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 0.8 B 120 million 1.5 C 80 million 2.2 D 80 million 1.0 E 60 million 1.5 Kish's beta coefficient can be found as a weighted average of its stocks' betas. The risk-free rate is 6%, and you believe th

following probability distribution for future market returns is realistic: Probability Market Return 0.1 -29 % 0.2 0 0.4 13 0.2 28 0.1 55 What is the equation for the Security Market Line (SML)? (Hint: First determine the expected market return.) ri = 6.0% + (6.7%)bi ri = 3.9% + (7.4%)bi ri = 3.9% + (6.7%)bi ri = 6.0% + (7.4%)bi ri = 7.3% + (8.6%)bi Calculate Kish's required rate of return. Do not round intermediate calculations. Round your answer to two decimal places. % 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 15%, and its estimated beta is 1.4. Should Kish invest in the new company? The new stock 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

Probablity Return

0.1 -29 %

0.2 0%  

0.4 13 %

0.2 28 %

0.1 55 %

Expected market return = 0.1 * (-29%) + 0.2*0 +0.4* 13% + 0.2* 28% + 0.1*55% =13.4%

Equation of SML :

ri = 6.0% + (13.4% - 6%)bi = 6.0% + 7.4%* bi

Portfolio Beta

Stock   Investment (in mi) Stock’s Beta Weight* Beta

A         160   0.8 (160/500)*0.8

B         120 1.5 (120/500)*1.5

C         80 2.2 (80/500)*2.2

D         80 1.0 (80/500)*1

E          60 1.5 (60/500)*1.5

Total = 500 Portfolio Beta = 1.308

Kish Required rate of Return = 6.0% + 7.4%* 1.308 = 15.6792%

Kish received a proposal where the expected return is 15% and beta is 1.4.

Required rate of return for investing in new company  = 6.0% + 7.4%* 1.4 = 16.36%

Required rate of return is minimum return required for a given risk or beta.

In this case, the expected return of 15% is lower than the required return of 16.36%. Kish should not invest in the company.

The expected rate of return that will make Kish indifferent to purchasing the stock is 16.36%. Answer

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