The stock price of DL Inc. is $49, the security’s expected rate of return is 14%, the risk-free rate of return is 4%, and the market risk premium is 8%. What will be the security’s current price if the covariance of its rate of return with the market portfolio halves on a permanent basis but everything else remains the same?

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Answer 1
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Answer: The new stock price of DL Inc. would be $37.50 if the covariance of its rate of return with the market portfolio halves on a permanent basis but everything else remains the same.

If the covariance of the security's rate of return with the market portfolio halves on a permanent basis but everything else remains the same, the security's new beta would be half its initial beta. The beta of a security is the covariance of the security's rate of return with the market portfolio divided by the variance of the market portfolio.The CAPM formula is used to compute the expected rate of return on a security, and it is as follows: Required return = risk-free rate of return + (beta x market risk premium).

The current price of DL Inc. stock can be calculated using the CAPM formula as follows: Beta = covariance of DL Inc. with the market portfolio/variance of the market portfolio= ?/ (8 x 8) = ?/64 where beta is unknown.Covariance of DL Inc. with the market portfolio = 0.5, Covariance of DL Inc. with the market portfolio = 0.5 x Var (DL Inc.)/Var (Market) = 0.5 Covariance of DL Inc. with the market portfolio is half the original covariance.

The beta for the security = 0.5 Covariance of DL Inc. with the market portfolio = 0.5 x ?Var (DL Inc.)/Var (Market) = 0.5 (0.5 x ?Var (DL Inc.)/Var (Market)) = ?Var (DL Inc.)/ (2 x Var (Market))Required rate of return = 4% + (0.5 x 8%) = 8%.DL Inc.'s current stock price = Dividend per share/ (required rate of return - growth rate) = $3/ (8% - 0%) = $37.50.

Therefore, the new stock price of DL Inc. would be $37.50 if the covariance of its rate of return with the market portfolio halves on a permanent basis but everything else remains the same.

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