Question

SECURITY MARKET LINE

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	2.0
C	80 million	3.9
D	80 million	1.0
E	60 million	2.7

Kish's beta coefficient can be found as a weighted average of its stocks' betas. The risk-free rate is 4%, and you believe the following probability distribution for future market returns is realistic:

Probability	Market Return
0.1	(5%)
0.2	9
0.4	11
0.2	13
0.1	16

1. What is the equation for the Security Market Line (SML)? (Hint: First determine the expected market return.)
   
   1. r_i = 2.9% + (5.9%)b_i
   2. r_i = 2.9% + (5.0%)b_i
   3. r_i = 4.0% + (5.9%)b_i
   4. r_i = 1.6% + (7.1%)b_i
   5. r_i = 4.0% + (5.0%)b_i

• 
  
• 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 1.5. Should Kish invest in the new company?
  The new stock

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 -5%] + [0.2 x 9%] + [0.4 x 11%] + [0.2 x 13%] + [0.1 x 16%]

= -0.5% + 1.8% + 4.4% + 2.6% + 1.6% = 9.9%

According to SML,

ri = rf + bi[rm - rf]

= 4% + bi[9.9% - 4%]

= 4% + bi[5.9%]

Hence, Statement III is correct.

b).

bP = [Wi x bi]

= [(16/50) x 0.6] + [(12/50) x 2.0] + [(8/50) x 3.9] + [(8/50) x 1.0] + [(6/50) x 2.7]

= 0.192 + 0.480 + 0.624 + 0.160 + 0.324 = 1.78

ri = 4% + bi[5.9%]

= 4% + [1.78 x 5.9%] = 4% + 10.50% = 14.50%

c). Required rate of return on new stock = 4% + (5.9%) 1.5 = 12.85%. It has an expected return rate of 15% on the new stock. It is above the 12.85% required rate of return on an investment with a risk of beta= 1.5.

Since the Rc = 12.85% and is less than 15%, the new stock should be purchased.

d). Kish would only be indifferent to purchasing the stock when e(r) = 15%