Investment Analysis (FIN 383) Fall Homework 5

Transcription

1 Investment Analysis (FIN 383) Fall 2009 Homework 5 Instructions: please read carefully You should show your work how to get the answer for each calculation question to get full credit The due date is Tuesday, November 10, Late homework will not be graded. Name(s): Student ID

2 1. Compute the expected return for a three-stock portfolio with the following: a. 13.3% b. 14.6% c. 29.3% d. 32.4% 1. b 10* * *0.5 = A portfolio is considered to be efficient if. a. there is no other portfolio with a higher expected return b. there is no other portfolio with a lower risk c. there is no other portfolio offers a higher expected return with a higher risk d. there is no other portfolio offers a lower risk with the same expected return 2. d 3. Which of the following is (are) most correct concerning a two-stock portfolio? a. The portfolio should have no company specific risk. b. Portfolio standard deviation can never be a weighted average of the two stocks' standard deviations. c. Portfolio return is a weighted average of the two stocks' returns. d. All of the above are correct. 3. c 4. The maximum benefit of diversification can be achieved by combining securities in a portfolio where the correlation coefficient between the securities is. a. between 0 and -1 b. 0 c. -1 d c 5. A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 20% while stock B has a standard deviation of return of 30%. Stock A comprises 40% of the portfolio while stock B comprises 60% of the portfolio. What is the standard deviation of return on the portfolio if the correlation coefficient between the returns on A and B is 0.5? a. 23.1% b. 25% c. 26% d. 24.7% 5. a 2 2 σ = (.4) (.2) 2 + (.6) 2 (.3) σ 2 =.0532 σ = (.4)(.6)(.2)(.3)(.5)

3 6. A portfolio is composed of two stocks, A and B. Stock A has an expected return of 10% while stock B has an expected return of 18%. What is the proportion of stock A in the portfolio so that the expected return of the portfolio is 16.4%? a. 0.2 b. 0.8 c. 0.4 d a E(Rp) = (Wa)E(Ra) + (1-Wa)E(Rb) = Wa(0.10) + (1-Wa)(0.18) Wa = Which of the following portfolios cannot lie on the efficient frontier? 7. b a. Portfolio X b. Portfolio Y c. Portfolio Z d. All portfolios should lie on the efficient frontier. 8. The standard deviation of return on stock A is 0.25 while the standard deviation of return on stock B is If the covariance of returns on A and B is 0.06, the correlation coefficient between the returns on A and B is. a. 0.2 b. 0.6 c. 0.7 d d Correlatio n =.06/[.25(.30)] =.8 9. Careful selection of different stocks from different industries can eliminate the risk of a portfolio. a. Nonsystematic b. Market c. Total d. All of the above. 9. a 10. A positive covariance between two stocks' returns indicates that the two stocks' returns. a. move in opposite direction b. move in the same direction c. have the same risk d. have no relationship

4 10. b 11. What happens typically to the portfolio's risk when more stocks are added to a 5-stock portfolio? a. The portfolio's market risk would decrease. b. The portfolio's total risk would decline. c. The portfolio's unsystematic would decrease. d. Both B and C above are correct. 11. d 12. Which of the following statements are correct concerning diversifiable risks? I. Diversifiable risks can be essentially eliminated by investing in several unrelated securities. II. The market rewards investors for diversifiable risk by paying a risk premium. III. Diversifiable risks are generally associated with an individual firm or industry. IV. Beta measures diversifiable risk. a. I and III only b. II and IV only c. I and IV only d. II and III only e. I, II, and III only 12. a 13. Which of the following statements concerning nondiversifiable risk are correct? I. Nondiversifiable risk is measured by standard deviation. II. Systematic risk is another name for nondiversifiable risk. III. The risk premium increases as the nondiversifiable risk increases. IV. Nondiversifiable risks are those risks you can not avoid if you are invested in the financial markets. a. I and III only b. II and IV only c. I, II, and III only d. II, III, and IV only e. I, II, III, and IV 13. d 14. Which one of the following is an example of a nondiversifiable risk? a. a well respected president of a firm suddenly resigns b. a well respected chairman of the Federal Reserve suddenly resigns c. a key employee of a firm suddenly resigns and accepts employment with a key competitor d. a well managed firm reduces its work force and automates several jobs e. a poorly managed firm suddenly goes out of business due to lack of sales 14. b

5 15. Which of the following risks are relevant to a well-diversified investor? I. systematic risk II. unsystematic risk III. market risk IV. nondiversifiable risk a. I and III only b. II and IV only c. II, III, and IV only d. I, II, and IV only e. I, III, and IV only 15. e 16. Which one of the following is an example of systematic risk? a. the price of lumber declines sharply b. airline pilots go on strike c. the Federal Reserve increases interest rates d. a hurricane hits a tourist destination e. people become diet conscious and avoid fast food restautants 16.c 17. Which one of the following is an example of unsystematic risk? a. the inflation rate increases unexpectedly b. the federal government lowers income taxes c. an oil tanker runs aground and spills its cargo d. interest rates decline by one-half of one percent e. the GDP rises by 2 percent more than anticipated 17. c 18. Which of the following actions help eliminate unsystematic risk in a portfolio? I. spreading the retail industry portion of a portfolio over five separate stocks II. combining stocks with bonds in a portfolio III. adding some international securities into a portfolio of U.S. stocks IV. adding some U.S. Treasury bills to a risky portfolio a. I and III only b. I, II, and IV only c. I, III, and IV only d. II, III, and IV only e. I, II, III, and IV 18. e

6 The following information is for question Abigail Grace has a $900,000 fully diversified portfolio. She subsequently inherits ABC Company common stock worth $100,000. Her financial advisor provided her with the following estimates: The correlation coefficient of ABC stock returns with the original portfolio returns is The inheritance changes Grace s overall portfolio and she is deciding whether to keep the ABC stock. Assuming Grace keeps the ABC stock, calculate the: i. Expected return of her new portfolio which includes the ABC stock. E(r NP ) = w OP E(r OP ) + w ABC E(r ABC ) = ( ) + ( ) = 0.728% ii. Covariance of ABC stock returns with the original portfolio returns. Cov = r σ OP σ ABC = = iii. Standard deviation of her new portfolio which includes the ABC stock. σ NP = [w OP2 σ OP2 + w ABC2 σ ABC2 + 2 w OP w ABC (Cov OP, ABC )] 1/2 = [( ) + ( ) + ( )] 1/2 = % 2.27%

7 20. If Grace sells the ABC stock, she will invest the proceeds in risk-free government securities yielding 0.42 percent monthly. Assuming Grace sells the ABC stock and replaces it with the government securities, calculate the: (remember the standard deviation of government securities = 0) a. Expected return of her new portfolio which includes the government securities. E(r NP ) = w OP E(r OP ) + w GS E(r GS ) = ( ) + ( ) = 0.645% b. Covariance of the government security returns with the original portfolio returns. Cov = r σ OP σ GS = = 0 c. Standard deviation of her new portfolio which includes the government securities. σ NP = [w OP2 σ OP2 + w GS2 σ GS2 + 2 w OP w GS (Cov OP, GS )] 1/2 = [( ) + ( ) + ( )] 1/2 = 2.133% 2.13%

8 21. George Stephenson s current portfolio of $2.0 million is invested as follows: (K) Stephenson soon expects to receive an additional $2.0 million and plans to invest the entire amount in an index fund that best complements the current portfolio. Stephanie Coppa, CFA, is evaluating the four index funds shown in the following table for their ability to produce a portfolio that will meet two criteria relative to the current portfolio: (1) maintain or enhance expected return and (2) maintain or reduce volatility. Each fund is invested in an asset class that is not substantially represented in the current portfolio. (K) State which fund Coppa should recommend to Stephenson. Justify your choice by describing how your chosen fund best meets both of Stephenson s criteria. No calculations are required. Fund D represents the single best addition to complement Stephenson's current portfolio, given his selection criteria. First, Fund D s expected return (14.0 percent) has the potential to increase the portfolio s return somewhat. Second, Fund D s relatively low correlation with his current portfolio (+0.65) indicates that Fund D will provide greater diversification benefits than any of the other alternatives except Fund B. The result of adding Fund D should be a portfolio with approximately the same expected return and somewhat lower volatility compared to the original portfolio. The other three funds have shortcomings in terms of either expected return enhancement or volatility reduction through diversification benefits. Fund A offers the potential for increasing the portfolio s return, but is too highly correlated to provide substantial volatility reduction benefits through diversification. Fund B provides substantial volatility reduction through diversification benefits, but is expected to generate a return well below the current portfolio s return. Fund C has the greatest potential to increase the portfolio s return, but is too highly correlated to provide substantial volatility reduction benefits through diversification.