Question

You plan to invest in the Kish Hedge Fund, which has total capital of R500 million invested in five stocks:

Stock	Investment	Stock's Beta Coefficient
A	160 million	0.5
B	120 million	1.2
C	80 million	1.8
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 6%, and you believe the following probability distribution for future market returns is realistic:

Probability	Market Return
0.1	(28%)
0.2	0
0.4	12
0.2	30
0.1	50

1. What is the equation for the Security Market Line (SML)
2. Calculate Kish's required rate of return.
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 R50 million, it has an expected return of 15%, and its estimated beta is 1.5. Should Kish invest in the new company? At what expected rate of return should Kish be indifferent to purchasing the stock?

Answer 1

Answer-a:

Required rate of return = Risk free rate + Beta × (Market return - Risk free rate)

                         = 0.1 (-28%) + 0.2(0%) + 0.4(12%) + 0.2(30%) + 0.1(50%) = 13%

Risk free rate = 6%

6% + (13% - 6%) = 7%

6% + 7%

Answer-b:

Required rate of return = Risk free rate + Beta × (Market return - Risk free rate)

                                     = 6% + 1.088 × (13% - 6%)

                                     = 13.62%

0.5 Working note: Amount Weighted Stock invested investment A 160 0.32 B 120 0.24 C 0.16 D 0.16 0.12 500 1.00 Beta coefficient Wt x Beta 0.16 1.2 0.288 0.288 1.01 0.16 1.6 0.192 1.088 80 60

Answer-c:

Required rate of return = Risk free rate + Beta × (Market return - Risk free rate)

                                     = 6% + 1.5 × (13% - 6%)

                                     = 16.5%

As the new company's stock CAPM return of 16.5% is greater than the expected rate of return of 15%, this stock is over valued. Kish should not invest in the new company.