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	0.4
B	120 million	1.3
C	80 million	1.9
D	80 million	1.0
E	60 million	1.8

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	-28	%
0.2	0
0.4	11
0.2	32
0.1	55

A. What is the equation for the Security Market Line (SML)? (Hint: First determine the expected market return.)

1. r_i = 3.0% + (12.2%)b_i
2. r_i = 0.6% + (10.5%)b_i
3. r_i = 0.6% + (12.2%)b_i
4. r_i = 3.0% + (10.5%)b_i
5. r_i = 6.8% + (9.1%)b_i

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 16%, and its estimated beta is 1.4. Should Kish invest in the new company?

The new stock -Select- (should/not should) 3 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

The Beta of the fund is the weighted average beta of individual stocks

So, fund beta = 160/500*0.4+ 120/500*1.3 +80/500* 1.9+ 80/500*1 + 60/500*1.8

= 1.12

The Expected Return of the market is the probability weighted return

E(R_m) = 0.1* (-28%) + 0.2* 0% +0.4*11% +0.2*32% + 0.1*55%

=13.5%

A. The equation is given by

R_i =Risk free rate + Beta_i *(Expected Market return - Risk free rate)

R_i = 3% + Beta_i * ( 13.5% - 3%)

= 3% + 10.5% * Beta_i(option IV is correct)

B. Kish's required rate of return depends upon its Beta and given by the SML

R_k = 3% + 1.12 * 10.5%

=3% +11.76% = 14.76%

The required rate of return is 14.76%

C)The new stock has an expected return of 16% and a required rate (given by SML) of

R_s = 3% +10.5% *1.4 = 3% +14.7% =17.70%

As the required rate is higher than the expected rate, this is an overpriced stock and should not be purchased

Kish should be indifferent to purchase the stock when the expected rate is equal to required rate i.e. when the expected rate of return is 17.70%