Question

Suppose you have invested $100,000 in the following four stocks.

Security Amount invested Beta Average Return Stock A 20000 0.75 14 Stock B 25000 1.1 13 Stock C 30000 1.36 16 Stock D 25000 1.88 25

The risk-free rate is 5% and the expected market risk premium is 10%.

Assume CAPM holds.

Required:   i. Write the equation of the security market line (SML).
(1 mark)

ii. Calculate the expected returns of each of the stock and determine which of the stocks that you would recommend to buy.

iii. Calculate the portfolio beta and also the required rate of return of the portfolio.

Answer 1

i. Write the equation of the security market line (SML).

If CAPM holds, the equation of the security market line (SML) is as follows -

Required rate of Return on stock = risk free rate + ?* market risk premium

Where,

Risk free rate = 5%

Market risk premium, = 10%

And ? of stock =?

Therefore

Required rate of Return on stock = 5% + ?* 10%

ii. Calculate the expected returns of each of the stock and determine which of the stocks that you would recommend to buy.

Putting the values of beta (?) of different stocks in the equation to calculate the expected returns of each stock

Expected Return of stock A = 5% + 0.75 * 10%

= 5% +7.5% = 12.5%

Expected Return of stock B = 5% + 1.1 * 10%

= 5% +11% = 16%

Expected Return of stock C = 5% + 1.36 * 10%

= 5% +13.6% = 18.60%

Expected Return of stock D = 5% + 1.88 * 10%

= 5% +18.80% = 23.80%

I will recommend to buy stock B and stock C because these stocks are under-valued stocks as their expected return is more than their average return.

iii. Calculate the portfolio beta and also the required rate of return of the portfolio.

Portfolio beta on the basis of investments in each stock, Total Portfolio investment = $ 100,000

Portfolio beta = ? (stock’s investment amount/ Portfolio value) * beta of stock

= ($20,000/ $100,000) * 0.75 + ($25,000/ $100,000) * 1.1 + ($30,000/ $100,000) * 1.36 + ($25,000/ $100,000) * 1.88

= 1.303

Therefore portfolio beta is 1.303

The expected return of the portfolio = Sums of (Expected return of stock * their portfolio weight)

= 12.5% * ($20,000/ $100,000) + 16% * ($25,000/ $100,000) + 18.60% * ($30,000/ $100,000) + 23.80% * ($25,000/ $100,000)

= 18.03%

The expected return of the portfolio is 18.03%