Principles of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
12th Edition
ISBN: 9781259144387
Author: Richard A Brealey, Stewart C Myers, Franklin Allen
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 7, Problem 8PS
Portfolio betas A portfolio contains equal investments in 10 stocks. Five have a beta of 1.2; the remainder have a beta of 1.4. What is the portfolio beta?
- a. 1.3.
- b. Greater than 1.3 because the portfolio is not completely diversified.
- c. Less than 1.3 because diversification reduces beta.
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Students have asked these similar questions
The beta coefficient
A stock’s contribution to the market risk of a well-diversified portfolio is called Q1. ______risk. It can be measured by a metric called the beta coefficient, which calculates the degree to which a stock moves with the movements in the market.
Q2. Based on your understanding of the beta coefficient, indicate whether each statement in the following table is true or false:
Statement
True
False
Over time, a stock with a beta of 1.0 produces a return that goes up and down with a 1:1 relationship with the return on the market.
Beta measures the volatility in stock movements relative to the market.
A stock that is more volatile than the market will have a beta of less than 1.0.
Q1. Option 1 Unsystematic or Option 2 Relevant.
Please provide true or false answers. Thank you!
Problem 1
You are given the following information about stock X and the market portfolio, M:
Riskless Asset (f)
Stock X
Market Portfolio (M)
E(r)
0.04 (4%)
?
0.10
σ
0.00
0.30
0.20
You are not given the expected return of stock X. The correlation of the returns on the stock X and
the market portfolio is equal to 0.4.
a) What is the beta (6) of stock X?
b) Assuming the CAPM holds, what is the expected return on stock X?
c) You have $1,000 to invest in some combination of the risk-free asset, stock X, and the market
portfolio. You are thinking of investing $300 in the risk free asset, $400 in stock X, and $300
in the market portfolio. What is the overall expected return, standard deviation and beta of
this portfolio?
Question 1
a. Explain why it is important to have diversification in a portfolio.
b. The following table represents a portfolio of two (2) assets:
State of
Probability of
Return of
Return of
Nature
State of
Stock
Stock B
Nature
under
under
Different
Different
State of
State of
Nature
Nature
Вoom
0.3
20%
25%
Normal
0.5
10%
20%
Recession
0.2
5%
10%
i. What is the expected return on Stock A and Stock B?
ii. What is the standard deviation of returns of Stock A and Stock
B?
iii. Which Stock is more volatile?
c. Suppose you use J$100 000 to construct a portfolio comprising of Stock
A and stock B,
such that you invest J$30 000 and J $70 000 in Stock A and Stock B
respectively. Also
you have done some research and estimated the Beta (B) of the Stocks to
be: Stock
A=0.75 and Stock B=0.50.
Use the expected returns calculated for each stock in (b), above to
calculate the following:
i. The expected return on the portfolio
ii. Calculate the expected beta of the portfolio. ,
iii. Explain briefly how…
Chapter 7 Solutions
Principles of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Ch. 7 - Expected return and standard deviation A game of...Ch. 7 - Standard deviation of returns The following table...Ch. 7 - Average returns and standard deviation During the...Ch. 7 - Portfolio risk True or false? a. Investors prefer...Ch. 7 - Risk and diversification In which of the following...Ch. 7 - Portfolio risk To calculate the variance of a...Ch. 7 - Portfolio betas Suppose the standard deviation of...Ch. 7 - Portfolio betas A portfolio contains equal...Ch. 7 - Prob. 9PSCh. 7 - Prob. 10PS
Ch. 7 - Stocks vs. bonds Each of the following statements...Ch. 7 - Prob. 12PSCh. 7 - Prob. 13PSCh. 7 - Portfolio risk Hyacinth Macaw invests 60% of her...Ch. 7 - Portfolio risk a) How many variance terms and how...Ch. 7 - Portfolio risk Table 7.9 shows standard deviations...Ch. 7 - Portfolio risk Your eccentric Aunt Claudia has...Ch. 7 - Stock betas There are few, if any, real companies...Ch. 7 - Portfolio risk You can form a portfolio of two...Ch. 7 - Portfolio risk Here are some historical data on...Ch. 7 - Portfolio risk Suppose that Treasury bills offer a...Ch. 7 - Beta Calculate the beta of each of the stocks in...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Similar questions
- 6. Consider the following performance data for two portfolio managers (A and B) and a common benchmark portfolio: BENCHMARK MANAGER A MANAGER B Return Weight Weight Weight Return Return Stock 0.5 -4.0% 0.6 -5.0% 0.3 -5.0% Bonds 0.3 -3.5 0.2 -2.5 0.4 -3.5 0.1 Cash 0.3 0.3 0.3 0.3 0.3 Evaluation of Asset Management a. Calculate (1) the overall return to the benchmark portfolio, (2) the overall return to Manager A's actual portfolio, and (3) the overall return to Manager B's actual portfo- lio. Briefly comment on whether these managers have under- or outperformed the benchmark fund. b. Using attribution analysis, calculate (1) the selection effect for Manager A, and (3) the allocation effect for Manager B. Using these numbers in conjunction with your results from part (a), comment on whether these managers have added value through their selection skills, their allocation skills, or both.arrow_forwardIf an investor that owns a portfolio with 3 stocks increases their portfolio to 30 stocks, which of the following is MOST LIKELY to happen? Select one: a. risk would increase b. the Sharpe ratio would increase c. return would decrease d. Sharpe would decreasearrow_forward3arrow_forward
- An Equity has a beta of 0.9 and an expected return of 9%. A risk free asset currently earns 2%. i.) What is the expected return on a portfolio that is equally invested in two assets? ii.) If a portfolio of the two assets has an expected return of 6%, what is its beta? iii.) If a portfolio of the two assets has a beta of 1.5, what is its weight ? Iv.) If a portfolio of the two assets has a beta of 1.5, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain.arrow_forwardConsider the following data. Stock Standard Deviation Beta X 5% 1.37 Y 8% 0.61 To minimize risk, you should choose Stock _____ if held individually and Stock _____ if held as part of a well-diversified portfolio. X; Y Y; X There is not enough information to determine which stocks to hold. Y; Y X; Xarrow_forward5. Portfolio Beta Portfolio beta can be computed in the same way as portfolio return was computed. If stock A had a beta of 1.5 and stock B had a beta of -0.60, the beta of a portfolio comprised of both these stocks would be: Portfolio beta =WABA + WBBB = 0.3 (1.5) + 0.70 (-0.6) = 0.45 + (-0.42) = 0.03 The Excel application is also similar to how it was for potfolio return. Since you know the result for portfolio beta already (0.03), try and obtain it again in Excel. Note: There is no need to compute the beta of the market. It is 1 by defaultarrow_forward
- Suppose that a mutual fund manager has a $20 million portfolio with a beta of 1.2. Also suppose that the risk free rate is 4.5% and the market risk premium is 6%. The manager expects to receive an additional $5 million, which is to be invested in a number of new stocks to add to the portfolio. After these stocks are added, the manager would like the fund's required rate of return to be 10.5%. For notation, let r represent the required return, let RF represent the risk free rate, let b represent the beta of a group of stocks, and T'm represent the market return. According to the video, which equation most closely describes the security market line (SML)? Or=TRF-bx (TM - TRF) Ⓒr=TRF+b× (™M - TRF) b ○ r = TRF + TM-TRF Or=rRF+bx (M+TRF) Hint: Recall that the manager wants the new required rate of return for the portfolio to remain at 10.5%. Using the equation you just identified, and plugging in the relevant information, yields a beta of the portfolio, after the new stocks have been added,…arrow_forward2.arrow_forward7. The following data are available to you as portfolio manager: Security Estimated return (%) Beta A 40 3.0 B 35 2.5 30 1.0 D 17.5 1.8 E 20.0 1.5 Market Index 25 2.0 Govemment Security 17 a) In terms of the security market line, which of the securities listed above are underpriced? b) Assuming that a portfolio is constructed using equal proportions of the five securities listed above, calculate the expected retum and risk of such a portfolio.arrow_forward
- 4. Consider the following equation of the CAPM: E(R) = 5%+B₁*10% P is an equally-weighted portfolio composed of the risk-free rate and stocks A, B and C. The following characteristics are given with respect to the three stocks: Stock Po E(P) E(D) В A 100 112 5 1.1 B 5 5.5 1 0.7 с 10 8 4 1.3 Compute the expected alpha of this portfolio.arrow_forwardConsider the following information: Portfolio Expected Return Standard Deviation Risk-free 7% 0% Market 11.6 28 A 10.0 17 Required: a. Calculate the Sharpe ratios for the market portfolio and portfolio A. (Round your answers to 2 decimal places.) b. If the simple CAPM is valid, is the above situation possible?arrow_forwarda. Based on the following information, calculate the expected return and standard deviation for each of the following stocks. What are the covariance and correlation between the returns of the two stocks? Calculate the portfolio returm and portfolio standard deviation if you invest equally in each asset. Returns State of Economy Prob J K Recession 0.25 -0.02 0.034 Normal 0.6 0.138 0.062 Boom 0.15 0.218 0.092 b. A portfolio that combines the risk-free asset and the market portfolio has an expected return of percent and a standard deviation of 10 percent. The risk-free rate is 4 percent, and the Page 7 of 33 expected return on the market portfolio is 12 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a 45 corelation with the market portfolio and a standard deviation of 55 percent? C. Suppose the risk-free rate is 4.2 percent and the market portfolıo has an expected return of 10.9 mercent Tibemadkat normfeliobasiabiamance…arrow_forward
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