Question

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. %

Answer #1

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

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
0.7
B
120 million
1.1
C
80 million
1.7
D
80 million
1.0
E
60 million
1.6
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...

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Investment
Stock's Beta Coefficient
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B
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C
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1.8
D
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E
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Probability
Market Return...

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