Problem 1 Consider the following information about three stocks: Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom Average Poor 0.2 40% 15% 7% 0.3 15% 30% 7% 0.3 5% -5% 7% Recession 0.2 -20% 5% 7% Your portfolio manager has invested 30% of your money in Stock A, 50% in Stock B, and 20% in Stock C. a) What is the expected return of your portfolio? b) What is the covariance between Stocks A and B? c) What is the correlation coefficient between Stocks B and C? d) What is the standard deviation of your portfolio? Hint: Instead of using the portfolio variance formula for three stocks, you can save time by calculating the return on the portfolio for all four states of the economy, and then calculate the standard deviation of these portfolio returns.

Problem 1 Consider the following information about three stocks: Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom Average Poor 0.2 40% 15% 7% 0.3 15% 30% 7% 0.3 5% -5% 7% Recession 0.2 -20% 5% 7% Your portfolio manager has invested 30% of your money in Stock A, 50% in Stock B, and 20% in Stock C. a) What is the expected return of your portfolio? b) What is the covariance between Stocks A and B? c) What is the correlation coefficient between Stocks B and C? d) What is the standard deviation of your portfolio? Hint: Instead of using the portfolio variance formula for three stocks, you can save time by calculating the return on the portfolio for all four states of the economy, and then calculate the standard deviation of these portfolio returns.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Returns State of Economy Prob J K Recession 0.25 -0.02 0.034 Normal 0.6 0.138 0.062 Boom 0.15 0.218 0.092 Based on the following information, a.What are the covariance and correlation between the returns of the two stocks? b.Calculate the portfolio return and portfolio standard deviation if you invest equally in each asset.
Read the information for 3 stocks X, Y and Z below. Rate of return when state occurs (For Stock X, Y, and Z) State of Economy Probability of State Stock X Stock Y Stock Z Boom 0.3 0.4 0.45 0.6 Normal 0.5 0.2 0.15 0.08 Recession 0.2 0 -0.3 -0.4 If your portfolio includes 35 percent of X, 40 percent of Y and 25 percent of Z, answerthe following questions: (a) Calculate the portfolio expected return.(b) Calculate the variance and the standard deviation of the portfolio (c) If the expected T-bill rate is 3.80 percent, calculate the expected risk premiumon the portfolio.
Consider the following information: State of Economy Probability of State of Economy Rate of Return if State Occurs Stock A Stock B Recession 0.30 0.05-0.15 Normal 0.55 0.15 0.15 Boom 0.15 0.20 0.35 Calculate the expected return for the two stocks.
Returns State of Economy Prob J K Recession 0.25 -0.02 0.034 Normal 0.6 0.138 0.062 Boom 0.15 0.218 0.092 Based on the following information, 1. calculate the expected return and standard deviation for each of the following stocks. 2.What are the covariance and correlation between the returns of the two stocks? 3.Calculate the portfolio return and portfolio standard deviation if you invest equally in each asset.
Plz show the formula step by step. There is the following table shows the probabilities of occurrence of 3 states and the expected rate of returns on stocks A and B State Probability Expected rate ofReturns on Stock A Expected rate ofReturns on Stock B Boom 0.5 0.25 0.20 Neutral 0.3 0.15 0.10 Recession 0.2 0.05 0.02 (A) Calculate the expected rates of returns and standard deviations of stocks A and B. The colleague has given you his forecasts of stocks C and D as follows: State Probability Expected rate ofReturns on Stock C Expected rate ofReturns on Stock D Boom 0.7 0.40 -0.10 Bust 0.3 -0.05 0.30 She would like to invest 80% of his money in stock C and 20% of her money in stock D to construct a portfolio.(B) Calculate the portfolio's expected rate of returns and its standard deviation
Consider the following information on two stocks: P(State) Stock A Stock B Boom 20% 30% 20% Normal 50% 12% -5% Slow 15% 4% 8% Recession 15% -10% 10% $Investment Beta Asset A $35,000 1.45 Asset B $15,000 0.85 Q1. Calculate the weight of A in the portfolio. (Enter percentages as decimals and round to 4 decimals) Q2. Calculate the expected return on the portfolio. (Enter percentages as decimals and round to 4 decimals) Q3. Calculate the standard deviation of the portfolio. (Enter percentages as decimals and round to 4 decimals).
State of Economy Probability of State of Economy Rate of Return if State Occurs Stock A Stock B Recession 0.20 0.05 -0.17 Normal 0.55 0.08 0.12 Boom 0.25 0.13 0.29 a) The expected return of Stock A b) The expected return of Stock B c) The expected return of Portfolio where you invest $35,000 in Stock A and $45,000 in Stock B d) Suppose Stock A has a beta of 0.8 and Stock B has a beta of 1.3. If you invest $35,000 in Stock A and $45,000 in Stock B, what is the beta of this portfolio? e) Expected return on the market (RM ) is 10% and the risk-free (rf) is 4%. What must the the expected return on the portfolio according to CAPM? (Use the beta you have calculated in section d) for CAPM)
An analyst gathers the following data: * Expected (estimated) rate of return on the market = 15% * Risk Free Rate = 8% * Expected (estimated) rate of return on stock X = 17% * Stock X's beta = 1.75 Using these data and the capital asset pricing model, which of the following statements about X's stock is true? Stock X is: a. properly valued b. overvalued by 1.75% c. undervalued by 1.40% d. undervalued by 0.25%
Consider the following information about three stocks: State of Economy Probability of State of Economy Rate of Return If State Occurs Stock A Stock B Stock C Boom .25 .13 .29 .60 Normal .60 .08 .11 .13 Bust .15 .02 −.18 −.45 a-1. If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio expected return? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a-2. What is the variance? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., .16161.) a-3. What is the standard deviation? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. If the expected T-bill rate is 3.70 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g.,…
What is the expected return of an equally weighted portfolio comprised of the following three stocks? State ofEconomy Probability ofState of Economy Rate of Returnif State Occurs Stock A Stock B Stock C Boom .25 .19 .13 .07 Normal .72 .15 .05 .13 Bust .03
(Expected rate of return and risk) Syntex, Inc. is considering an investment in one of two common stocks. Given the information that follows, which investment is better, based on the risk (as measured by the standard deviation) and return? Common Stock A Common Stock B Probability Return Probability Return0.20 10% 0.15 -4% 0.60 16% 0.35 7%0.20 21% 0.35 13% 0.15 20% a) Syntex, Inc. is considering an investment in one of two common stocks. Given the information that follows, what is the expected rate of return for stock A? What is the standard deviation? b. Syntex, Inc. is considering an investment in one of two common stocks. Given the information that follows, what is the expected rate of return for stock B? What is the standard deviation? c. Based on the risk (as measured by the standard deviation) and return of each stock, which…
Consider a three-factor APT model. The factors and associated risk premiums are: Factor Risk Premium (%) Change in gross national product (GNP) +6.9 Change in energy prices 0.4 Change in long-term interest rates +2.6 Calculate expected rates of return on the following stocks. The risk-free interest rate is 4.8%. A stock whose return is uncorrelated with all three factors. (Enter your answer as a percent rounded to 1 decimal place.) A stock with average exposure to each factor (i.e., with b = 1 for each). (Enter your answer as a percent rounded to 1 decimal place.) A pure-play energy stock with high exposure to the energy factor (b = 1.9) but zero exposure to the other two factors. (Enter your answer as a percent rounded to 2 decimal places.) An aluminum company stock with average sensitivity to changes in interest rates and GNP, but negative exposure of b = –1.9 to the energy factor. (The aluminum company is energy-intensive and suffers when energy prices…

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