Table 1: Data for Mean-Variance Portfolio Optimization Stock A Stock B Stock C 2% 8% 2% 12% Return Volatility Correlation A B C 10% 18% A 1 B -0.2 1 C 0.7 0.1 1
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There are three stocks, A, B, and C, with the following expected return, volatility, and correlation data. You are asked to generate a mean-variance portfolio, the expected return of which should be no less than 8%. What’s your optimal allocation (portfolio weights) for those three stocks?
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- Find out the 1- standard deviation 2- variance weight Investment*expected return stock weight Investment Investment Amount expected return stock stocks 0.261 1.45 75000 0.18 Alba Co. 0.0504 0.56 75000 0.09 Batelco Co. 0.0371 0.1 75000 0.371 Delmon poultry. 0.3485 225000 TotalSuppose that the index model for stocks A and B is estimated from excess returns with the following results: RA= 4.0% + 0.50RM + eA RB= -1.2% + 0.7RM + eB sigmaM= 17% ; R-squareA = 0.26 ; R-squareB= 0.18 Break down the variance of each stock to the systematic and firm-specific components (write in decimal form, rounded to 4 decimal places). Risk for A Risk for B Systematic Firm-specificReturns on stocks X and Y are listed below: Period 1 2 3 4 5 6 7 Stock X 7% 1% -2% -3% 5% 11% 5% Stock Y -4% 10% 4% 8% 7% -1% -3% Consider a portfolio of 70% stock X and 30% stock Y. What is the (population) variance of portfolio returns? Please round your answer to six decimal places. Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.
- 11-3 Given the following information on a portfolio of Stock X and Stock Y, what is the portfolio standard deviation? Probability of boom state = 20% Probability of normal state = 80% Expected return on X = 13% Expected return on Y = 11% Variance on X = 0.0036 Variance on Y = 0.0144 Portfolio weight on X = 50% Portfolio weight on Y = 50% Correlation between X and Y = –1 Select one: a. 1% b. 2% c. 3% d. 6% e. 9%The standard deviation of return on stock A is 15% and the standard deviation on stock B is 15%. The correlation coefficient between the returns on stock A and B is -.25%. The rate of return for stocks A and B is 15% and 15% respectively. What is the standard deviation of return on the minimum-variance portfolio? a) 11.73% b) 12.00% c) 8.80% d) 9.35%Suppose the index model for stocks A and B is estimated with the following results: rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB, σM = 20%, and RM = rM − rf . The regression R2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. Total: (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?
- assume that the following data available for the portfolio, calculate the expected return, variance and standard deviation of the portfolio given stock A account for 45% an stock B account for 55% of you portfolio? A B Expexted return 12.5% 18.5% standard deviation of return 15% 20% correlation of cofficient(p) 0.4The following information are available: [3] Stock A Stock B Expected Return 16% 12% Standard Deviation 5% 8% Coefficient of Correlation 0.60 What is the co-variance between stock A & B? What is the expected return and risk of a portfolio in which A and B have weights of 0.60 and 0.40 respectively?Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + .7RM + eARB = −2% + 1.2RM + eBσM = 20%; R-squareA = .20; R-squareB = .12Break down the variance of each stock into its systematic and firm-specific components.
- Given: Expected return Share A(ȓA) =15% Expected return Share B (ȓB) = 15% Expected return Portfolio A and B (ȓAB) = 15% By using the above information, demonstrate the rate of risk (variance and standard deviation) for each of: (i) Share A (ii) Share B (iii) Portfolio A and BSuppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively.(a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?
