Question

The current market stock price of Zoombra Corporation is $40, the security's expected return is 10%, the riskless rate of interest is 2%, and the return on the market portfolio is 12%.

1. What will be the expected return on Zoombra's stock, if the covariance of its rate of return with the market portfolio doubles?
2. What will be the Zoombra's price, if the covariance of its rate of return with the market portfolio doubles?
3. How is your result consistent with our understanding that assets with higher systematic risks must pay higher returns on average?

Answer 1

Answer 1 Required rate of return = 18%

According to CAPM

Re = Rf + β(Rm-Rf)

where Re = Expected Return; Rf = Risk free return, Rm = Return on Market Portfolio; β = Beta of Security

Now as per question Re = 10%; Rf = 2%, Rm = 12%; β = ?

As per CAPM

10 = 2 + β(12 - 2) =»   8 = 10 β    » Thus     β = 0.8

Also   β = Covariance / Variance of Market Return. So if covariance doubles β will also doubles (1.6) as Variance of Market Return remains same.

So New Required rate of return = 2 + 1.6(12 - 2) = 18%

Answer 2   Price = $ 22. 22

Assuming the stock pays a level perpetual dividend then its original dividend should be Price = Div / Re

=» 40 = Div / 10%           =» Div = 40*10% = 4

Since Re is now increased to 18%, Price = Div / Re = $ 4 / 0.18 = $ 22. 22

Answer 3

As the risk increase, the required return from stock increases. However the dividend remains same and as a result the price of the stock decreases to commensurate with the increased risk