Investment Analysis (FIN 670 Fall 2009 Homewok 5 Instuctions: please ead caefully You should show you wok how to get the answe fo each calculation question to get full cedit The due date is Tuesday, Novembe 10, 2009. Late homewok will not be gaded. Name(s: tudent ID
1. Compute the expected etun fo a thee-stock potfolio with the following: a. 13.3% b. 14.6% c. 29.3% d. 32.4% 2. A potfolio is consideed to be efficient if. a. thee is no othe potfolio with a highe expected etun b. thee is no othe potfolio with a lowe isk c. thee is no othe potfolio offes a highe expected etun with a highe isk d. thee is no othe potfolio offes a lowe isk with the same expected etun 3. Which of the following is (ae most coect concening a two-stock potfolio? a. The potfolio should have no company specific isk. b. Potfolio standad deviation can neve be a weighted aveage of the two stocks' standad deviations. c. Potfolio etun is a weighted aveage of the two stocks' etuns. d. All of the above ae coect. 4. The maximum benefit of divesification can be achieved by combining secuities in a potfolio whee the coelation coefficient between the secuities is. a. between 0 and -1 b. 0 c. -1 d. +1 5. A potfolio is composed of two stocks, A and. tock A has a standad deviation of etun of 20% while stock has a standad deviation of etun of 30%. tock A compises 40% of the potfolio while stock compises 60% of the potfolio. What is the standad deviation of etun on the potfolio if the coelation coefficient between the etuns on A and is 0.5? a. 23.1% b. 25% c. 26% d. 24.7% 6. A potfolio is composed of two stocks, A and. tock A has an expected etun of 10% while stock has an expected etun of 18%. What is the popotion of stock A in the potfolio so that the expected etun of the potfolio is 16.4%? a. 0.2 b. 0.8 c. 0.4 d. 0.6
7. Which of the following potfolios cannot lie on the efficient fontie? a. Potfolio X b. Potfolio Y c. Potfolio Z d. All potfolios should lie on the efficient fontie. 8. The standad deviation of etun on stock A is 0.25 while the standad deviation of etun on stock is 0.30. If the covaiance of etuns on A and is 0.06, the coelation coefficient between the etuns on A and is. a. 0.2 b. 0.6 c. 0.7 d. 0.8 9. Caeful selection of diffeent stocks fom diffeent industies can eliminate the isk of a potfolio. a. Nonsystematic b. Maket c. Total d. All of the above. 10. A positive covaiance between two stocks' etuns indicates that the two stocks' etuns. a. move in opposite diection b. move in the same diection c. have the same isk d. have no elationship 11. What happens typically to the potfolio's isk when moe stocks ae added to a 5-stock potfolio? a. The potfolio's maket isk would decease. b. The potfolio's total isk would decline. c. The potfolio's unsystematic would decease. d. oth and C above ae coect.
12. Which of the following statements ae coect concening divesifiable isks? I. Divesifiable isks can be essentially eliminated by investing in seveal unelated secuities. II. The maket ewads investos fo divesifiable isk by paying a isk pemium. III. Divesifiable isks ae geneally associated with an individual fim o industy. IV. eta measues divesifiable isk. 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 13. Which of the following statements concening nondivesifiable isk ae coect? I. Nondivesifiable isk is measued by standad deviation. II. ystematic isk is anothe name fo nondivesifiable isk. III. The isk pemium inceases as the nondivesifiable isk inceases. IV. Nondivesifiable isks ae those isks you can not avoid if you ae invested in the financial makets. 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 14. Which one of the following is an example of a nondivesifiable isk? a. a well espected pesident of a fim suddenly esigns b. a well espected chaiman of the Fedeal Reseve suddenly esigns c. a key employee of a fim suddenly esigns and accepts employment with a key competito d. a well managed fim educes its wok foce and automates seveal jobs e. a pooly managed fim suddenly goes out of business due to lack of sales 15. Which of the following isks ae elevant to a well-divesified investo? I. systematic isk II. unsystematic isk III. maket isk IV. nondivesifiable isk 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 16. Which one of the following is an example of systematic isk? a. the pice of lumbe declines shaply b. ailine pilots go on stike c. the Fedeal Reseve inceases inteest ates d. a huicane hits a touist destination e. people become diet conscious and avoid fast food estautants
17. Which one of the following is an example of unsystematic isk? a. the inflation ate inceases unexpectedly b. the fedeal govenment lowes income taxes c. an oil tanke uns agound and spills its cago d. inteest ates decline by one-half of one pecent e. the GDP ises by 2 pecent moe than anticipated 18. Which of the following actions help eliminate unsystematic isk in a potfolio? I. speading the etail industy potion of a potfolio ove five sepaate stocks II. combining stocks with bonds in a potfolio III. adding some intenational secuities into a potfolio of U.. stocks IV. adding some U.. Teasuy bills to a isky potfolio 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 19. All things equal, divesification is most effective when a. secuities' etuns ae positively coelated. b. secuities' etuns ae uncoelated. c. secuities' etuns ae high. d. secuities' etuns ae negatively coelated. e. A and C. 20. An investo who wishes to fom a potfolio that lies to the ight of the optimal isky potfolio on the Capital Allocation Line must: a. lend some of he money at the isk-fee ate and invest the emainde in the optimal isky potfolio. b. boow some money at the isk-fee ate and invest in the optimal isky potfolio. c. such a potfolio cannot be fomed. d. invest only in isky secuities. e. and D 21. Potfolio theoy as descibed by Makowitz is most concened with a. the elimination of systematic isk. b. the identification of unsystematic isk. c. the effect of divesification on potfolio isk. d. active potfolio management to enhance etuns. e. none of the above 22. ecuity C has expected etun of 12% and standad deviation of 20%. ecuity D has expected etun of 15% and standad deviation of 27%. If the two secuities have a coelation coefficient of 0.7, what is thei covaiance? a. 0.038 b. 0.070 c. 0.018 d. 0.013 e. 0.054
The following infomation is fo question 23-26 Abigail Gace has a $900,000 fully divesified potfolio. he subsequently inheits AC Company common stock woth $100,000. He financial adviso povided he with the following estimates: The coelation coefficient of AC stock etuns with the oiginal potfolio etuns is 0.40. 23. The inheitance changes Gace s oveall potfolio and she is deciding whethe to keep the AC stock. Assuming Gace keeps the AC stock, calculate the: i. Expected etun of he new potfolio which includes the AC stock. ii. Covaiance of AC stock etuns with the oiginal potfolio etuns. iii. tandad deviation of he new potfolio which includes the AC stock.
24. If Gace sells the AC stock, she will invest the poceeds in isk-fee govenment secuities yielding 0.42 pecent monthly. Assuming Gace sells the AC stock and eplaces it with the govenment secuities, calculate the: (emembe the standad deviation of govenment secuities = 0 a. Expected etun of he new potfolio which includes the govenment secuities. b. Covaiance of the govenment secuity etuns with the oiginal potfolio etuns. c. tandad deviation of he new potfolio which includes the govenment secuities. 25. Detemine whethe the systematic isk of he new potfolio, which includes the govenment secuities, will be highe o lowe than that of he oiginal potfolio. Explain biefly
26. ased on convesations with he husband, Gace is consideing selling the $100,000 of AC stock and acquiing $100,000 of XYZ Company common stock instead. XYZ stock has the same expected etun and standad deviation as AC stock. He husband comments, It doesn t matte whethe you keep all of the AC stock o eplace it with $100,000 of XYZ stock. tate whethe he husband s comment is coect o incoect. Justify you esponse.
27. Geoge tephenson s cuent potfolio of $2.0 million is invested as follows: (K tephenson soon expects to eceive an additional $2.0 million and plans to invest the entie amount in an index fund that best complements the cuent potfolio. tephanie Coppa, CFA, is evaluating the fou index funds shown in the following table fo thei ability to poduce a potfolio that will meet two citeia elative to the cuent potfolio: (1 maintain o enhance expected etun and (2 maintain o educe volatility. Each fund is invested in an asset class that is not substantially epesented in the cuent potfolio. (K tate which fund Coppa should ecommend to tephenson. Justify you choice by descibing how you chosen fund best meets both of tephenson s citeia. No calculations ae equied.
The following data apply to question 28--32 A pension fund manage is consideing 3 mutual funds. This fist is a stock fund, the second is a long-tem govenment and copoate bond fund, and the thid is a T-bill money maket fund that yields a ate of 8%. The pobability distibution of the isky funds is as follows Expected etun tandad deviation tock fund ( 20% 30% ond fund ( 12% 15% The coelation between the fund etuns is 0.10. 28. What ae the investment popotions in the minimum vaiance potfolio of the two isky funds, what is the expected value and standad deviation of its ate of etun? (The weight of stock in the minimum vaiance potfolio is calculated using the following fomula 2 σ Cov(, w Min ( = 2 2 σ + σ 2Cov(,
29. Now, assume you decide to include T-bill into you complete potfolio. olve numeically fo the popotions of each asset and fo the expected etun and standad deviation of the optimal isky potfolio (the optimal isky potfolio is the combination of stock and bond fund that gives investo the best isk-etun tade-off when combining with T-bill (The popotion of the optimal isky potfolio invested in the stock fund is given by:, ]Cov( E( [E( ] [E( ] [E(, ]Cov( [E( ] [E( w f f 2 f 2 f f 2 f + σ + σ σ = 30. What is the ewad-to-vaiability atio of the best feasible CAL?
31. uppose now that you potfolio must yield an expected etun of 14% and be efficient, that is, on the best feasible CAL. a. What is the standad deviation of you potfolio? b. What is the popotion invested in the T-bill fund and each of the two isky funds? 32. If you wee to use only the two isky funds and still equie an expected etun of 14%, what would be the investment popotions of you potfolio? Compae its standad deviation to that of the optimal potfolio in the pevious poblem (#31. What do you conclude?
33. tocks offe an expected ate of etun of 10% with a standad deviation of 20%, and gold offes an expected etun of 5% with a standad deviation of 25%. a. In light of the appaent infeioity of gold to stocks with espect to both mean etun and volatility, would anyone hold gold? Explain you answe b. How would you answe (a if the coelation coefficient between gold and stocks wee 1.0? Could these expected etuns, standad deviations, and coelation epesent an equilibium fo the secuity maket (i.e., if no one chooses to hold gold, would the situation be thee fo long time?