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

A-

Risk Free Rate = 3%

Market Risk Premium = 7%

The formula for market risk premium is Expected Return on the Market Portfolio - Risk Free Rate

Using the above formula we have:

7% = Return on Market Portfolio - 3%

Return on market Portfolio = 7% + 3% = 10%

If we have invested 40% in the market portfolio and 60% in the risk free asset

The Expected Return = 40% * Expected Return on Market + 60% * Risk Free Rate

Expected Return = 40% * 10% + 60% * 3% = 4% + 1.8% = 5.8%

Expected Return = 5.8%

B-

(i)

Risk Free Rate = 7%

Market Risk Premium = 8%

Using the same formula as in A given

We have Expected Return on the Market as = 7% + 8% = 15%

Expected Return = (Price after 1 year + Dividend - Price today) / Price Today

Required Return = Using CAPM = Risk Free Rate + Beta * (Market Risk Premium)

For Stock X:

Stock Price Today = $20

Stock Price 1 year ahead = $22

Dividend = $2

Beta = 1

Using the Above mentioned formula's:

Expected Return = (22 + 2 - 20) / 20 = 4/20 = 20%

Required Return = 7% + 1*8% = 15%

For Stock Y:

Stock Price Today = $30

Stock Price 1 year ahead = $32

Dividend = $1.78

Beta = 0.9

Expected Return = (32+1.78-30) / 30 = 3.78 / 30 = 12.6%

Required Return = 7% + 0.9*8% = 14.2%

(ii)

Stock X is worth Investing in because its expected Return is higher than its required return. Fro Stock Y the expected return is lower than its required return as in stock Y is not being able to generate sufficient returns as expected by its investors whereas stock X is generating a return of 20% as against a required return of 15%.

C-

The correlation explains the movement of One asset depending upon the movement of the other correlated asset. A positive correlation means that the stocks move in the same direction of change and a negative correlation means that if one stock moves up the other goes down.

A Diversification benefit is achieved when we are able to achieve negative correlation so in that case our portfolio will be compensated by one negative movement because the other stock will move in the other direction and cover our losses. However we would not like to have a perfectly negative correlation otherwise there will be no room for profits.

So in this case Stock A&B will provide the greatest diversification benefit since it has the lowest correlation of -0.66

D-

Systematic Risk is also called a Non Diversifiable risk. This is the risk which the investor accepts to bear when he makes an investment. He is compensated for the same. So higher the Systematic Risk, higher will be the expected investment retun.

Unsystematic Risk is also called as Diversifiable risk. An Investor is not compensated for carrying Diversifiable risk. So the extra expected return on carrying high Diversifiable risk is 0.