Question

The market price of a security is $26. Its expected rate of return is 13%. The risk-free rate is 5% and the market risk premium is 7.0%. What will be the market price of the security if its correlation 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. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

$16.125≅ $16.13

Step-by-step explanation:

in the question

Correlation coefficient β doubles

we know that

Required return= risk free return + (market risk premium)*β

0.13= 0.05 + 0.07*β

β= 1.1428

current β of 1.1428

now
`k=(D)/(P)`

where

k= expected return

D= expected dividend after the end of the year

P= current market prize per share

`D=P* k`

`D=26*0.13` =3.38

so current dividend is $3.38 per share

now, when β doubles it become 2.28

hence required return = 0.05 +0.07*2.28

= 0.2096

=20.96%

The dividend remains the same D= $3.38

now
`k=(D)/(P)`

`P=(D)/(k)`

`P=(3.38)/(0.2096)`

=$16.125

so, when the β doubles, the prize of the market per share becomes $16.125