UPENN: LOOSE LEAF CORP.FIN W/CONNECT
17th Edition
ISBN: 9781260361278
Author: Ross
Publisher: McGraw-Hill Publishing Co.
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Textbook Question
Chapter 11, Problem 38QP
Minimum Variance Portfolio Assume Stocks A and 8 have the following characteristics:
| Stock | Expected Return(%) | Standard Deviation(%) |
| A | 9 | 33 |
| B | 15 | 62 |
The covariance between the re turns on the two stocks is .001.
- a. Suppose an investor holds a portfolio consisting of only Stock A and Stock B. Find the portfolio weights, XA and XB, such that the variance of her portfolio is minimized.
(Hint: Remember that the sum of the two weights must equal 1.)
- b. What is the expected return on the minimum variance portfolio?
- c. If the covariance between the returns on the two stocks is –.05, what are the minimum variance weights?
- d. What is the variance of the Portfolio in part (c)?
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Students have asked these similar questions
Portfolios A and B are both well-diversified. The risk-free rate is 8%. The return for the market is 10%.
Portfolio A has an expected return of 15% and beta of 1.1. Portfolio B has an expected return of 9% and beta
of 0.20. Portfolio A's variance is 9%, whilst Portfolio B's variance is 5.5%.
Calculate for Portfolio A and Portfolio B the following:
1. Sharpe's Measure,
2. Treynor's Measure,
3. Jensen's Measure.
Which is the better portfolio according to each measure?
The variance (risk) of an N-asset portfolio can be written as:
o² = 2 + 2/11
-Cov
where o² is the average variance of stocks in the portfolio and Cov is the average
covariance between each pair of stocks in the portfolio. This result suggests that a
well-diversified portfolio with a sufficiently large number of stocks will have
O a zero total risk (variance)
a zero covariance with other assets
a zero diversifiable (nonsystematic) risk
a zero market (systematic) risk
(a) Calculate the expected rate of return, variance and standard deviation of Stock X & Stock Y.
(b) Assume that the covariance between Stock X and Stock Y is -0.005. Calculate the expected rate of return, variance and standard deviation of Jenny’s portfolio. {Hint: you can express your answers for the variance and standard deviation in decimals or percentage form:• For decimals, the covariance in your equation should be -0.005• For percentage, the covariance in your equation should be -50%2(= -50/10000)]
(c) Explain why, in general, the portfolio risk is lower than the weighted average of individual stocks’ risk.
(d) Suppose the risk-free rate is 4%, the market risk premium is 15% and the betas for stocks X and Y are 1.2 and 0.2 respectively. Using the CAPM model, estimate the required rates ofreturn of Stock X and Stock Y.
(e) Given the results above, are Stocks X and Y overpriced or underpriced? Explain.
Chapter 11 Solutions
UPENN: LOOSE LEAF CORP.FIN W/CONNECT
Ch. 11 - Diversifiable and Nondiversifiable Risks In broad...Ch. 11 - Systematic versus Unsystematic Risk Classify the...Ch. 11 - Expected Portfolio Returns If a portfolio has a...Ch. 11 - Diversification True or false: The most important...Ch. 11 - Portfolio Risk If a portfolio has a positive...Ch. 11 - Beta and CAPM Is it possible that a risky asset...Ch. 11 - Covariance Briefly explain why the covariance of a...Ch. 11 - Prob. 8CQCh. 11 - Prob. 9CQCh. 11 - Prob. 10CQ
Ch. 11 - Determining Portfolio Weights What are the...Ch. 11 - Portfolio Expected Return You own a portfolio that...Ch. 11 - Portfolio Expected Return You own a portfolio that...Ch. 11 - Portfolio Expected Return You have 10,000 to...Ch. 11 - Prob. 5QPCh. 11 - Calculating Returns and Standard Deviations Based...Ch. 11 - Calculating Expected Returns A portfolio is...Ch. 11 - Returns and Standard Deviations Consider the...Ch. 11 - Returns and Standard Deviations Consider the...Ch. 11 - Calculating Portfolio Betas You own a stock...Ch. 11 - Calculating Portfolio Betas You own a portfolio...Ch. 11 - Using CAPM A stock has a beta of 1.15, the...Ch. 11 - Using CAPM A stock has an expected return of 13.4...Ch. 11 - Using CAPM A stock has an expected return of 13.4...Ch. 11 - Using CAPM A stock has an expected return of 11.2...Ch. 11 - Prob. 16QPCh. 11 - Prob. 17QPCh. 11 - Reward-to-Risk Ratios Stock Y has a beta of 1.20...Ch. 11 - Prob. 19QPCh. 11 - Portfolio Returns Using information from the...Ch. 11 - Prob. 21QPCh. 11 - Portfolio Returns and Deviations Consider the...Ch. 11 - Analyzing a Portfolio You want to create a...Ch. 11 - Prob. 24QPCh. 11 - Prob. 25QPCh. 11 - Prob. 26QPCh. 11 - Prob. 27QPCh. 11 - Prob. 28QPCh. 11 - Correlation and Beta You have been provided the...Ch. 11 - CML The market portfolio has an expected return of...Ch. 11 - Beta and CAPM A portfolio that combines the...Ch. 11 - Beta and CAPM Suppose the risk-free rate is 4.7...Ch. 11 - Systematic versus Unsystematic Risk Consider the...Ch. 11 - SML Suppose you observe the following situation:...Ch. 11 - Prob. 35QPCh. 11 - Prob. 36QPCh. 11 - Prob. 37QPCh. 11 - Minimum Variance Portfolio Assume Stocks A and 8...Ch. 11 - Prob. 1MCCh. 11 - Prob. 2MC
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