Question

Question 5 (25 marks / Risk, Return and CAPM)
(Each of the following parts is independent.)
(a) 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%?  

(b) 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

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

(c) 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

1. Calculation of required return of portfolio:

Required return = weight risk free asset * return from risk free asset + weight market portfolio * market risk premium

= 0.60* 3 + 0.40* 7

= 1.80 + 2.80 = 4.60%

hence the required return of portfolio = 4.60%

a. Calculation of expected return:

Expected return = [Dividend + (price _{end of year} - price _today )]/ Price _today

Expected return for Stock X = [2 + (22 - 20)] / 20 = 20%

Expected return for Stock Y = [1.78 + (32 - 30)] / 30 = 12.60%

b. Calculation of required return using CAPM model:

Required return ​= Rrf ​+ βa​∗(Rm​ − Rrf​)

Required return Stock X = % 7+ 1 * 8% = 15%

Required return Stock Y = = 7% + 0.90 * 8% = 14.20%

From above analysis we can make out that the investor should invest in Stock X as its expected return is greater than required return whereas Stock Y expected return is less than required return.

where:

Rrf​=Risk-free rate

Rm​=Expected return of the market

βa​=The beta of the security

(Rm​−Rrf​)=Equity market premium

3. Pair of stock A & B with correlation -0.66 offers the greatest diversification benefit, as the lesser the correlation between the assets in the portfolio (in this case 2 assets) the greater the benefit of diversification. As the lowest correlation among option is between pair of assets A & B (i.e., - 0.66), it will offer the maximum risk reduction.

4. Total risk consist of Systematic risk + unsystematic risk

a. Systematic risk:

• This risk is also called non-diversifiable risk.
• This is the part of the total risk which cannot be diversified away irrespective of the fact that we have any asset in the portfolio.
• This risk effects the overall market and not just particular stock or industry.
• Examples: Exchange rate risk, interest rate risk, inflation

Importance in determining investment return: for this type of risk the investor should demand extra compensation (Ii.e., demand higher returns for such risk).

b. Unsystematic risk:

• This risk is also called diversifiable risk or residual risk.
• This is the part of the total risk which can be diversified (reduced) away just by allocating funds to various assets (i.e., by creating a portfolio).
• This risk effects a single company or a small group of company.
• Examples: quality of management, labour strike in company, bad corporate governance.

Importance in determining investment return: The risk of loss in one asset is reduced by profit in another stock which is achieved through diversification.