Test Bank to accompany Modern Portfolio Theory and Investment Analysis, 9 th Edition

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1 Test ank to accopany Modern ortfolo Theory and Investent Analyss, 9 th Edton Test ank to accopany Modern ortfolo Theory and Investent Analyss, 9th Edton Copleted download lnk: Related download lnk: Solutons Manual for Modern ortfolo Theory and Investent Analyss 9th Edton by Elton Gruber rown Goetzann MODERN ORTFOLIO THEORY AND INVESTMENT ANALYSIS 9 TH EDITION ELTON, GRUER, ROWN, & GOETZMANN The followng exa questons are organzed accordng to the text's sectons. Wthn each secton, questons follow the order of the text's chapters and are organzed as ultple choce, true-false wth dscusson, probles, and essays. The correct answers and the correspondng chapter(s) are ndcated below each queston. ART : ORTFOLIO ANALYSIS ART Secton 1: Mean Varance ortfolo Theory Multple Choce 1. The rsk on a portfolo of assets: a. s dfferent fro the rsk on the arket portfolo. b. s not nfluenced by the rsk of ndvdual assets. c. s dfferent fro the rsk of ndvdual assets. d. s negatvely correlated to the rsk of ndvdual assets. C Chapter: 4. Whch of the followng s correct of how the returns on assets ove together? a. ostve and negatve devatons between assets at slar tes gve a art - 1

2 Test ank Modern ortfolo Theory and Investent Analyss, 9 th Edton negatve covarance. b. ostve and negatve devatons between assets at dsslar tes gve a negatve covarance. c. ostve and negatve devatons between assets gve a zero covarance. d. ostve and negatve devatons between assets at dsslar tes gve a postve covarance. Chapter: 4 3. An effcent fronter s: a. a cobnaton of securtes that have the hghest expected return for each level of rsk. b. the cobnaton of two securtes or portfolos represented as a convex functon. c. a cobnaton of securtes that le below the nu varance portfolo and the axu return portfolo. d. a cobnaton of securtes that have an average expected return for each level of rsk. A Chapter: 5 4. Two copanes Aber and olt are anufacturers of glass. The securtes of the copanes are lsted and traded n the New York Stock Exchange. An nvestor s portfolo conssts of these two securtes n the proporton of 5/6 and 1/6 respectvely. Aber s securty has an expected return of 0% and a standard devaton of 8%. olt has an expected return of 15% and a standard devaton of 5%. The correlaton coeffcent between the two securtes s 0.6. Calculate the expected return and the standard devaton of the nvestor s portfolo. a. R 19.17% 7.0% b. R 0.19% 8.0% c. R 17% 7.0% d. R 18.19% 8.0% A Chapter: 6 robles 1. Consder the probablty dstrbuton below. (Note that the expected returns of A and have already been coputed for you.) State p(s) ra r Recesson Noral art -.

3 Modern ortfolo Theory and Investent Analyss, 9 th Edton Test ank oo Expected Return: a. Calculate the standard devatons of A and. b. Calculate the covarance and correlaton between A and. c. Calculate the expected return of the portfolo that nvests 30% n stock A and the rest n stock. d. Calculate the standard devaton of the portfolo n part b. a. A = [0.3 (.11. 1) ] + [0.4 (.13.1) ] + [0.3 (.7.1) ] = 0.06 = [0.3 (.16.06) ] + [0.4 ( ) ] + [0.3 (.04.06) ] = b. Cov(rA,r) = [0.3 (.11. 1)(.16.06)] + [0.4 (.13.1)(.06.06)] + [0.3 (.7.1)(.04.06)] = Corr(rA,r) = / ( )= c. E(rp) = 0.3(0.1) + 0.7(0.06)=0.07 d. Usng the standard devaton of each of the assets A and coputed n part a and covarance between the two assets coputed n part b: = [( ) + ( ) ( )] = Chapter: 4. Stock A has an expected return of 8% and a standard devaton of 40%. Stock has an expected return of 13% and standard devaton of 60%. The correlaton between A and s -1 (.e., they are perfectly negatvely correlated). Show that you can for a zero rsk portfolo by nvestng w A n A and the rest n. A Copyrght 014 John Wley & Sons, Inc. art - 3

4 ortfolo Expected Return Test ank Modern ortfolo Theory and Investent Analyss, 9 th Edton 0.6 w A 0.6 Thus, The varance of the portfolo s gven by: Ths portfolo has zero varance hence, t s rskless. Ths confrs what we learned n class when two securtes are perfectly negatvely correlated, t s possble to for a zero-rsk portfolo by cobnng the. Chapter 5 3. The followng dagra shows the nvestent opportunty set for portfolos contanng stocks A and. You need to know that: ont A on the graph represents a portfolo wth 100% n stock A ont represents a portfolo wth 100% n stock 9.00% 8.00% z A 7.00% 6.00% x y w 5.00% 4.00% 3.00%.00% 1.00% 0.00% 0.00% 0.50% 1.00% 1.50%.00%.50% 3.00% ortfolo Standard Devaton art - 4.

5 Modern ortfolo Theory and Investent Analyss, 9 th Edton Test ank a. Is the correlaton between A and greater than, equal to, or less than 1. How do you know? b. Whch labeled pont on the graph represents the nu varance portfolo? c. Whch labeled pont on the graph represents a portfolo wth 88% nvested n stock A and the rest n? d. If A and are the only nvestents avalable to an nvestor, whch of the labeled portfolos are effcent? e. Suppose a rsk-free asset exsts, allowng an nvestor to nvest or borrow at the rskfree rate of 3%. If the above graph s drawn perfectly to scale, whch labeled pont represents the optal rsky portfolo. f. Under the assuptons n part (e), would t be wse for an nvestor to nvest all of hs or her oney n stock A? Why or why not? a. Less than 1. Correlaton can t be greater than 1, and f correlaton equaled 1 (eanng that A and were perfectly postvely correlated), then the IOS between A and would be a straght lne. b. x c. z. Ths should be obvous, snce a portfolo wth 88% n A wll be uch closer to A than on the curve. You can also confr atheatcally by notng fro the graph that E(rA) 8.5% and E(r) 4.5%. Thus, a portfolo wth 87% n A wll have E(r) 0.88(.085) + 0.1(.045) = 0.080, whch s approxately the expected return of portfolo z n the graph. d. x, y, z, and A e. y. Note on the graph that the tangency lne fro the rsk-free asset ntercepts the IOS at y. Copyrght 014 John Wley & Sons, Inc. art - 5

6 Test ank Modern ortfolo Theory and Investent Analyss, 9 th Edton 9.00% 8.00% z A ortfolo Expected Return 7.00% 6.00% 5.00% 4.00% 3.00% x y w.00% 1.00% 0.00% 0.00% 0.50% 1.00% 1.50%.00%.50% 3.00% ortfolo Standard Devaton f. No. When the nvestor has the ablty to borrow or lend at the rsk-free rate, only the portfolos on the tangency lne are effcent. Note n the graph above that by borrowng at the rsk-free rate and nvestng everythng n the optal rsky portfolo (y, n ths case), the nvestor can create portfolos that that donate A. Chapter: 5 and 6 Essay 1. Descrbe what s sevarance? Gve reasons why sevarance s not used as a easure of dsperson. Sevarance s a easure of dsperson that consders only the devatons of the returns whch are below the average desred returns. Ths ay be useful as the only returns that alar an nvestor are the returns that are below the desred level. For a well-dversfed equty portfolo, syetrcal dstrbuton s a reasonable assupton and hence, varance s also an approprate easure of downsde rsk. Furtherore, snce eprcal evdence shows that ost of the assets exstng n the arket have returns that are reasonably syetrcal, sevarance s not needed because f returns on an asset are syetrcal the sevarance s proportonal to the varance. Thus, n ost of the cases, not the sevarance, but the varance, s used as art - 6.

7 Modern ortfolo Theory and Investent Analyss, 9 th Edton Test ank a easure of dsperson. Chapter: 4. Under what condton wll addng a securty wth a hgh standard devaton decrease the rsk of a portfolo? The rsk of a cobnaton of assets s dfferent fro a sple average of the rsk of ndvdual assets. The standard devaton of a cobnaton of two assets ay be less than the varance of ether of the assets theselves. Addng a securty wth a hgh standard devaton to a portfolo can reduce the overall rsk of portfolo f the securty s negatvely correlated to the bulk of securtes n the portfolo. In a condton where two securtes are perfectly negatvely correlated, the securtes wll ove together but n opposte drectons. The standard devaton of such a portfolo wll be saller than a portfolo whose securtes are postvely correlated. If two securtes are perfectly negatvely correlated, t should always be possble to fnd soe cobnaton of these two securtes that has zero rsk. A zero rsk portfolo wll always nvolve postve nvestent n both the securtes. Chapter: 5 3. Wth the help of a dagra show, how would you dentfy a ray wth the greatest slope as an effcent fronter where rskless lendng and borrowng s present? We understand that the exstence of rskless lendng and borrowng ples that there s a sngle portfolo of rsky assets that s preferred to all other portfolos. In the return standard devaton space, ths portfolo plots on the ray connectng the rskless asset and the rsky portfolo that les farthest n the counter clockwse drecton. We can udge fro the below gven graph that the ray R F s preferred by the nvestors to any other portfolo or rays lke R F A. The effcent fronter s the entre length of the ray extendng through R F and. Copyrght 014 John Wley & Sons, Inc. art - 7

8 Test ank Modern ortfolo Theory and Investent Analyss, 9 th Edton The slope of the lne connectng a rskless asset and a rsky portfolo s the expected return on the portfolo nus the rsk-free rate dvded by the standard devaton of the return on the portfolo. Thus, the effcent set s deterned by fndng a portfolo wth the greatest rato of excess return to standard devaton that satsfes the constrant that the su of the proportons nvested n the assets equals 1. Chapter: 6 ART Secton : Splfyng the ortfolo Selecton rocess Multple Choce 1. If the returns on dfferent assets are uncorrelated: a. an ncrease n the nuber of assets n a portfolo ay brng the standard devaton of the portfolo close to zero. b. there wll be lttle gan fro dversfcaton. c. dversfcaton wll result n rsk averagng but not n rsk reducton. d. the expected return on a portfolo of such assets should be zero. A Chapter: 4. Usng the Sharpe sngle-ndex odel wth a rando portfolo of U.S. coon stocks, as one ncreases the nuber of stocks n the portfolo, the total rsk of the portfolo wll: a. approach zero. b. approach the portfolo's systeatc rsk. c. approach the portfolo's non-systeatc rsk. d. not be affected. Chapter: 7 art - 8.

9 Modern ortfolo Theory and Investent Analyss, 9 th Edton Test ank 3. What s the concept behnd the ndexes used n the Faa and French Model? a. For portfolos wth standard devatons that c the pact of the varables. b. For portfolos wth returns that are opposte to the pact of the varables. c. For portfolos wth returns that c the pact of the varables. d. For portfolos wth standard devatons that are opposte to the pact of the varables. C Chapter: 8 4. Whch of the followng s true of a cutoff rate? a. The cutoff rate s be deterned by dvdng the eta wth the dfference between average return and return on the rskfree rate of the securtes. b. All securtes whose return s above the cutoff rate are selected n the arket portfolo. c. The cutoff rate s coputed fro the characterstcs of all securtes n the optu portfolo. d. All securtes whose rsk s below the cutoff rate are selected n the optu portfolo. C Chapter: 9 True-False Wth Dscusson 1. Dscuss whether the followng stateent s true or false: One can always construct a ult-ndex odel that explans ore of the returns on a securty than a sngle-ndex odel does. True The sngle-ndex odel assues that the stock prces ove together only because of coon oveent n the arket. Hence, the sngle ndex-odel derves returns on securtes wth the help of the arket oveent n whch the securtes are beng traded. Although, accordng to any researchers, there are nfluences beyond the arket that cause stocks to ove together. The ult-ndex odel ncludes two dfferent types of schees that have been put forth for handlng addtonal nfluences. Hence, the ultndex odel takes nto consderaton the return on securtes by ntroducng addtonal sources of covarance. y addng these addtonal nfluences, the ult-ndex odel explans ore of the returns to the general return equaton of the sngle-ndex odel. Chapter: 8. Dscuss whether the followng stateent s true or false: A ult-ndex odel wll predct returns better than a sngle-ndex odel. False The ult-ndex odel les n an nteredate poston between the full hstorcal Copyrght 014 John Wley & Sons, Inc. art - 9

10 Test ank Modern ortfolo Theory and Investent Analyss, 9 th Edton correlaton atrx and the sngle-ndex odel n ts ablty to reproduce the hstorcal correlaton atrx. Addng ore ndexes coplcates thngs but result n a ore accurate representaton of the hstorcal correlaton atrx. However, ths does not ply that future correlaton atrces wll be forecast ore accurately. Chapter: 8 robles 1. Consder the followng data for assets A and : RA 10% R 19% A 3% 5% A A 0.4. a. Calculate the expected return, varance, and beta of a portfolo constructed by nvestng 1/3 of your funds n asset A and /3 n asset. b. If only the rskless asset and assets A and are avalable, fnd the optu rsky-asset portfolo f the rsk-free rate s 8%. a. Expected return on a portfolo = 1 R R 16% XR To construct the portfolo wth nvestents A and, the varance of the portfolos wll have to be calculated as: N 1 X N N 1 1 X X %. The eta of a portfolo can be calculated by the followng ethod: N 1 X b. Calculatng for arket varance we get,. art - 10.

11 Modern ortfolo Theory and Investent Analyss, 9 th Edton Test ank Hence, 7.14 Now, e ( ea 6.43 e ) Securty Mean Return Excess Return eta Excess Return Over eta R R F e e 1 R R F e 1 e e A Z C C A = 4.50 C = ( C 1 1 R R 1 e F e C *) (As s lower than the excess return over rsk, we consder rate C *) R RF C * e C as the cutoff Z A Z Therefore, the optu portfolo wll have ts proporton of X 9.17% X 19.17%. Chapter: 7 and 9 A. Consder the followng data for assets A,, and C R A 1% R 8% R C 6% A Assue the varance of the arket portfolo s 0 and that a rskless asset exsts. Set up the C ea e ec Copyrght 014 John Wley & Sons, Inc. art - 11

12 Test ank Modern ortfolo Theory and Investent Analyss, 9 th Edton frst-order condtons for the optu rsky-asset portfolo. Assung a rsk free rate of 5%, we get the followng values for the optu portfolo: Secu rty Mean Return Excess Return eta Excess Return over eta A C The cutoff rate C of for an optu portfolo can be found by the followng equaton: C 1 1 R 1 R F e e e R R F R R F e 1 e 1 e e C A (0 0.11) C ( ) C C (0 0.36) C 4.50 (C*) C C. 95 A C The rato of excess return over eta s hgher than the cutoff rate of 4.50 for only securty A. Hence, we conclude that only securty A s ncluded n the frst order equaton of the optal rsky portfolo. Chapter: 9 3. Consder the followng hstorcal data for the returns on assets A and and the arket portfolo: erod Asset A Asset Market ortfolo 1 10% 6% 4% 3% 6% 1% 3 5% % 5% 4 % 4% % 5 1% % 1% a. What s the covarance between asset A and asset? b. If the beta of asset s 0.5, what s the systeatc return and non-systeatc return for asset n each perod? a. erod Asset A Asset Asset A Average A (1) Asset Average () (1 ) art - 1.

13 Modern ortfolo Theory and Investent Analyss, 9 th Edton Test ank Total 15 0 Average 3 4 Hence, the Covarance (A, ) = 5 = 0.4 b. Fro the gven nforaton, we know that the average return on asset s 4%, average return on arket s.6% and the eta of asset s 0.5. ased on ths nforaton, we can fnd the value of systeatc return ( ) and unsysteatc return ( e ). Hence,. 7 R R M To fnd the value of the unsysteatc rsk for all perods, we used the followng forula: R R e erod M R M R e R RM R M RM Hence, the systeatc return wll rean.7% for all perods. The unsysteatc return wll be 1.3% for perod 1,.8% for perod, 3.% for perod 3, 0.3% for perod 4 and 1.% for perod 5. Chapter: 7 4. The annual returns of Wonder Wdgets, Inc. and the S& 500 Coposte Index over the last ten years were as follows: Year Wonder Wdgets S& % 8.5% 10% 4.0% 3 1% 14.0% 4 0% 15.0% 5 0% 14.0% Copyrght 014 John Wley & Sons, Inc. art - 13

14 Test ank Modern ortfolo Theory and Investent Analyss, 9 th Edton 6 15% 6.0% 7 5% 37.0% 8 30% 4.0% 9 10% 7.0% 10 3% 6.5% Fnd the followng for Wonder Wdgets: a. eta (βw, slope of regresson lne) b. Alpha (W, ntercept of regresson lne) c. Unsysteatc varance (σ W β Wσ ) d. Correlaton coeffcent (ρ) Year R t R Mt Rt R t Rt Rt Rt RtRt Rt Rt Rt Rt R t Total Mean R t R t a. eta: Rt Rt Rt Rt 10 Rt Rt t t t1 = 0.89 t1 = b. Alpha: R t R t t 10 t1 1 e = c. Unsysteatc Varance: e Rt R d. Correlaton Coeffcent: = 0.89 = art - 14.

15 Modern ortfolo Theory and Investent Analyss, 9 th Edton Test ank Chapter: 7 5. You are the penson fund anager for a aor unversty wth $100 llon n an ndex fund that nvests n the S& 500 stocks. (The fund holds all the stocks n the ndex n proporton to ther arket values.) Due to recent pressure fro student groups, the regents have decded to dvest theselves of the stocks of frs that nvest n South Afrca. You estate that ths wll elnate 100 of the 500 stocks n your portfolo. You have been asked to evaluate the effect of the dvestture decson. You estate that the correlaton between acceptable and elnated stocks s 0.6. You also have the followng data: Acceptable Stocks Elnated Stocks Nuber of Frs Total Market Value $3 bllon $ bllon Average eta Standard Devaton 5% 30% a. What wll the effect of the dvestent be on the beta of your portfolo? (Report the beta before and after the dvestent.) b. How wll dvestent affect the standard devaton of your portfolo? (Report the standard devaton before and after the dvestent.) c. Assue that the standard devaton of the overall arket s 0%. What s the effect of dvestent on the proporton of your portfolo's rsk that s unsysteatc? (Report the proporton before and after the dvestent.) 3 a. X (efore dvestent) 5 5 After dvestent, the eta s gven as 1. N b. X X X 1 N N = 4.19% (efore dvestent). After dvestent, the standard devaton s gven as 5% c. If the standard devaton of the overall arket s 0%, and the standard devaton of the portfolo before dvestent was 4.19%. n 1 X e n X 1 e Copyrght 014 John Wley & Sons, Inc. art - 15

16 Test ank Modern ortfolo Theory and Investent Analyss, 9 th Edton n X 1 e 1.01% (unsysteatc rsk before elnaton) n e n X 1 Chapter: 7 X 1 e.5% (unsysteatc rsk after elnaton) 6. A securty analyst works for a large nsttuton that uses the sngle-ndex odel as part of ts portfolo-anageent schee. The securty analyst beleves the followng values are relevant for the four stocks she follows RA e 14% 7.5 R ec 1% 9 RC ed 8% 10. RD 11% A C 1.0 D 1.0 ea 15 The nsttuton assues that the rsk-free rate s 6%, and short sellng s not allowed. The nsttuton accepts the Sharpe sngle-ndex odel and uses the procedure descrbed by Elton, Gruber and adberg (EG) to deterne the optu rsky-asset portfolo for the nsttuton to hold. The procedure s to copute Z e rankng crteron for asset C * where the rankng crteron s as descrbed by EG and where C * depends on all rsky assets the nsttuton holds. The nsttuton's anageent has deterned that C * = 3. a. Whch stocks that the analyst follows wll be held n the nsttuton's optu portfolo? b. If the su of the Z's for all the nsttuton's stocks n the optu portfolo s equal to 4, what fracton of the nsttuton's optu portfolo wll each of the stocks that the analyst follows represent? e c. Why should (dversfable rsk) enter nto the optal soluton? Securty Mean Return Excess Return R R ) ( F eta Excess Return over eta A C D a. f C * 3, the stocks A,, and D can be held n the optu portfolo, as ther e art - 16.

17 Modern ortfolo Theory and Investent Analyss, 9 th Edton Test ank excess return over eta s hgher than the cutoff rate. b. If the su of Zs ' for all the nsttuton s stocks n the optu portfolo equals 4, the fracton of the nsttuton s optu portfolo wll be represent as ZA/4, Z/4, and ZD/4. Hence, n ths case, the fracton of the nsttuton s optu portfolo can be found by usng the followng equaton: R RF Z C e Z Z Z A D Therefore, the fracton of the portfolo s ZA =0.13/4, Z = 0.0/4, and ZD = 0.0/4. Therefore, Stock A has a proporton of 3%, Stock has a 5% proporton and Stock D has a proporton of 5%. c. e s denoted as the varance of a stock s oveent that s not assocated wth the oveent of arket ndex. The resdual varance plays an portant role n deternng how uch to nvest n each securty. Chapter: 9 Essays 1. What s a stock's own varance and what s the covarance between two stocks f one accepts the Sharpe sngle-ndex odel? Explan why each s what t s. In a sngle-ndex odel for expected return, a securty s varance has two parts, unque rsk and arket-related rsk. The covarance depends only on the arket rsk. That s why the sngle-ndex odel ples that the only reason securtes ove together s a coon response to arket oveents. The odel s basc equaton s R R e. Where, denotes the expected value of the coponent of return nsenstve to the return on the arket, represents the rando eleent of the coponent, and s the constant eta used to easure the expected change n return on the securty n coparson to the return on arkets. The E R R varance of return on any securty s e E varance of e e as E R R R R e. Fro ths we understand that the. The covarance between any two securtes s descrbed. After substtutng the returns and average returns of the securtes wth the sngle-ndex odel, we get the stock s varance and the covarance between two stocks. We can hence fnd that the varance of a securty s return s Copyrght 014 John Wley & Sons, Inc. art - 17

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