EBK INVESTMENTS
11th Edition
ISBN: 9781259357480
Author: Bodie
Publisher: MCGRAW HILL BOOK COMPANY
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Chapter 7, Problem 16PS
Summary Introduction
To calculate: Expected return of portfolio.
Introduction: Expected return is the expected value of the probable distribution of
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Suppose that you have $1 million and the following two opportunities from which to construct a portfolio:
a. Risk-free asset earning 13% per year.
b. Risky asset with expected return of 27% per year and standard deviation of 40%.
If you construct a portfolio with a standard deviation of 28%, what is its expected rate of return? (Do not round your intermediate
calculations. Round your answer to 1 decimal place.)
Expected return on portfolio
%
Suppose you have $2,000 to invest. The market portfolio has an expected return of 10.5 percent and a standard deviation of 16 percent. The risk-free rate is 3.75 percent.
How much should you invest in the risk-free asset if you wish to have a 15 percent return on the portfolio?
In this problem we assume that the annual expected rate of return of the market portfolio is 22%
and the annual risk-free rate is 2%. The standard deviation of the market portfolio returns is 22%.
Assume the market is in equilibrium such that the Capital Asset Pricing Model (CAPM) holds: the
market portfolio is efficient.
If you have $1,000 to invest, how should you allocate it to achieve an annual expected return of
26%?
Invest $260 in the risk-free asset and $740 in the market portfolio
Invest $800 in the risk-free asset and $200 in the market portfolio
Invest $1,200 in the risk-free asset and sell short $200 in the market portfolio
Borrow $260 at the risk-free rate and invest $1,260 in the market portfolio
Invest $200 in the risk-free asset and $800 in the market portfolio
Borrow $200 at the risk-free rate and invest $1,200 in the market portfolio
Chapter 7 Solutions
EBK INVESTMENTS
Ch. 7 - Prob. 1PSCh. 7 - Prob. 2PSCh. 7 - Prob. 3PSCh. 7 - Prob. 4PSCh. 7 - Prob. 5PSCh. 7 - Prob. 6PSCh. 7 - Prob. 7PSCh. 7 - Prob. 8PSCh. 7 - Prob. 9PSCh. 7 - Prob. 10PS
Ch. 7 - Prob. 11PSCh. 7 - Prob. 12PSCh. 7 - Prob. 13PSCh. 7 - Prob. 14PSCh. 7 - Prob. 15PSCh. 7 - Prob. 16PSCh. 7 - Prob. 17PSCh. 7 - Prob. 18PSCh. 7 - Prob. 19PSCh. 7 - Prob. 20PSCh. 7 - Prob. 21PSCh. 7 - Prob. 22PSCh. 7 - Prob. 23PSCh. 7 - Prob. 1CPCh. 7 - Prob. 2CPCh. 7 - Prob. 3CPCh. 7 - Prob. 4CPCh. 7 - Prob. 5CPCh. 7 - Prob. 6CPCh. 7 - Prob. 7CPCh. 7 - Prob. 8CPCh. 7 - Prob. 9CPCh. 7 - Prob. 10CPCh. 7 - Prob. 11CPCh. 7 - Prob. 12CPCh. 7 - Prob. 13CP
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- You invest R100 in a risky asset with an expected rate of return of 15% and a standard deviation of 20% and a T-bill with a rate of return of 4%. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 9%. What is the percentage invested in risky asset ?What is the percentage invested in risk-free asset ?arrow_forwardYou 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. 2.4arrow_forward2. Consider the following investment: A portfolio that pays a 30% rate of return with a probability of 60% or a 15% rate of return with a probability of 40%. If you invest $50,000 in this portfolio, what would be your expected profit?arrow_forward
- Assume the riskless rate of interest is 2% per year, and the expected rate of return on the market portfolio is 8% per year. According to the CAPM, what is the efficient way for an investor to achieve an expected rate of return of 5% per year? If the standard deviation of the rate of return on the market portfolio is 4%, what is the standard deviation of the portfolio producing the 5% expected return? • Plot the CML and locate the foregoing portfolios on the same graph. • Plot the SML and locate the foregoing portfolios on the same graph.arrow_forwardConsider a risky portfolio. The end - of - year cash flow derived from the portfolio will be either $70,000 or $200,000 with equal probabilities of 0.5. The alternative risk - free investment in T - bills pays 2% per year. Required: If you require a risk premium of 8%, how much will you be willing to pay for the portfolio? Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio? Now suppose that you require a risk premium of 12 % . What price are you willing to pay?arrow_forwardAssume you have two assets A and B. You know the expected return and standard deviation of returns for each asset. This information is shown in the table below. You plan to put 50% of your wealth into each assets. What would the expected return be for the portfolio? Asset A B 0.03 0.27 0.135 0.15 returns 12% 15% standard deviations 20% 40%arrow_forward
- Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $75,000with a probability of 25%, $125,000 with a probability of 50%, or $140,000 with a probability of 25%.The alternative risk-free investment in T-bills pays 4% per year. a) If you require a risk premium of 8%, how much will you be willing to pay for the portfolio?b) What is the Sharpe ratio of the portfolio if you can purchase it at the price calculated above?arrow_forwardWhat is the expected return of a portfolio that has $8,000 invested in S and $2,000 invested in T? The risk-free rate is 6% and the market portfolio's return is 14%. Do you expect the investment to be a good one for the coming year if betas for the two portfolio components are 0.6 and 1.3, respectively?arrow_forwardThe risk-free rate is currently 3.3%, and the market return is 14.8%. Assume you are considering the following investments: Investment Beta A 1.54 B 1.16 C 0.51 D 0.11 E 2.14 . a. Which investment is most risky? Least risky? b. Use the capital asset pricing model (CAPM) to find the required return on each of the investments. c. Find the security market line (SML), using your findings in part b. d. On the basis of your findings in part c, what relationship exists between risk and return? Explain.arrow_forward
- Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $150,000 or $290,000 with equal probabilities of 0.5. The alternative risk-free investment in T-bills pays 3% per year. Required: a. If you require a risk premium of 7%, how much will you be willing to pay for the portfolio? b. Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio? c. Now suppose that you require a risk premium of 12%. What price are you willing to pay? Complete this question by entering your answers in the tabs below. Required A Required B Required C If you require a risk premium of 8%, how much will you be willing to pay for the portfolio? Note: Do not round your intermediate calculations. Round your answer to the nearest whole dollar amount. Price Required A Required B >arrow_forwardNow assume that your portfolio only includes a risky asset, Asset C and a risk-free asset, Asset D. If the expected return on Asset D is 18%, the expected return on your po is 12% and the percentage of your wealth allocated to Asset C is 30%, what is the risk-free rate?arrow_forwardConsider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $95,000 or $360,000 with equal probabilities of 0.5. The alternative risk-free investment in T-bills pays 6% per year. a. If you require a risk premium of 9%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest whole dollar amount.) Price b. Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio? (Round your answer to the nearest whole number.) Rate of return % c. Now suppose that you require a risk premium of 13%. What price are you willing to pay? (Round your answer to the nearest whole dollar amount.) Pricearrow_forward
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