Question

(Each of the following parts is independent.)

1. According to the Capital Asset Pricing theory, what return would be required by an investor whose portfolio is made up of 40% of the market portfolio (m) and 60% of Treasury bills (i.e. risk-free asset)?  Assume the risk-free rate is 3% and the market risk premium is 7%?   

2. You are considering investing in the following two stocks. The risk-free rate is 7 percent and the market risk premium is 8 percent.

Stock	Price Today	Expected Price in 1 year	Expected Dividend in 1 year	Beta
X	$20	$22	$2.00	1.0
Y	$30	$32	$1.78	0.9

1. Compute the expected and required return (using CAPM) on each stock.   
2. Which asset is worth investing? Support your answer with calculations.   

3. Which pair of stocks used to form a 2-asset portfolio would have the greatest diversification effect for the portfolio? Briefly explain.

	Correlation
Stocks A & B	-0.66
Stocks A & C	-0.42
Stocks A & D	0
Stocks A & E	0.75

  

(d)       Explain the terms systematic risk and unsystematic risk and their importance in determining        investment return.   

Answer 1

A. As per CAPM, the return is calculated as,

R= Rf + Beta * (Rm - Rf)

where Rf = Risk free rate

Rm = Retun on market

Here, for a 2 asset portfolio, the return is calcuated as,

R = R1* W1 + R2 * W2 where 1 & 2 are the 2 assets which are market portfolio and treasury bills in this case.

1 is market portfolio and 2 is Treasury bills. hence R1=7% R2=3% W1 =40%  W2= 60%

Thus,

R = 7*0.4 + 3*0.6 = 2.8+1.8 =4.6%

B. 1. Rf= 3% Risk premium i Rm-Rf = 7%

As per the CAPM formulae above,

RX = 3+Beta*7 = 3+1*7 = 10%

RY= 3+Beta*7= 3+0.9*7 = 9.3%

This is the return expected as per CAPM.

Stock return is calculated as R = (P2-P1)+D1/P1

This RX = (22-20)+2/20 = 25%

RY = (32-30)+1.78/30 = 12.6%

2. From the above calculation, the stock X is a better performer than Y both as per the CAPM required return being higher and the expected stock return being higher. Thus invest in X

C.The more different the 2 stocks are, the more negative the correlation between them will be (which means when one goes upwards, the other goes downwards), the greater the diversification benefits will be. Thus among the listed pairs, stock A& B have a most negative correlation making them the best pair providing the best diversification benefit.

D. Systematic risk is the undiversifiable risk that exists in the market which cannot be completely eliminated even after diversifying the portfolio.

Unsystematic risk is the diversifiable company specific risk that exists while trading on any particular stock/company. This risk is due to the company or sector or country specific parameters which can be eliminated or atleast minimize  if the portfolio is diversified sufficiently.

In making any portfolio, one needs to assess both these risks to have a better judgment of what risks to take and what not to take, at what costs & expected benefit and what hedges to use if needed.