Question

Themarketpriceofasecurityis$50.Itsexpectedrateofreturnis14%.Therisk-freerateis6%, and the market risk premium is 8.5%. What will be the market price of the security if its correla- tion coefficient with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity.

Answer 1

$31.82

Step-by-step explanation:

market price $50

expected rate of return /Re) = 14%

Div = $50 x 14% = $7

risk free rate (Rf) = 6%

market premium (Rm - Rf) = 8.5%

beta = ?

14% = 6% + (beta x 8.5%)

beta x 8.5% = 14% - 6% = 8%

beta = 8% / 8.5 = 0.941

if beta doubles to 1.882, then Re will be:

Re = 6% + (1.882 x 8.5%) = 22%

new market price of the stocks = $7 / 22% = $31.818 = $31.82