1. Calculate the expected return and standard deviation of a portfolio that is 80% Large Cap Stocks and 20% Corporate Bonds. Show your work. The expected return on Large Cap Stocks is 12% with a standard deviation of 20%. The expected return on Corporate Bonds is 6% with a standard deviation of 8%. The correlation between Large Cap stocks and corporate bonds is 0.17. SHOW YOUR WORK FOR ALL THE QUESTIONS. 2. Using the data in Question #1, calculate the Minimum Variance Portfolio (MVP) weights for a 2- asset portfolio of Large Cap Stocks and Corporate Bonds.
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- (4) Please answer the following short questions with what you have learned. There is a portfolio of two assets - 30% investment in Stock A and 70% investment in Stock B. The correlation of returns between Stock A and Stock B is 0.50. The covariance between these two stocks is 0.0043, and the standard deviation of the return of Stock B is 26%. Requirements: (a) Please calculate the standard deviation of the return of Stock A. (b) Please calculate the standard deviation of the return of portfolio. (c) If we increase more and more different stocks in the portfolio, will it always decrease the risk (standard deviation) of the return of the portfolio? Please explain your answer in detail.In-class Example 4: Portfolio Risk Return Suppose that a portfolio of stocks has an expected return E(rS) = 12% and a standard deviation of returns sS = 20%. A portfolio of corporate bonds has an expected return E(rB) = 6% and a standard deviation sB = 9%. a) What is the expected portfolio return and portfolio standard deviation for an equally weighted combination of the stock and bond portfolio if the correlation between stock and bond portfolio returns, rSB, is -0.5? b) Suppose you require a portfolio expected return of 15% per year. What weights must you assign to the stock and bond portfolios to achieve this expected return? What is the standard deviation of returns for this combination portfolio if the correlation between stock and bond returns is -0.5? C) Suppose that the standard deviation of the market (sM) is 15% and the correlation between the stock portfolio and the market is 0.7. What is the beta of the stock portfolio?f. Estimate Bartman's and Reynolds's betas by running regressions of their returns against the index's returns. Round your answers to four decimal places. Bartman's beta: fill in the blank 30 Reynolds's beta: fill in the blank 31 Are these betas consistent with your graph? These betas consistent with the scatter diagrams. g. Assume that the risk-free rate on long-term Treasury bonds is 4.5%. Assume also that the average annual return on the Winslow 5000 is not a good estimate of the market's required return—it is too high. So use 9% as the expected return on the market. Use the SML equation to calculate the two companies' required returns. Round your answers to two decimal places. Bartman's required return: fill in the blank 33 % Reynolds's required return: fill in the blank 34 % h. If you formed a portfolio that consisted of 50% Bartman and 50% Reynolds, what would the portfolio's beta and required return be? Round your answer for the portfolio's beta to four decimal places and…
- a. Determine Stock X's beta coefficient. b. Determine the arithmetic average rates of return for Stock X and the NYSE over the period given. Calculate the standard deviations of returns for both Stock X and the NYSE. c. Assume that the required return on equity, re, for Stock X is equal to its average return. Likewise, assume that the market return is equal to the NYSE's average return. Using the information calculated, what is the assumed risk-free rate in the CAPM equation? Hint: Solve algebraically for rf in, re = r¡ + B(rm – r;)Suppose that there exist two securities (A and B) with annual expected returns equal to ra = 3% and rg = 5% and standard deviations equal to o4 = 7% and oB = 10% respectively. The correlation coefficient between the returns of these securities is p = -0.5. What is the expected return and the standard deviation of an equally weighted portfolio consisting of the securities A and B? Describe every step of your calculations in detail. What is the expected return and the standard deviation of a portfolio consisting of the securities A and B, if the relevant weights are chosen to minimize the risk of the portfolio? Present the minimisation problem and describe every step of your calculations in detail. How could an investor maximize diversification benefits? Critically discuss and explain in detail.You are given the following data: Risk-free rate is 4.1 percent, market return is 6.5 per cent, and market volatility is 12.2 per cent. The return of a portfolio is 11 per cent, its volatility is 15.2214 per cent, and its beta is 0.7. Calculate the measure called the Information ratio. A. 0.193 B. 0.414 C. 0.548 D. 4.500
- Karen Kay, a portfolio manager at Collins Asset Management, is using thecapital asset pricing model (CAPM) for making recommendations to her clients.Her research department has developed the information shown in the followingexhibit.Forecast Returns, Standard Deviations, and BetasForecast Return Standard Deviation BetaLow β stock (X) 14.0% 36% 0.8High β stock (Y) 17.0% 25% 1.5Market index 14.0% 15% 1.0Risk-free rate 5.0%(a) Calculate expected return and alpha for each stock.(b) Identify and justify which stock would be more appropriate for an investorwho wants to add this stock to a well-diversified equity portfolio.(c) Now consider Karen employs the “Betting Against Beta” strategy and let, , and denote the portfolio weights of the investmentin each of the asset classes (e.g. risk-free asset, low beta stock, market index,high beta stock, respectively) such that .According to its investment mandate, Collins Asset Management shouldtarget a gross leverage of 2.3. How much does she have to…What is the formula for the Sharpe Ratio for a two-asset portfolio of stocks and bonds with equal expected returns, i.e., E(RS)= E(RB), and a perfect negative correlation. Can use XS, sS for the portfolio weight and standard deviation of stocks, and XB, sB for the portfolio weight and standard deviation of bonds.Suppose that the capital asset pricing model (CAPM) applies. The risk premium of a stock is 3 percent and the risk premium of the market portfolio is 2. The standard deviation of the market portfo- lio is 6. Compute the covariance between the stock and the market portfolio.
- 2. Suppose that the market model for stocks A and B is estimated with the following results: RA = 1% +0.9*RM+EA RB = -2% + 1.1*RM+EB The standard deviation of the markets returns is 20% and firm specific risk (standard deviation) equals 30% for A and 10% for B. a. Compute the risk (standard deviation) of each stock and the covariance between them. Suppose we form an equally weighted portfolio of stocks A and B. What will be the nonsystematic standard deviation of that portfolio? b.When working with the CAPM, which of the following factors can be determined with the most precision? a. The beta coefficient of "the market," which is the same as the beta of an average stock. b. The beta coefficient, bi, of a relatively safe stock. c. The market risk premium (RPM). d. The most appropriate risk-free rate, rRF. e. The expected rate of return on the market, rM.Suppose that you observe the following information in Table 2 for stocks A and B: Table 2 Expected Return (%) 11% Stock Beta A 0.8 B 14% 1.5 The risk-free rate of return is 6% and the expected rate of return on the market index is 12%. Using the Single-Index Model, calculate the alpha of both stocks. Show your calculations. Explain what the alpha of the single-factor model represents and interpret your results.