Question

The following table contains three shares: A, B, and C.

Table 1

SHARES

Beta

STD (annual)

Forecast for June 2020

Dividend

Stock Price

A

0.50

40%

$1.50

$50

B

2.00

45%

$0.85

$100

C

0.00

15%

$1.65

$35

The risk-free rate is 2.5%, and the market required return is 10%. The market’s standard deviation is 15%. Assume that the next dividend will be paid after one year, at t=1.

a. What is the expected rate of return for each share according to CAPM? Then, calculate the portfolio return, assuming 30% of its value is invested in A, 50% in B, and 20% in C. ​​​​​​​​

Relevant formulas

• E(Ri) = rf + βx(E(RM)-rf)

• E(Rp) = wxE(RA)+ wxE(RB)+ wxE(RC)

b. If you are a risk-averse investor, and you want to construct your portfolio with shares A, B, and C, how would you decide on your portfolio weights to minimise your portfolio’s overall risk? Assume that you have an efficient portfolio, and you can effectively diversify away unsystematic (specific) risk, which is included in the standard deviation (STD).

Note: no calculation is required just suggest the weights of the shares in your portfolio considering shares A, B, and C. Explain your answer.

c. If you are a risk-taker investor, and you want to construct your portfolio with shares A, B, and C, how would you decide on your portfolio weights to maximise your portfolio’s total return? Assume the CAPM is correct and the expected future returns are those calculated in (a).

Note: no calculation is required just suggest the weights of the shares in your portfolio considering shares A, B, and C. Explain your answer. ​​

d. In equilibrium, all the shares must have the same reward to risk ratio. The reward-to-risk ratio for all shares in the market is 7.50%. Reading the Financial Review, you spotted that the market return for shares A, B, and C are 6%, 10%, and 1% respectively. Use the reward-to-risk ratio to analyse if the shares in Table 1 are correctly priced. Explain your answer and what would happen in this market. (Your answer should be approx. 250 words)

e. From the investor’s point of view, a well-diversified portfolio makes sense. However, is this the case for the firm? For instance, would an investor be more attracted to a diversified firm than an undiversified one? (Your answer should be approx. 250 words)

Answer 1

a) As per CAPM

expected rate of return = risk free rate+ beta of share * (market rate of return - risk free rate)

So,

expected rate of return of Share A = 2.5%+ 0.5*(10%-2.5%) = 6.25%

expected rate of return of Share B = 2.5%+ 2*(10%-2.5%) = 17.50%

expected rate of return of Share C = 2.5%+ 0*(10%-2.5%) = 2.50%

Portfolio return =0.3*6.25%+0.5*17.50%+0.2*2.50% = 0.11125 or 11.125%

b) If we have an efficient portfolio, Beta is representative of the risk

As the beta of Share C is 0, to minimise the risk, the entire portfolio must be invested in C so as to reduce the risk of the portfolio to Zero.

So, the weights of A , B and C should be 0%, 0% and 100% respectively

c)  To maximise your portfolio’s total return, all the amount must be invested in share B as it has the highest return of 17.50%.

So, the weights of A , B and C should be 0%,100% and 0% respectively

d) As the market return for shares A, B, and C are 6%, 10%, and 1% respectively , all the shares are incorrectly priced and all are overpriced. The most mispricing is that in Asset B and Asset C. In the market, these assets are likely to be sold by the Investors, once their overpricing is realised. This selling will correct the pricing of the shares.

e )For an investor in a firm, diversification is also useful as it protects the firm from sector specific risks and thereby decreases its risk. This lowers the required rate of return of Investors making it an attractive investment opportunity