You are thinking of buying a stock priced at $ 100 per share. Assume that the risk-free rate is about 4.5 % and the market risk premium is 6.0 %. If you think the stock will rise to $ 117 per share by the end of the year, at which time it will pay a $ 1.00 dividend, what beta would it need to have for this expectation to be consistent with the CAPM? g

Beta is 2.25

Explanation:

The return total return on the stock can be computed using the holding period return stated below:

=Pi-Po+D/Po

Pi is the expected price of the bond at year end which is $117

Po is the initial stock price of $100

D is the dividend expected at year end

holding period return=($117-$100+$1)/$100=18.00%

In Capital Asset Pricing Model,expected return formula is as follows:

expected return=risk free rate+beta*market risk premium

18.00% =4.5%+Beta*6.0%

18.00%-4.5%=Beta*6.00%

13.500%=Beta *6.00%

Beta=13.500% /6.00%

Beta=2.25

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