a. What is the average expected return, r, for each asset over the 3-year period? b. What is the standard deviation, s, for each asset's expected return? c. What is the average expected return, rp, for each of the portfolios?
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- A particular firm’s portfolio is composed of two assets, which we will call" A" and "B." Let X denote the annual rate of return from asset A, and let Y denote the annual rate of return from asset B. Suppose that E(X) = 0.15, E(Y) = 0.20, SD (X) = 0.05, SD (Y) = 0.06, and CORR (X, Y) = 0.30. Use a spreadsheet to perform the following analysis. (a) What is the expected return of investing 50% of the portfolio in asset A and 50% of the portfolio in asset B? What is the variance of this return? (b) Replace CORR (X, Y) = 0.30 by CORR (X, Y) = 0.60, 0, -0.30, and -0.60 and answer the questions in part (a). What is the impact of correlation on the expected returns and its variance? Explain why this is so. (c) Suppose that the fraction of the portfolio that is invested in asset B is f, and so the fraction of the portfolio that is invested in asset A is (1 – f). Let f vary from f = 0.0 to f = 1.0 in increments of 5% (that is, f = 0.0, 0.05, 0.10, 0.15, ...), and compute the mean and the…Leon has in his investment a portfolio that paid him the rate of returns of 14 %, -13%, 15.6%, 17% and 19.5% over the past five years. Required: a)Calculate the arithmetic average return (AAR) and geometric average return (GAR) of the portfolio? If someone asks you what is the actual compounding rate of return of Leon’s portfolio over the past five year, which one (AAR or GAR) will be a better answer? b)Following is forecast for economic situation and Leon’s portfolio returns next year, calculate the expected return, variance and standard deviation of the portfolio. State of economy Probability Rate of returns Mild Recession 0.25 -2.5% Normal 0.45 13.5% Growth 0.30 20% c) Assume that expected return of the stock A in Leon’s portfolio is 13.2%. Beta of this stock is 1.2, risk free rate is 3.5%. Calculate market portfolio rate of return, which is used to compute the expected return of this stock by Capital Asset Pricing Model (CAPM)?Leon has in his investment a portfolio that paid him the rate of returns of 14 %, -13%, 15.6%, 17% and 19.5% over the past five years. Required: Calculate the arithmetic average return (AAR) and geometric average return (GAR) of the portfolio? If someone asks you what is the actual compounding rate of return of Leon’s portfolio over the past five year, which one (AAR or GAR) will be a better answer? (2 marks) Following is forecast for economic situation and Leon’s portfolio returns next year, calculate the expected return, variance and standard deviation of the portfolio. (4 marks) State of economy Probability Rate of returns Mild Recession 0.25 -2.5% Normal 0.45 13.5% Growth 0.30 20% c) Assume that expected return of the stock A in Leon’s portfolio is 13.2%. Beta of this stock is 1.2, risk free rate is 3.5%. Calculate market portfolio rate of return, which is used to compute the expected return of this stock by Capital Asset Pricing Model…
- Suppose you are considering investing your entire portfolio in three assets A, B and C. You expect that after you invest, four possible mutually exclusive scenarios will occur, with associated returns (in %) for each of the three assets as listed below. The probability of each scenario is given below (Attached image). Find the expected returns and standard deviations of Asset A, B & C. (HINT: the expected return is given by the probability-weighted sum of returns in each scenario. The expected standard deviation is given by the square root of the probability-weighted sum of squared deviations from the expected return.) Is there any reason to invest in Asset A given its low expected return and high standard deviation?You are going to invest $50,000 in a portfolio consisting of assets X, Y, and Z, as follows; What is the expected return of this portfolio? Calculate the beta coefficient of the portfolioTalal can pick one of two investment portfolios - A and B. Each requires an initial outlay of $100,000 and each has a most likely annualrate of return of 18%. Estimated the returns associated with each investment. Past estimates indicate that the probabilities of thepessimistic, most likely, and optimistic outcomes are 30%, 50%, and 20%, respectively. Note that the sum of these probabilities mustequal 100%; that is, they must be based on all the alternatives considered.Question:1. Explain him about risk aversion, risk neutrality and risk seeking on the bases of standard deviation and coefficient of variation.DetailsAsset AAsset B1.Initial Investment$100.000$100,000Rate of Return - Pessimistic16%10%Rate of Return - Most likely18%18%Rate of Return - Optimistic20%26%
- You are evaluating various investment opportunities currently available and you have calculated expected returns and standard deviations for five different well-diversified portfolios of risky assets:Portfolio Expected Return Standard DeviationQ 7.8% 10.5%R 10.0 14.0S 4.6 5.0T 11.7 18.5U 6.2 7.5a. For each portfolio, calculate the risk premium per unit of risk that you expect to receive ([E(R) − RFR]/σ). Assume that the risk-free rate is 3.0 percent.b. Using your computations in Part a, explain which of these five portfolios is most likely tobe the market portfolio. Use your calculations to draw the capital market line (CML).c. If you are only willing to make an investment with σ = 7.0%, is it possible for you toearn a return of 7.0 percent?d. What is the minimum level of risk that would be necessary for an investment to earn7.0 percent? What is the composition of the portfolio along the CML that will generatethat expected return?e. Suppose you are now willing to make an investment…David established an investment portfolio of two blue chips four years ago: Gold share and Silver Bond. Gold share accounts for 65% of his investment portfolio. Required: If David’s portfolio has provided the returns of 9.5%, 11.3%, - 12.5% and 15.6% over the past four years, respectively. Calculate geometric average return of the portfolio for this period? Assume that the below data is available for David’s portfolio performance, calculate the expected return, variance and standard deviation of the portfolio. Assume that expected return of the Gold share in David’s portfolio is 14.5%. The share’s beta coefficient is 1.5. Market risk premium is 7.5. Calculate the risk-free rate using Capital Asset Pricing Model Assume that David bought 2000 of Gold shares in his portfolio for a price of $75 each, the dividend paid for this stock is $7/stock each year. The current market price of this share is $135. Calculate the capital gain yield of this investment after four yearsYou are going to invest $20,000 in a portfolio consisting of assets X, Y, and Z, as follows: Asset Annual Return Probability Beta Proportion X 10% 0.50 1.2 0.333 Y 8% 0.25 1.6 0.333 Z 16% 0.25 2.0 0.333 Given the information in Table 5.2, The beta of the portfolio in Table 8.2, containing assets X, Y, and Z is ________. Select one: a. 1.6 b. 2.0 c. 1.5 d. 2.4
- Suppose you are considering investing your entire portfolio in three assets A, B and C. You expect that after you invest, four possible mutually exclusive scenarios will occur, with associated returns (in %) for each of the three assets as listed below. The probability of each scenario is given below. A B C Probabilities return 0.05 0.50% -3.60% 3.60% 0.35 0.60% 2.75% 0.15% 0.45 3.66% 1.45% 0.45% 0.15 -4.80% -0.60% 6.30% Find the expected returns and standard deviations of Asset A, B & C. (HINT: the expected return is given by the probability-weighted sum of returns in each scenario. The expected standard deviation is given by the square root of the probability-weighted sum of squared deviations from the expected return.) Is there any reason to invest in Asset A given its low expected return and high standard deviation?You have a portfolio of three assets at the beginning of the year: Asset 1 is 30% of the portfolio, Asset 2 is 40% of the portfolio, and Asset 3 is 30% of the portfolio. During the year, Asset 1 has a return of 4%, Asset 2 has a return of 12%, and Asset 3 has a return of -20%. What was the return on your portfolio for the year?Assume you are considering a portfolio containing Asset 1 and Asset 2. Asset 1 will represent 37% of the dollar value of the portfolio, and asset 2 will account for the other 63%. Assume that the portfolio is rebalanced at the end of each year. The expected returns over the next 6 years, 2021–2026, for each of these assets are summarized in the following table: Data table (Click on the icon here in order to copy the contents of the data table below into a spreadsheet.) Projected Return Year Asset L Asset M 2021 −9% 33% 2022 15% 5% 2023 26% −9% 2024 4% 18% 2025 −9% 33% 2026 33% −18% . a. Calculate the expected portfolio return, rp, for each of the 6 years. b. Calculate the average expected portfolio return, rp, over the 6-year period. c. Calculate the standard deviation of expected portfolio returns, sp, over…