Suppose that the risk free rate is 5 and the market portfolio has an expected return of 13 with a volatility of 18 Monsters Inc has a 24 volatility and a correlation with the market of 60 while California Gold Mining has a 32 volatility and a correlation with the market of 7 Assume the CAPM assumptions hold. Monsters' required return is closest to: a. 15.5%
b. 11.5%
c. 13.0%
d. 10.0%

The answer is option (b) 11.5 %

Explanation:

Solution

Given that

Risk free rate =Rf

= 5%

The market portfolio expected return is = E[Rm]

= 13%

Volatility or standard deviation of market return=σm

=18%

Volatility or standard deviation of Monsters' Inc. return =σi

=24%

The correlation of Monsters' Inc. return with the market = 0.6

Thus

Beta of Monsters' Inc. is computed by applying the formula shown below:

βi =Cov (i,M)/σ²m =ρ * σi *σm/σ²m

= ρ * σi/ σm

Here,

Cov(i,m) is the Covariance between the stick and the market return which is given by the formula below:

Cov(i,m) = ρ* σi*σm

ρ refers to the correlation between the stock i return and Market return

Hence, Beta of Monsters' Inc. becomes:

βi = (0.6*24%)/18% = 0.8

Now we compute the required return on Monsters Inc we will use the CAPM Equation given as:

CAPM Equation:

E[Ri] = Rf + βi*(E[Rm]-Rf)

So,

The Required return on Monsters' Inc. stock = E[Ri] =5% + 0.8*(13% - 5%)

= 5%+6.4%

=11.4%

Therefore Monsters' required return is nearest to: 11.4 % or 11.5%

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the answer is a.

by: nicholas dooley