Suppose that • Return Ri:35% RM:28% • Volatility σi: 42% σM: 30% • Find a portfolio combination with the same level of risk than the benchmark (market)
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Suppose that
• Return Ri:35% RM:28%
• Volatility σi: 42% σM: 30%
• Find a portfolio combination with the same level of risk than the
benchmark (market)
According to Modigliani’s Risk adjustment performance measure, a portfolio can be levered or de-levered, that is shift upward or downward, to match the risk level of the market.
Step by step
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- You have observed the following returns over time: Assume that the risk-free rate is 6% and the market risk premium is 5%. What are the betas of Stocks X and Y? What are the required rates of return on Stocks X and Y? What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds) is 7.0%, and that the market risk premium is 5%. What is the required rate of return on the firms stock?An analyst has modeled the stock of a company using the Fama-French three-factor model. The market return is 10%, the return on the SMB portfolio (rSMB) is 3.2%, and the return on the HML portfolio (rHML) is 4.8%. If ai = 0, bi = 1.2, ci = 20.4, and di = 1.3, what is the stock’s predicted return?
- c) Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is foundto be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the requiredreturn on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B(B). (10 marks)d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to payreturns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standarddeviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also hasstandard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whetherasset A and B are overvalued or undervalued, and explain why. (10 marks)(Hint: Beta of asset i (??) =???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)Suppose the risk free rate is 2, 32%, the expected return of the market portfolio is 5, 64% and the beta of stock X-Bros S. A. is 1. 10. What is the expected cost of equity of X-Bros S. A. (in percent)?Using CAPM to determine the expected rate of return for risky assets, consider the following example stocks, assuming that you have already compute the betas Stock Beta A 0.70 B 1.00 C 1.15 D 1.40 E -0.30 Assume that we expect the economy’s RFR to be 5 percent (0.05) and the expected return on the market portfolio (E(RM)) to be 9 percent (0.09), 1, what would this imply? With these inputs, what would the be the following required rate of returns for these five stocks, show the formula for each in your calculations.
- The expected rate of return on a market portfolio is 7 percent. The riskless rate of interest is 4 percent. The beta of a company is 1.37. What is the required rate of return on this company's common equity?Portfolio Risk and Return: You are given the following distributions of returns for assets (single stock or portfolio) A, B, and C. Economic Conditions Probability Return on asset A B C Boom .30 60% 50% 10% Normal .40 40 30 50 Bust .30 20 10 90 Find the expected return (think of this as the mean return) and standard deviation of B and C. (A’s expected return is 40% and its standard deviation is 15.49%)Questions C and D is required. c) Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B (B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to pay returns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standard deviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also has standard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i ( , where are standard deviations of asset i and market portfolio, is the correlation between asset i and the market portfolio)
- Questions C and D is required. Thank you.c) Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B (B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to pay returns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standard deviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also has standard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i ( , where are standard deviations of asset i and market portfolio, is the correlation between asset i and the market portfolio)Suppose that the S&P 500, with a beta of 1.0, has an expected return of 13% and T-bills provide a risk-free return of 4%. What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P 500 of (i) 0; (ii) 0.25; (iii) 0.50; (iv) 0.75; (v) 1.0? How does expected return vary with beta?Consider a CAPM economy. The risk free rate (rf ) is 4% and the expected market return (rM )is 10%. (a) Stock 1: β = 0.90. Compute the expected return of stock 1. (b) Stock 2: β = 1.1. Compute the expected return of stock 2. (c) Portfolio 1: The proportions invested in stock 1, stock 2, and risk free asset are 30%, 30%,and 40%, respectively. Compute the beta and expected return of portfolio 1. (d) Portfolio 2: The proportions invested in stock 1, stock 2, and risk free asset are 50%, 60%,and -10%, respectively. Compute the beta and expected return of portfolio 2.
