INVESTMENTS-CONNECT PLUS ACCESS
11th Edition
ISBN: 2810022611546
Author: Bodie
Publisher: MCG
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Chapter 13, Problem 7PS
Summary Introduction
To calculate:To plot the capital market line with 9 stocks and the available 3 portfolios on a graph of average returns in comparison to the SD.Also compare the mean-variance efficiency of the three portfolios and the market index.
Introduction:Capital market line (CML) is a graph that mirrors the normal return of a portfolio comprising of every single imaginable extent between the market portfolio and a risk-free resource.
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Please answer all parts (a-d) with explanations thx.
Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively.(a) What is the variance of each stock?
(b) What is the firm-specific risk of each stock?
(c) What is the covariance between the two stocks?
Consider the expected return and standard deviation of the following two assets:
Asset 1: E[r1]=0.1 and σ1=0.2
Asset 2: E[r2]=0.3 and σ2=0.4
(a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation
space for the cases: (i) ρ12= -1, (ii) ρ12=0.
(b) Suppose ρ12=-1. Which portfolio has the minimal variance? What is the variance and
expected return of that portfolio?
(c) Derive the formula for the variance of a portfolio with four assets.
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- Suppose the average return on Asset A is 6.6 percent and the standard deviation is 8.6 percent and the average return and standard deviation on Asset B are 3.8 percent and 3.2 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. a. What is the probability that in any given year, the return on Asset A will be greater than 11 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the probability that in any given year, the return on Asset B will be greater than 11 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. In a particular year, the return on Asset A was −4.25 percent. How likely is it that such a low return will recur at some point in the future? (Do…arrow_forwarduppose the average return on Asset A is 7.1 percent and the standard deviation is 8.3 percent, and the average return and standard deviation on Asset B are 4.2 percent and 3.6 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. a. What is the probability that in any given year, the return on Asset A will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the probability that in any given year, the return on Asset B will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. In a particular year, the return on Asset A was −4.38 percent. How likely is it that such a low return will recur at some point in the future? (Do not round…arrow_forwardSuppose that there are four risky assets whose expected returns E(r) and variance- covariance matrix (S) are shown in the spreadsheet below. We also consider the portfolio weights of two portfolios x and y of risky assets (see Cells B8:E9): 1 8 Portfolio x 9 Portfolio y A FOUR-ASSET PORTFOLIO PROBLEM Variance-covariance, S 20 Portfolio variance, 21 Portfollo standard deviation o 0.10 0.01 0.03 0.05 11 Portfolio x and y statistics: Mean, variance, covariance, correlation 12 Mean, Ejr, 13 Variance, 14 Covariance() 15 Correlation P 16 17 Calculating returns of combinations of Portfolio x and Portfolio y 18 Proportion of x 19 Mean portfolio return, r 0.01 0.30 0.06 -0.04 0.20 0.20 10.50% 0.1216 0.0714 0.4540 ? ? ? 0.3 0.03 0.06 0.40 0.02 0.30 0.10 ? 0.05 0.02 0.50 0.40 0.10 0.10 0.60 Mean, Er Variance, 0.2014 Question il Question ili Mean returns E(r) ? 7% 9% 11% 20% Question i i. Write the Excel formula used to estimate the mean and variance of portfolio y in cells E12 and E13,…arrow_forward
- 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.arrow_forwardFollowing is information for the required returns and standard deviations of returns for A, B, and C. The correlation coefficients for each pair also are shown below in a matrix. Which is the portfolio you will recommend AB, AC, or BC, and why? A B C Required Rate of return 7% 10% 20% Standard Deviation 33% 54% 90% Coefficient A,B 0.16 Coefficient A,C 0.19 Coefficient B,C 0.17arrow_forwardCalculate the (a) expected return, (b) standard deviation, and (c) coefficient of variation for an investment with the following probability distribution: Probability Payoff 0.45 32.0% 0.35 -4.0% 0.20 -20.0%arrow_forward
- A3arrow_forwardExpected return and standard deviation. Use the following information to answer the questions: a. What is the expected return of each asset? b. What is the variance and the standard deviation of each asset? c. What is the expected return of a portfolio with 12% in asset J, 52% in asset K, and 36% in asset L? d. What is the portfolio's variance and standard deviation using the same asset weights from part (c)? Hint: Make sure to round all intermediate answers you will type. a. What is the expected return of asset J? (Round to four decimal places.) Data table (Click on the following icon in order to copy its contents into a spreadsheet.) Return on Asset J in State of Economy Boom Growth Stagnant Recession Probability of State 0.24 0.36 0.21 0.19 State 0.050 0.050 0.050 0.050 Return on Asset K in State 0.230 0.120 0.020 -0.060 Return on Asset L in State 0.250 0.190 0.065 - 0.190arrow_forwardAssuming that the rates of return associated with a given asset investment are normally distributed; that the expected return, r, is 18.7%; and that the coefficient of variation, CV, is 1.88, answer the following questions: a. Find the standard deviation of returns, sigma Subscript rσr. b. Calculate the range of expected return outcomes associated with the following probabilities of occurrence: (1) 68%, (2) 95%, (3) 99%.arrow_forward
- c. Suppose the risk-free rate is 4.2 percent and the market portfolio has an expected return of 10.9 percent. The market portfolio has a variance of .0382. Portfolio Z has a correlation coefficient with the market of .28 and a variance of .3285. According to the capital asset pricing model, what is the expected return on Portfolio Z?arrow_forwardConsider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 7%, and the market's average return was 14%. Performance is measured using an index model regression on excess returns. Index model regression estimates R-square Residual standard deviation, o(e) Standard deviation of excess returns. i. Alpha ii. Information ratio iii. Sharpe ratio iv. Treynor measure Stock A a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.) % Stock A 1% +1.2(rm rf) % 0.635 11.3% 22.6% Stock B % % Stock B 2% +0.8( rm -rf) b. Which stock is the best choice under the following circumstances? 0.466 20.1% 26.9% i. This is the only risky asset to be held by the investor. ii. This stock will be mixed with the rest of the investor's portfolio, currently composed solely of holdings in the market-index fund. iii. This is one of many stocks that the investor is analyzing to form an actively managed stock…arrow_forwardConsider the following variance-covariance matrix for Security A, Security B, and the Market: Variance-Covariance Matrix A B Market A 0.562500 0.091875 0.028125 0.091875 0.122500 0.021000 B Market 0.028125 0.021000 0.022500 For the coming year, the Market Risk Premium is 5.5 percent and the risk-free rate is 2.0 percent. Determine the required return for Security A using both the Capital Market Line and the Security Market Line (CAPM). What is the (absolute) difference between these two required returns? 12.375% O 16.875% 20.625% Ⓒ 7.700% 6.300%arrow_forward
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