Suppose you invest your money in equal proportions in the two securities A and B

Question

Suppose you invest your money in equal proportions in the two securities A and B, whose properties are shown below: The variance of the market portfolio is .0002 and the correlation coefficient between the returns to stocks A and B is 0.60. Assuming both stocks are expected to pay the same future dividends which stock should have the higher price today? Explain. Assuming the stocks pay the same future dividends, the stock with the higher price today should be the stock with the lower return. The stock with the lower expected return is the stock with the lower risk. The relevant measure of risk is the beta, therefore the stock with the lower beta should have the lower expected return. Since Stock A has a lower beta, it should have a lower expected return, and higher price. What is the expected return on your portfolio? What is the portfolio standard deviation? Are there any benefits to combining stocks A and B into a portfolio? What is the portfolio beta? If the portfolio return behaves in accordance with CAPM, and the risk free rate is 8%, then what must the expected return on the market portfolio is?

Explanation / Answer

b) Expected portfolio return = 50% * Return of Stock A + 50% * Return of Stock B

= 50% * 12% + 50% * 13%

= 12.5%

c) Portfolio standard deviation = sqrt[(50% * SD of Stock A)2 + (50% * SD of Stock B)2 + 2 * 50% * SD of Stock A * 50% * SD of Stock B * Correlation between Stock A & Stock B]

= sqrt[(50% * 2.1%)2 + (50% * 2.9%)2 + 2 * 50% * 2.1% * 50% * 2.9% * 0.60]

= 2.24%

d) The combination of the stocks have resulted in moderation of risk (standard deviation) of the pertfolio while the risk has also come down alongwith the same.

e) Portdolio beta = 50% * beta of Stock A + 50% * beta of Stock B

= 50% * 1.1 + 50% * 1,2

= 1.15

f) Portfolio expected return = Risk free return + Portfolio beta * (Expected return of Market portfolio - Risk free rate)

=> 12.5% = 8% + 1.15 * (Expected return of Market portfolio - 8%)

=> Expected return of Market portfolio = 11.91%

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