | 0.2 | 0.1 |
Market return (x) | -30% | 0% | 12% | 30% | 48% |
P*X | -3% | 0% | 5% | 6% | 5% |
Expected return (sum of P*X) | 12.6% |
the SML equation is
Ri = Rf + (Rm - Rf) *Bi
where Re is required return of a given stock e
Rf is the risk free rate of return and Be is the beta coefficient of stock e
therefore Ri = 3 % + 9.6% *Bi
correct answer is option 3
Answer 2)
Stock | A | B | C | D | E |
Beta | 0.6 | 1.4 | 2 | 1 | 1.9 |
Weight | 160 | 120 | 80 | 80 | 60 |
Beta*Weight | 96 | 168 | 160 | 80 | 114 |
Sum of weights | 500 | ||||
Portfolio Beta (Sum of Beta *Weight/ Sum of weight) | 1.236 | ||||
therefore required return is 3 + 9.6*1.236 = 14.87%
Answer to part 3)
For beta 1.4
the required return is 3 + 9.6*1.4 = 16.44
hence Kish shall accept the proposal with 17% return since it is more than the required return
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