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

You have been provided the following data about the securities of three firms, the market portfolio, and the risk-free asset:

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

2 3 4 a) b) Security Firm A Firm B Firm C The market portfolio The risk free asset Expected return Standard deviation Correlation Beta 0.103 0.38 0.37 0.78 0.147 0.42 0.57 1.33 0.167 0.58 0.42 1.35 0.12 0.18 1 1.00 0.05 Expected return = Risk free rate + beta*(market return - risk free rate) Expected return of Firm A = 0.05+0.78*(0.12-0.05) = 10.460% Expected return of Firm B =0.05+1.33*(0.12-0.05) = 14.310% Expected return of Firm C = 0.05+1.35*(0.12-0.05) = 14.450% 0 0 Sharpe ratio = (return on asset-risk free rate 0.13947 Sharpe ratio for firm A= (0.103 -0.05)/0.38 = 0.23095| Sharpe ratio for firm B= (0.147 -0.05)/0.42 = 0.20172 Sharpe ratio for firm C= (0.167 -0.05)/0.58 = We'll use the this formula to calculate Beta of asset. Beta of Asset = (Standard Deviation of Asset x Correlation with market) / Standard deviation of market We'll use the this formula to calculate correlation of firms. Alternatively, Correlation of Firm A = (Beta x Standard deviation of market) / Standard deviation of Firm A Alternatively, Standard deviation of Firm B = (Beta x Standard deviation of market) / Correlation of Firm B Firm A: Sell Firm A has lower correlation with the market portfolio, meaning it is providing higher diversification benefit in the portfolio. However, it is providing lower return than the market portfolio. It's sharpe ratio is the lowest among the three, so should sell Firm A The correlation of market portfolio with itself is 1. The correlation of risk free asset with market portfolio is 0. The standard deviation of risk free asset is 0. Firm B: Buy Firm B has higher correlation with the market portfolio, meaning it is providing less diversification benefit in the portfolio. However, it is providing higher return than the market portfolio. It's sharpe ratio is highest in among the three, so should buy firm B Firm C:Buy Firm C has relatively lower correlation with the market portfolio, meaning it is providing more diversification benefit in the portfolio. It is providing higher return than the market portfolio. Furthermore, It's sharpe ratio is quite high, so should buy firm C