Concept explainers
Consider the two (excess return) index~m0del regression results for stocks A and B. The risk-free rate over the period was
Stock A | Stock B | |
Index model regression estimates |
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R-square |
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Residual standard deviation. |
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Standard deviation of excess returns |
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a. Calculate the following statistics for each stock:
i. Alpha
ii. Information ratio
iii. Sharpe ratio
iv. Treynor’s measure
b. Which stock is the best choice under the following circumstances?
i. This IS the only risky asset to be held by the investor.
ii. This stock will be mixed with the zest 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 portfolio.
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Chapter 18 Solutions
Essentials Of Investments
- Consider the two (excess return) Index-model regression results for stocks A and B. The risk-free rate over the period was 4%, and the market's average return was 11%. Performance is measured using an Index model regression on excess returns. Stock A Stock B Index model regression estimates R-square 1% +1.2(rm -rf) 2% +0.8(M-r) Residual standard deviation, d(e) Standard deviation of excess returns 0.683 12.1% 23.4% 0.49 20.9% 28.5% Required: a. Calculate the following statistics for each stock: b. Which stock is the best choice under the following circumstances? Answer is complete but not entirely correct. Complete this question by entering your answers in the tabs below. Required A Required B Calculate the following statistics for each stock: Note: Round your answers to 4 decimal places. Stock A Stock B i. Alpha 1.0000 % 2.0000 % ii. Information ratio 0.0826 0.0957 iii. Sharpe ratio 0.4017 0.2667 iv. Treynor measure 0.0783x 0.0950 xarrow_forwardConsider the two (excess return) index model regression results for A and B: RA = 0.8% + 1RM R-square = 0.588 Residual standard deviation = 10.8% RB = –1.2% + 0.7RM R-square = 0.452 Residual standard deviation = 9% a. Which stock has more firm-specific risk? A. Stock A B. Stock B Which stock has greater market risk? A. Stock A B. Stock B b. For which stock does market movement has a greater fraction of return variability? A. Stock A B. Stock B c. If rf were constant at 4.5% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)arrow_forwardConsider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 6%, and the market’s average return was 13%. Performance is measured using an index model regression on excess returns. Stock A Stock B Index model regression estimates 1% + 1.2(rM − rf) 2% + 0.8(rM − rf) R-square 0.588 0.442 Residual standard deviation, σ(e) 10.5% 19.3% Standard deviation of excess returns 21.8% 25.3% a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.) stock A (%) Stock B (%) i. Alpha ii. Information ratio iii. Sharpe ratio iv. Treynor measure b. Which stock is the best choice under the following circumstances? i. This is the only risky asset to be held by the investor ii. This stock will be mixed with the rest of the investors' portfolio, currently composed solely of holdings in the market-index fund. iii. This is one…arrow_forward
- Consider the two (excess return) index model regression results for A and B. RA = 1.5% + 1.7RM R-square = 0.622 Residual standard deviation = 12% RB = -2.4 % +1.3RM R-square=0.468 Residual standard deviation = 9.8% Required: a. Which stock has more firm-specific risk? b. Which stock has greater market risk? c. For which stock does market movement explain a greater fraction of return variability? d. If rf were constant at 5.5% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A? Complete this question by entering your answers in the tabs below. Required A Required B Required C Required D If rf were constant at 5.5% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A? Note: Negative value should be indicated by a minus sign. Round your answer to 2 decimal places. Intercept %arrow_forwardYou run a regression for the Tesla stock return on a market index to estimate the SML equation and find the following Excel output: Multiple R R-Square Adjusted R-Square Standard Error Observations Intercept Market = 0.28 0.25 0.02 40.01 60 13.35 and 0.97 0.8 and 0.1 0.28 and 0.25 0.26 and 1.36 0.2 and 0.75 Coefficients Standard Error t-Stat p-Value 0.2 0.75 The resulting SML equation for Laternios is given by: Er Laternios] 13.35 0.26 0.80 0.97 1.36 0.10 + __ × (E[rM] - rf)arrow_forwardSuppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 0.03 + 0.7 RM + eA RB = -0.02+ 1.2 RM + eB σM =0.20; R-square A = 0.25 R-square B = 0.20 What is the standard deviation of A & B, respectively? Group of answer choices 0.54, 0.28 0.28, 0.54 0.45, 0.50 0.50, 0.45arrow_forward
- Consider the two (excess return) index model regression results for A and B: RA = 0.8% + 1RM R-square = 0.588 Residual standard deviation = 10.8% RB = –1.2% + 0.7RM R-square = 0.452 Residual standard deviation = 9% a. Which stock has greater market risk? multiple choice A. Stock A B. Stock B b. For which stock does market movement has a greater fraction of return variability? multiple choice A. Stock A B. Stock B c. If rf were constant at 4.5% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)arrow_forward1. Assume a two-factor model explains stock returns. Regression estimates of stocks A and B on the two factors are given below. Stock B, B, A 1.2 -0.5 4 в 3.5 -0.8 2.0 3 Assume further that factor one has expected return of 10 and standard deviation of 8. Factor two has expected return of 5 and standard deviation of 6. a) Calculate expected returns for A and B. b) Calculate standard deviations for A and B. c) Calculate expected return on a portfolio that invests 60% in A and 40% in B.arrow_forwardConsider the two (excess return) index model regression results for A and B: RA = 0.8% + 1RM R-square = 0.588 Residual standard deviation = 10.8% RB = –1.2% + 0.7RM R-square = 0.452 Residual standard deviation = 9% a. Which stock has more firm-specific risk? multiple choice A. Stock A B. Stock B Which stock has greater market risk? multiple choice 2 A. Stock A B. Stock B b. For which stock does market movement has a greater fraction of return variability? multiple choice 3 A. Stock A B. Stock B c. If rf were constant at 4.5% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)arrow_forward
- Consider information given in the table below and answers the question asked thereafter: State Probability return on stock A Return on stock B A 0.15 10% 9% B 0.15 6% 15% C 0.10 20% 10% D 0.18 5% -8% E 0.12 -10% 20% F 0.30 8% 5% Calculate covariance and coefficient of correlation between the returns of thestocks A and B.v. Now suppose you have $100,000 to invest and you want to a hold a portfoliocomprising of $45,000 invested in stock A and remaining amount in stock B.Calculate risk and return of your portfolio.arrow_forwardThe index model has been estimated using historical excess return data for stocks A, B, and C, with the following results: RA = 0.02 + 0.9RM + eA RB = 0.04 + 1.2RM + eB RC = 0.10 + 1.ORM + eC OM oM = 0.22 o(eA) = 0.21 o(eB ) = 0.11 o(eC ) = 0.23 a. What are the standard deviations of stocks A, B, and C? b. Break down the variances of stocks A, B, and C into their systematic and firm-specific components. c. What is the covariance between the returns on each pair of stocks? d. What is the covariance between each stock and the market index?arrow_forwardConsider the two (excess return) index model regression results for A and B. RA= 0.9% + 1.1RM , R-square = 0.590, and Residual Standard Deviation = 11% RB= -1.4% + 0.6RM, R-square = 0.456, and Residual Standard Deviation = 9.2% Which stock has more firm-specific risk, market risk, and greater fraction of return variability for market movement? Also, if rf were constant at 4.4% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A (write as percentage, rounded to 2 decimal places)?arrow_forward