Finance question set - risk and return

Looking for help with these problems, thanks!

HW4 I. Risk & Return Queston 1 Consider the following information on the economy and specific stocks and bonds: You believe that scenario (I) - (III) all have the same probability. Being optimistic, you believe that scenario (IV) has a probability twice as much as that of any of the other three. State of the Economy (I) Depression (II) Recession (III) Normal (IV) Boom RA -20% -10% 30% 50% RB -5% 10% 15% 20% RC 5% 5% 5% 5% a. Calculate the expected returns for stock A, B, and C. b. Calculate the total risk (standard deviation) for stock A, B, and C. c. Calculate the covariance between stock A and B. d. What is the correlation coefficient between stock A and C. e. What is the expected return and total risk of a portfolio with equal investments in stock A and B? f. What is the expected return and total risk of a portolio with 25% in A, 25% in B, and the remainder in stock C? 8 Queston 2 Consider a risky investment A, which is expected to generate a +38% return if the economy enters a boom state next year and a 14% return if the economy enters a recession. The probability of a recession state is one-and-a-half times as high as a boom state. A risk-free treasury bill has a return of 2%. What is the expected return on a portfolio where you borrow $75,000 at the risk free rate and invest this together with $125,000 of your own money in the risky investment? Queston 3 You have a portolio with a fifth of your money invested in Apple Computers, and the remaining part of your money is invested in Yahoo stock. The expected return on Apple is 20%. The expected return on your portfolio is 22.5%, the expected return on the market portfolio is 9%, and the return on T-bonds is 2%. What is the beta and expected return for Yahoo assuming the CAPM holds? Queston 4 Top-Risk Inc. has a beta of 3.8, while Safeway Inc. has a beta of -0.8. Risk-free T-bills ofer a 4.5% return and the market risk premium is 16.5%. You form a portfolio with equal amounts in all three assets (Top-Risk Inc., Safeway Inc., and T-bills). Assume the CAPM model holds. What is the expected return for the portolio? Queston 5 The Eagle Clothing Group has a beta of 0.6 and an expected return of 13%. Falcon Technologies Incorporated has a beta of 1.3 and an expected return of 23%. Both companies are believed to trade at fair prices. (a) Given this information, what is the risk-free rate of return? (b) Given this information, what is the expected return on the market portolio? Queston 6 Consider the following information about two stocks X and Y: Expected Return Standard Deviation () Covariance with Market Portfolio X Y 0.18 (18%) 0.06 0.00108 0.12 0.02 0.00036 The correlation between stocks X and Y is 0.2 and the risk-free rate of return is 8%. The market risk premium is 7% and the market portfolio has a standard deviation of 3%. a. Calculate the beta () for each stock based on the actual observations. b. Calculate the unsystematic risk for X and Y. c. Would you purchase X and Y given the above information? Explain your answer. d. Explain why it is irrational to invest in Y only? e. Assume you combine the two stocks in a portfolio with the goal to create an expected return of 15%. What proportion of your money should you invest in each of these stocks? f. Calculate the standard deviation of the portfolio from part (g). g. Calculate the beta of the portolio from part (g). h. Consider an investment in a combination of the two stocks that generates the same expected return as the market. Is this portfolio eficient? Why or why not? HW4 I. Risk & Return Queston 1 Consider the following information on the economy and specific stocks and bonds: You believe that scenario (I) - (III) all have the same probability. Being optimistic, you believe that scenario (IV) has a probability twice as much as that of any of the other three. State of the Economy (I) Depression (II) Recession (III) Normal (IV) Boom RA -20% -10% 30% 50% RB -5% 10% 15% 20% RC 5% 5% 5% 5% a. Calculate the expected returns for stock A, B, and C. b. Calculate the total risk (standard deviation) for stock A, B, and C. c. Calculate the covariance between stock A and B. d. What is the correlation coefficient between stock A and C. e. What is the expected return and total risk of a portfolio with equal investments in stock A and B? f. What is the expected return and total risk of a portolio with 25% in A, 25% in B, and the remainder in stock C? 8 Queston 2 Consider a risky investment A, which is expected to generate a +38% return if the economy enters a boom state next year and a 14% return if the economy enters a recession. The probability of a recession state is one-and-a-half times as high as a boom state. A risk-free treasury bill has a return of 2%. What is the expected return on a portfolio where you borrow $75,000 at the risk free rate and invest this together with $125,000 of your own money in the risky investment? Queston 3 You have a portolio with a fifth of your money invested in Apple Computers, and the remaining part of your money is invested in Yahoo stock. The expected return on Apple is 20%. The expected return on your portfolio is 22.5%, the expected return on the market portfolio is 9%, and the return on T-bonds is 2%. What is the beta and expected return for Yahoo assuming the CAPM holds? Queston 4 Top-Risk Inc. has a beta of 3.8, while Safeway Inc. has a beta of -0.8. Risk-free T-bills ofer a 4.5% return and the market risk premium is 16.5%. You form a portfolio with equal amounts in all three assets (Top-Risk Inc., Safeway Inc., and T-bills). Assume the CAPM model holds. What is the expected return for the portolio? Queston 5 The Eagle Clothing Group has a beta of 0.6 and an expected return of 13%. Falcon Technologies Incorporated has a beta of 1.3 and an expected return of 23%. Both companies are believed to trade at fair prices. (a) Given this information, what is the risk-free rate of return? (b) Given this information, what is the expected return on the market portolio? Queston 6 Consider the following information about two stocks X and Y: Expected Return Standard Deviation () Covariance with Market Portfolio X Y 0.18 (18%) 0.06 0.00108 0.12 0.02 0.00036 The correlation between stocks X and Y is 0.2 and the risk-free rate of return is 8%. The market risk premium is 7% and the market portfolio has a standard deviation of 3%. a. Calculate the beta () for each stock based on the actual observations. b. Calculate the unsystematic risk for X and Y. c. Would you purchase X and Y given the above information? Explain your answer. d. Explain why it is irrational to invest in Y only? e. Assume you combine the two stocks in a portfolio with the goal to create an expected return of 15%. What proportion of your money should you invest in each of these stocks? f. Calculate the standard deviation of the portfolio from part (g). g. Calculate the beta of the portolio from part (g). h. Consider an investment in a combination of the two stocks that generates the same expected return as the market. Is this portfolio eficient? Why or why not