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	0.7
B	120 million	1.2
C	80 million	2.3
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 5%, and you believe the following probability distribution for future market returns is realistic:

Probability	Market Return
0.1	-30%
0.2	0
0.4	14
0.2	31
0.1	54

1. What is the equation for the Security Market Line (SML)? (Hint: First determine the expected market return.)
   
   1. r_i = 3.8% + (9.2%)b_i
   2. r_i = 3.8% + (7.7%)b_i
   3. r_i = 5.0% + (9.2%)b_i
   4. r_i = 8.5% + (11.0%)b_i
   5. r_i = 5.0% + (7.7%)b_i
   
   -Select ONE
   
2. Calculate Kish's required rate of return. Do not round intermediate calculations. Round your answer to two decimal places.
     %
3. 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 14%, and its estimated beta is 1.4. Should Kish invest in the new company?
   The new stock -Select-should notshouldItem 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

a).

rM = [Pi x rMi]

= [0.1 x -30%] + [0.2 x 0%] + [0.4 x 14%] + [0.2 x 31%] + [0.1 x 54%]

= -3% + 0% + 5.6% + 6.2% + 5.4% = 14.2%

According to SML,

ri = rf + bi[rm - rf]

= 5% + bi[14.2% - 5%]

= 5% + bi[9.2%]

Hence, Statement III is correct.

b).

bP = [Wi x bi]

= [(16/50) x 0.7] + [(12/50) x 1.2] + [(8/50) x 2.3] + [(8/50) x 1.0] + [(6/50) x 1.6]

= 0.224 + 0.288 + 0.368 + 0.160 + 0.192 = 1.232

ri = 5% + bi[9.2%]

= 5% + [1.232 x 9.2%] = 5% + 11.33% = 16.33%

c). Required rate of return on new stock = 5% + (9.2%) 1.4 = 17.88%. It has an expected return rate of 14% on the new stock. It is below the 17.88% required rate of return on an investment with a risk of beta= 1.4.

Since the Rc = 17.88% and is greater than 14%, the new stock should not be purchased.

d). Kish would only be indifferent to purchasing the stock when e(r) = rc = 17.88%