Exam, questions and answers PDF

Preview

Summary

Download Exam, questions and answers PDF

Description

1. I nf or mi ngapor t f ol i ooft wor i skyasset s ,whatmustbet r ueoft hecor r el at i onc oeffi c i entbet ween t hei rr et ur nsi ft her ear et obegai nsf r om di v er s i f i c at i on?

So long as the correlation coefficient is below 1.0, the portfolio will benefit from diversification because returns on component securities will not move in perfect lockstep. The portfolio standard deviation will be less than a weighted average of the standard deviations of the component securities.

2.Thes t andar ddev i at i onoft hemar k et i ndexpor t f ol i oi s20%.St oc kAhasabet aof1. 5anda r esi duals t andar ddev i at i onof30%. a.Whatwoul dmak ef oral ar geri nc r eas ei nt hes t ock ' sv ar i anc e:ani nc r eas eof. 15i ni t sbet aoran i nc r eas eof3% ( f r om 30% t o33%)i ni t sr es i dual s t andar ddev i at i on? b.Ani nv es t orwhoc ur r ent l yhol dst hemar k et i ndexpor t f ol i odec i dest or educ et hepor t f ol i oal l oc at i on t ot hemar k eti ndext o90% andt oi nv es t10% i ns t oc kA.Whi c hoft hechangesi n( a)wi l l hav ea gr eat eri mpactont hepor t f ol i o' ss t andar ddev i at i on?

Total variance = Systematic variance + Residual variance = β2 Var(rM) + Var(e) When β = 1.5 and σ(e) = .3, variance = 1.52 × .22 + .32 = .18. In the other scenarios:

a. Both will have the same impact. Total variance will increase from .18 to .1989. b. Even though the increase in the total variability of the stock is the same in either scenario, the increase in residual risk will have less impact on portfolio volatility. This is because residual risk is diversifiable. In contrast, the increase in beta increases systematic risk, which is perfectly correlated with the market-index portfolio and therefore has a greater impact on portfolio risk.

3.St oc k sofferanex pec t edr at eofr et ur nof10% wi t has t andar ddev i at i onof20%,andgol doffer san ex pect edr et ur nof5% wi t has t andar ddev i at i onof25%. a.I nl i ghtoft heappar enti nf er i or i t yofgol dt os t oc kswi t hr es pec tt obot hmeanr et ur nandv ol at i l i t y , woul dany onehol dgol d?I fso,demonst r at egr aphi cal l ywhyonewoul ddos o. b.Howwoul dy ouans wer( a)i ft hecor r el at i onc oeffi c i entbet weengol dands t ock swer e1?Dr awa

gr aphi l l us t r at i ngwhyonewoul dorwoul dnothol dgol d.Coul dt hes eex pect edr et ur ns ,s t andar d devi at i ons ,andc or r el at i onr epr es entanequi l i br i um f ort hes ec ur i t ymar k et ?

a. Although it appears that gold is dominated by stocks, gold can still be an attractive diversification asset. If the correlation between gold and stocks is sufficiently low, gold will be held as a component in the optimal portfolio. 12% 10%

0.1

8% 6%

0.1 0.09 0.09 0.08 0.08 0.08 0.07 0.07 0.06 0.06 0.05

4%

Corr = -1 Corr = -0.5 Corr = 0 Corr = 0.5 Corr = 1

2% 0% 0%

5%

10%

15%

20%

25%

30%

b. If gold had a perfectly positive correlation with stocks, gold would not be a part of efficient portfolios. The set of risk/return combinations of stocks and gold would plot as a straight line with a negative slope. (Refer to the above graph when correlation is 1.) The graph shows that when the correlation coefficient is 1, holding gold provides no benefit of diversification. The stock-only portfolio dominates any portfolio containing gold. This cannot be an equilibrium; the price of gold must fall and its expected return must rise. 4.Geor geSt ephenson' sc ur r entpor t f ol i oof$2mi l l i oni si nv es t edasf ol l ows :

St ephensonsoonex pec t st or ecei v eanaddi t i onal$2mi l l i onandpl anst oi nv es tt heent i r eamounti n ani ndexf undt hatbestcompl ement st hec ur r entpor t f ol i o.St ephani eCoppa,i sev al uat i ngt hef our i ndexf undss howni nt hef ol l owi ngt abl ef ort hei rabi l i t yt opr oduc eapor t f ol i ot hatwi l l meett woc r i t er i a r el at i v et ot hec ur r entpor t f ol i o:( 1)mai nt ai norenhanceex pect edr et ur nand( 2)mai nt ai norr educ e v ol at i l i t y . Eac hf undi si nv es t edi nanas s etc l asst hati snots ubs t ant i al l yr epr es ent edi nt hec ur r entpor t f ol i o.

St at ewhi chf undCoppas houl dr ec ommendt oSt ephenson.J us t i f yy ourchoi c ebydesc r i bi nghowy our c hos enf undbes tmeet sbot hofSt ephens on' sc r i t er i a.

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 (+ .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.

5.Ar et hef ol l owi ngt r ueorf al s e ? a.St oc k swi t habet aofz er oofferanex pec t edr at eofr et ur nofz er o. b.TheCAPM i mpl i est hati nv es t or sr equi r eahi gherr et ur nt ohol dhi ghl yv ol at i l es ec ur i t i es . c .Youc anc ons t r uc tapor t f ol i owi t habet aof. 75byi nv es t i ng. 75oft hei nv es t mentbudgeti nTbi l l s andt her emai nderi nt hemar k etpor t f ol i o.

a. False. According to CAPM, when beta is zero, the “excess” return should be zero. b. False. CAPM implies that the investor will only require risk premium for systematic risk. Investors are not rewarded for bearing higher risk if the volatility results from the firm-specific risk, and thus, can be diversified. c. False. We can construct a portfolio with the beta of .75 by investing .75 of the investment budget in the market portfolio and the remainder in T-bills.

6.Cons i dert hef ol l owi ngt abl e,whi c hgi v esas ec ur i t yanal y s t ' sex pect edr et ur nont wos t oc ksf ort wo par t i c ul armar k etr et ur ns :

a.Whatar et hebet asoft het wos t ock s ? b.Whati st heex pect edr at eofr et ur noneac hs t ocki ft hemar k etr et ur ni sequal l yl i k el yt obe5% or 20%? c .I ft heTbi l lr at ei s8%,andt hemar k etr et ur ni sequal l yl i k el yt obe5% or20%,dr awt heSMLf ort hi s ec onomy . d.Pl ott het wosec ur i t i esont heSMLgr aph.Whatar et heal phasofeac h? e.Whathur dl er at es houl dbeusedbyt hemanagementoft heaggr ess i v ef i r mf orapr oj ectwi t ht he r i s kchar act er i s t i csoft hedef ensi v ef i r m' ss t oc k ?

a. The beta is the sensitivity of the stock's return to the market return, or, the change in the stock return per unit change in the market return. We denote the aggressive stock A and the defensive stock D, and then compute each stock's beta by calculating the difference in its return across the two scenarios divided by the difference in market return.

A =

D =

= 2.00

= 0.70

b. With the two scenarios equally likely, the expected rate of return is an average of the two possible outcomes: E(rA) = 0.5  (2% + 32%) = 17% E(rD) = 0.5  (3.5% + 14%) = 8.75%

c .TheSMLi sd e t e r mi ne db yt hef o l l o wi n g :Ex pe c t e dr e t ur ni st heTb i l lr a t e=8 % wh e nbe t ae q ua l sz e r o;be t af ort hema r k e ti s1. 0;a n dt hee xp e c t e dr a t eofr e t ur n f ort hema r k e ti s : 0.5  (20% + 5%) = 12.5% Thus, we graph the SML as following:

E( r ) SML A M

12. 5% D 8%

D

. 7

1. 0

2 . 0



The equation for the security market line is: E(r) = 8% + β(12.5% – 8%)

d. The aggressive stock has a fair expected rate of return of: E(rA) = 8% + 2.0 (12.5% – 8%) = 17% The security analyst’s estimate of the expected rate of return is also 17%. Thus the alpha for the aggressive stock is zero. Similarly, the required return for the defensive stock is: E(rD) = 8% + 0.7 (12.5% – 8%) = 11.15%

The security analyst’s estimate of the expected return for D is only 8.75%, and hence:

α

D

= actual expected return – required return predicted by CAPM

= 8.75% – 11.15% = –2.4% The points for each stock are plotted on the graph above.

e. The hurdle rate is determined by the project beta (i.e., 0.7), not by the firm’s beta. The correct discount rate is therefore 11.15%, the fair rate of return on stock D. 7.Suppos et hey i el dons hor t t er m gov er nments ecur i t i es( per c ei v edt ober i s k f r ee)i sabout4%. Suppos eal s ot hatt heexpect edr et ur nr equi r edbyt hemar k etf orapor t f ol i owi t habet aof1i s12%. Ac c or di ngt ot hecapi t alas setpr i ci ngmodel : a.Whati st heex pec t edr et ur nont hemar k etpor t f ol i o?

b.Whatwoul dbet heex pect edr et ur nonaz er obet as t oc k ? c .Suppos ey oucons i derbuyi ngas har eofs t oc katapr i ceof$40.Thes t ocki sex pect edt opaya di v i dendof$3nex ty earandt osel l t henf or$41.Thest oc kr i s khasbeenev al uat edatβ=−. 5.I s t hes t ockov er pr i cedorunder pr i c ed?

a. Since the market portfolio, by definition, has a beta of 1.0, its expected rate of return is 12%. b. β= 0 means the stock has no systematic risk. Hence, the portfolio's expected rate of return is the risk-free rate, 4%. c. Using the SML, the fair rate of return for a stock with β = –0.5 is: E(r) = 4% + (–0.5) (12% – 4%) = 0.0% The expected rate of return, using the expected price and dividend for next year: E(r) = ($41 + $3)/$40 – 1 = 0.10 = 10% Because the expected return exceeds the fair return, the stock must be underpriced.

8.Bas edonc ur r entdi v i dendyi el dsandex pect edcapi t algai ns ,t heex pect edr at esofr et ur non por t f ol i osAandBar e11% and14%,r es pec t i v el y .Thebet aofAi s. 8whi l et hatofBi s1. 5.TheTbi l l r at ei scur r ent l y6%,whi l et heex pec t edr at eofr et ur noft heS&P500I ndexi s12%.Thes t andar d devi at i onofpor t f ol i oAi s10% annual l y ,whi l et hatofBi s31%,andt hatoft hei ndexi s20%. a.I fy ouc ur r ent l yhol damar k et i ndexpor t f ol i o,woul dy ouchoos et oaddei t heroft hesepor t f ol i ost o y ourhol di ngs ?Ex pl ai n. b.I fi ns t eady oucoul di nv es tonl yi nbi l l sandoneoft hesepor t f ol i os ,whi chwoul dy ouchoose ?

a .Us i n gt heSML, t hee xp e c t e dr a t eofr e t ur nf ora n yp or t f o l i oPi s : E(rP) = rf + [E(rM) –rf ]

Sub s t i t ut i n gf o rpo r t f o l i o sAa ndB:

E(rA) = 6% + 0.8  (12% – 6%) = 10.8% < 11% E(rB) = 6% + 1.5  (12% – 6%) = 15.0% > 14%

He n c e , Por t f o l i oAi sd e s i r a bl ea n dPor t f o l i oBi sno t . b .THESHARPERATI OOFPORTFOLI OPI S

S= S (A) = (11% 5/10 S (B) = (14% 8/31 PORTFOLIO A WOULD BE BETTER ADDITION

9.Whi c hoft hef ol l owi ngs t at ement saboutt hes ec ur i t ymar k etl i ne( SML )ar et r ue ? a.TheSMLpr ov i desabenc hmar kf orev al uat i ngex pect edi nv es t mentper f or mance. b.TheSMLl eadsal li nv es t or st oi nv es ti nt hes amepor t f ol i oofr i s kyas s et s . c .TheSMLi sagr aphi cr epr es ent at i onoft her el at i ons hi pbet weenex pect edr et ur nandbet a. d.Pr oper l yv al uedas s et spl otex ac t l yont heSML.

a, c, and d are true; b is incorrect because the SML doesn’t require all investors to invest in the market portfolio but provides a benchmark to evaluate investment performance for both portfolios and individual assets.

10.Kar enKay ,apor t f ol i omanageratCol l i nsAs s etManagement ,i sus i ngt hec api t al as s etpr i c i ng model f ormaki ngr ecommendat i onst oherc l i ent s .Herr es ear chdepar t menthasdev el opedt he i nf or mat i ons howni nt hef ol l owi ngexhi bi t .

a.Cal c ul at eex pec t edr et ur nandal phaf oreac hs t ock . b.I dent i f yandj ust i f ywhi c hs t oc kwoul dbemor eappr opr i at ef orani nv es t orwhowant st o: i. Add this stock to a well-diversified equity portfolio.

ii. Hold this stock as a single-stock portfolio.

a. E(rX) = 5% + 0.8 (14% – 5%) = 12.2%

α

X

= 14% – 12.2% = 1.8%

E(rY) = 5% + 1.5 (14% – 5%) = 18.5%

α

= 17% – 18.5% = –1.5%

1.

For an investor who wants to add this stock to a well-diversified equity portfolio, Kay should recommend Stock X because of its positive alpha, while Stock Y has a negative alpha. In graphical terms, Stock X’s expected return/risk profile plots above the SML, while Stock Y’s profile plots below the SML. Also, depending on the individual risk preferences of Kay’s clients, Stock X’s lower beta may have a beneficial impact on overall portfolio risk.

2.

For an investor who wants to hold this stock as a single-stock portfolio, Kay should recommend Stock Y, because it has higher forecasted return and lower standard deviation than Stock X. Stock Y’s Sharpe ratio is:

Y

b.

(0.17 – 0.05)/0.25 = 0.48 Stock X’s Sharpe ratio is only: (0.14 – 0.05)/0.36 = 0.25 The market index has an even more attractive Sharpe ratio: (0.14 – 0.05)/0.15 = 0.60 However, given the choice between Stock X and Y, Y is superior. When a stock is held in isolation, standard deviation is the relevant risk measure. For assets held in isolation, beta as a measure of risk is irrelevant. Although holding a single asset in isolation is not typically a recommended investment strategy, some investors may hold what is essentially a single-asset portfolio (e.g., the stock of their employer company). For such investors, the relevance of standard deviation versus beta is an important issue.

11.Az er oi nv es t mentwel l di v er s i f i edpor t f ol i owi t hapos i t i v eal phacoul dar i s ei f : a.Theex pect edr et ur noft hepor t f ol i oequal sz er o. b.Thec api t almar k etl i nei st angentt ot heoppor t uni t ys et . c .Thel awofonepr i c er emai nsunv i ol at ed. d.Ar i s k f r eear bi t r ageoppor t uni t yex i s t s .

d

12.I ncont r astt ot hecapi t al ass etpr i c i ngmodel ,ar bi t r agepr i ci ngt heor y a.Requi r est hatmar k et sbei nequi l i br i um. b.Us esr i s kpr emi umsbasedonmi c r ov ar i abl es . c .Spec i f i est henumberandi dent i f i ess peci f i cf ac t or st hatdet er mi neexpect edr et ur ns . d.Doesnotr equi r et her est r i c t i v eas sumpt i onsconcer ni ngt hemar k etpor t f ol i o.

d 12.Suppos et hat ,af t erc onduct i ngananal y s i sofpas tst oc kpr i c es ,y oucomeupwi t ht hef ol l owi ng obs er v at i ons .Whi c hwoul dappeart ocont r adi c tt heweakf or m oft heeffi ci entmar k ethy pot hesi s ? a.Theav er ager at eofr et ur ni ss i gni f i c ant l ygr eat ert hanz er o. b.Thecor r el at i onbet weent her et ur ndur i ngagi v enweekandt her et ur ndur i ngt hef ol l owi ngweeki s z er o. c .Onec oul dhav emades uper i orr et ur nsbybuyi ngs t ockaf t era10% r i sei npr i ceands el l i ngaf t era 10% f al l . d.Onec oul dhav emadehi gher t hanav er agec api t algai nsbyhol di ngs t ock swi t hl owdi v i dendyi el ds .

C 13.A“ r andom wal k ”occ ur swhen: a. Stock price changes are random but predictable. b. Stock prices respond slowly to both new and old information. c. Future price changes are uncorrelated with past price changes. d. Past information is useful in predicting future prices. c 14.Whi c honeoft hef ol l owi ngwoul dbeabul l i s hs i gnal t oat ec hni cal anal y s tus i ngmov i ngav er age r ul es ? a.As t ockpr i c ec r os s esabov ei t s52weekmov i ngav er age. b.As t oc kpr i c ec r oss esbel owi t s52weekmov i ngav er age. c .Thes t oc k' smov i ngav er agei si nc r eas i ng. d.Thest oc k ' smov i ngav er agei sdec r eas i ng.

a...