Question

Correlation* Beta 0.78 1.33 Security Firm A Firm B Firm C The market portfolio The risk-free asset Expected Return Standard Deviation 0.103 0.38 0.147 0.167 0.58 0.12 0.18 0.05 0.57 0.42

a. Fill in the missing values in the table. (Leave no cells blank - be certain to enter 0 wherever required. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

b-1. What is the expected return of Firm A? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b-2. What is your investment recommendation regarding Firm A for someone with a well-diversified portfolio? Sell or Buy

b-3. What is the expected return of Firm B? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b-4. What is your investment recommendation regarding Firm B for someone with a well-diversified portfolio? Buy or Sell

b-5. What is the expected return of Firm C? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b-6. What is your investment recommendation regarding Firm C for someone with a well-diversified portfolio? Sell or Buy

Answer 1

a. $\beta$ _A = Cov(A,M)/($\sigma$_M²); $\rho$ (A,M) ₌ Cov(A,M)/($\sigma$_A*$\sigma$_M). Therefore, $\rho$ (A,M) = ($\beta$_A * $\sigma$ _M)/$\sigma$_A = 0.37

$\beta$B = Cov(B,M)/($\sigma$_M²); $\rho$ (B,M) ₌ Cov(B,M)/($\sigma$_B*$\sigma$_M). Therefore, $\sigma$ _B = ($\beta$B* $\sigma$ _M)/$\rho$(B,M) = 0.42

$\beta$C = Cov(C,M)/($\sigma$_M²); $\rho$ (C,M) ₌ Cov(C,M)/($\sigma$B*$\sigma$_M). Therefore, $\beta$ C = ($\rho$(C,M)* $\sigma$ _C)/$\sigma$_M = 1.35

Correlation of Market Portfolio with Market Portfolio is 1 & Beta for Market portfolio = 1. For Risk-free asset, standard deviation = 0, correlation with market = 0 & Beta = 0. Table below shows the filled-up values

	Expected Return	Std Dev	Correlation	Beta
Firm A	0.103	0.38	0.37	0.78
Firm B	0.147	0.42	0.57	1.33
Firm C	0.167	0.58	0.42	1.35
Market	0.12	0.18	1	1
Risk-free Asset	0.05	0	0	0

B. (1,2) -> Expected Return from A = 10.3%. As per CAPM, expected return of A for $\beta$ _A  is RA = Rf + $\beta$ _A *(RM-Rf) = 10.46%. As expected return from A is lower than return expected for its risk, investment recommendation for A in a well-balanced portfolio is sell.

B (3,4) -> Expected Return from B = 14.7%. As per CAPM, expected return of B for $\beta$ B is RB = Rf + $\beta$ B *(RM-Rf) = 14.31%. As expected return from B is higher than return expected for its risk, investment recommendation for B in a well-balanced portfolio is buy.

B (5,6) -> Expected Return from C = 16.7%. As per CAPM, expected return of C for $\beta$ C is RC = Rf + $\beta$ B *(RM-Rf) = 14.47%. As expected return from C is higher than return expected for its risk, investment recommendation for C in a well-balanced portfolio is buy.