MBA711 - Chapter 10 - Answers to All Questions

8/10/2019 MBA711 - Chapter 10 - Answers to All Questions

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Chapter 10, Solutions Cornett, Adair, and Nofsinger

CHAPTER 10 CALCULATING EXPECTED RETURN AND MARKET RISK

Questions

LG1 1. Consider an asset that provides the same return no matter what economic state occurs.What would be the standard deviation (or risk) o this asset! "#plain.

Since this asset has no variation in its return, it will have no standard deviation. $his couldbe shown mathematicall% be demonstratin& that each economic state's return is the sameas it avera&e. $hereore, all terms in the standard deviation summation euation are ero.$his asset would be known as a risk*ree asset.

LG1 +. Wh% is e#pected return considered orward*lookin&-! What are the challen&es orpractitioners to utilie e#pected return!

"#pected return is orward*lookin&- in the sense that it represents the return investorse#pect to receive in the uture as compensation or the market risk taken. $he challen&e isthat practitioners cannot precisel% know what the uture holds and thus what the e#pectedreturn should be. $hus, we create methods to estimate the e#pected return.

LG+ . /n +000, the S 200 /nde# earned 34.1 percent while the $*bill %ield was 2.4 percent.5oes this mean the market risk premium was ne&ative! "#plain.

$he market risk premium is a orward*lookin& tool and should alwa%s be positive.6ecause the market has risk, it will periodicall% have a ne&ative return or a small positivereturn that is smaller than the $*bill rate. $hus, realied returns over a short period o time

will sometimes show what appears to be a ne&ative risk premium. 7owever, historicalrisk premiums should be measured over lon& periods o time.

LG+ 8. 7ow mi&ht the ma&nitude o the market risk premium impact people's desire to bu%stocks!

"ver%bod% has a dierent level o risk aversion. eople who have a low level o riskaversion would be willin& to bu% stocks with hi&h risk . 7owever, people who have ahi&h level o risk aversion would onl% be willin& to bu% stocks with low risk. $hereore,the ma&nitude o the risk premium does impact who wants to bu% stocks.

LG 2. 5escribe how addin& a risk*ree securit% to modern portolio theor% allows investors todo better than the eicient rontier.

$he best portolios investors can hold with onl% risk% assets are the eicient portolios onthe eicient rontier. / investors can borrow and lend at a risk ree rate, then the% can dobetter. $o improve over the eicient rontier, investors should allocate their portolio tothe risk ree rate and to the market portolio. With the ri&ht wei&hts between the two, an

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investor can ind a portolio with the same level o risk as an eicient portolio but has ahi&her e#pected return.

LG 9. Show on a &raph like :i&ure 10.+ where a stock with a beta o 1. would be located on

the Securit% ;arket Line. $hen show where that stock would be located i it isundervalued.

:i&ure shownouwant to know i the ourth stock will make the portolio riskier or less risk%. Compare andcontrast how this would be assessed usin& standard deviation versus market risk (beta) asthe measure o risk.

?sin& standard deviation, %ou would need to determine how the ourth stock interactswith the three stocks alread% owned. $o do this %ou would have to compute thecorrelation between the new stock and each o the three alread% held. $hen, the portoliostandard deviation could be computed. / the new portolio standard deviation is lower

then the ori&inal portolio standard deviation, then addin& the new stock lowers the risk.@ course, the portions, or wei&hts o all the stocks will matter. 5eterminin& whetheraddin& a stock will increase or lower the risk o the portolio is much easier usin& beta. /the beta o the ourth stock is hi&her than the beta o the portolio, then it will increase therisk when added.

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LG A. 5escribe how dierent allocations between the risk*ree securit% and the marketportolio can achieve an% level o market risk desired. Give e#amples o a portolio rom aperson who is ver% risk averse and a portolio or someone who is not so averse to takin&risk.

Bn investor can allocate mone% between a risk*ree securit% that has ero risk (D0), andthe market portolio that has market risk (D1). / =2E o the portolio is invested in themarket, then the portolio will have a D0.=2. / onl% +2E is invested in the market, thenthe portolio will have a market risk o D0.+2. $he irst e#ample (D0.=2) mi&ht be takenb% a less risk averse investor while the second e#ample (D0.+2) illustrates the portolio oa more risk averse investor. 6% allocatin& the investment mone% between 0 and 100E intothe market portolio, an investor can achieve an% level o market risk desired.

LG8 4. Cisco S%stems has a beta o 1.AA. 5oes this mean that %ou should e#pect Cisco to earna return AA percent hi&her than the S 200 /nde# return! "#plain.

Fot uite. B beta o 1.AA means that Cisco's risk premium is AAE hi&her then the marketrisk premium. /n other words, we must account or the risk ree rate. $his relationship isshown in the CB; euation.

LG8 10. Fote rom $able 10.+ that some technolo&%*oriented irms (/ntel, and /6;) in the5ow ones /ndustrial Bvera&e have hi&h market risk while others (B$$, ;icrosot, andHerion) have low market risk. 7ow do %ou e#plain this!

Fot all technolo&% industries have the same level o risk. Fotice rom this e#ample thatthe more manuacturin& (hardware) tech companies have hi&her risk. $he service and

sotware tech companies have lower risk. $his ma% be an indication o the t%pe o assetsneeded b% the irms and the amount o debt reuired.

LG8 11. :ind a beta estimate rom three dierent sources or General "lectric (G"). Comparethese three values. Wh% mi&ht the% be dierent!

>ahooI :inance beta was 0.24. ;SF ;one% shows a beta o 0.=9. 7oovers lists a beta o0.A. $he beta sources ma% use (i) dierent market portolios, (ii) dierent time periods, or(iii) dierent time increments (annual returns versus months, weeks, etc.).

LG8 1+. / %ou were to compute beta %oursel, what choices would %ou make re&ardin& themarket portolio, the holdin& period or the returns (dail%, weekl%, etc.), and the number oreturns! usti% %our choices.

/t is common to use the S200, monthl% returns, and either three to ive %ears o data.

LG2 1. "#plain how the concept o a positive risk*return relationship breaks down i %ou cans%stematicall% ind stocks that are over*valued and under*valued.

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Consider two stocks< one stock has a beta o 0.4 and is undervalued, the other has a betao 1 and is overvalued. / beta perectl% e#plained e#pected returns, then the hi&her betastock would oer a hi&her e#pected return. 7owever, i %ou believe the lower beta stock is

undervalued, then %ou are sa%in& it will achieve a return hi&her than e#pected b% its beta.>ou also believe the overvalued stock will earn a return lower than e#pected b% its beta.$hus, %ou mi&ht e#pect the undervalued stock to outperorm the overvalued stock eventhou&h the risks o the two stocks su&&est otherwise.

LG2 18. 5etermine what level o market eicienc% each event is consistent withes, abubble can occur in a sin&le stock.

LG9 1=. / stock prices are not stron&*orm eicient, then what mi&ht be the price reaction to airm announcin& a stock bu%back! "#plain.

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$wo dierent ar&uments could be made. :irst, the price could increase with therealiation that this demand or stock will push up the stock price. Blternativel%, the pricecould decline i investors believe that the compan% does not have an% &ood product

related investments and thus must bu% back its stock.

LG= 1A. Compare and contrast the assumptions that need to be made to compute a reuiredreturn usin& CB; and the constant &rowth rate model.

When usin& the CB; to compute reuired return, %ou need to make assumptions aboutwhat the e#pected market return will be, what the risk ree rate will be, and what theuture beta o the irm will be. $he uture beta is commonl% similar to the recent past beta.$he risk ree rate is well estimated b% $*bill rates and the %ield curve. $hese two arereasonabl% estimated. 7owever, the stock market is ver% volatile and the uture marketreturn is diicult to estimate. $he constant &rowth rate model assumes that the &rowth o

the irm will remain constant. $he &rowth rate and the dividend must be assumed. :irmsdo not chan&e their dividends ver% much, so that estimation is not diicult. 7owever, thereuired rate is ver% sensitive to the estimated &rowth rate. 6oth models reuire diicultassumptions.

LG= 14. 7ow should %ou handle a case where reuired return computations rom CB; andthe constant &rowth rate model are ver% dierent!

:irst, e#amine the assumptions o each model. / no mistakes have been made, thencompute the reuired return or similar irms in the same industr%. ?se the CB; orconstant &rowth rate estimate that most resembles that o its competitors.

Probe!s

6asicroblems 10*1 E"#e$te% Return Compute the e#pected return &iven these three economic states,

their likelihoods,LG1 and the potential returnsou have a portolio with a beta o 1.+. What will be the newportolio beta i %ou keep 40 percent o %our mone% in the old portolio and 10 percent ina stock with a beta o 1.4!

Few portolio beta D 0.401.+ M 0.101.4 D 1.+=

LG 10*1+ Port*oio +et&>ou have a portolio with a beta o 1.1. What will be the new

portolio beta i %ou keep A2 percent o %our mone% in the old portolio and 12 percent ina stock with a beta o 0.2!

Few portolio beta D 0.A21.1 M 0.120.2 D 1.01

LG2 10*1 Sto$) M&r)et +ubbe$he Fasda stock market bubble peaked at 8,A19 in +000.$wo and a hal %ears later it had allen to 1,000. What was the percenta&e decline!

;arket decline D (1,000 3 8,A19) N 8,A19 D 30.=4+8 D 3=4.+8E

LG2 10*18 Sto$) M&r)et +ubbe$he apanese stock market bubble peaked at A,419 in 14A4.

$wo and a hal %ears later it had allen to 12,400. What was the percenta&e decline!

;arket decline D (12,400 3 A,419) N A,419 D 30.2418 D 324.18E

LG= 10*12 Re(uire% Returnaccar's current stock price is O=.10 and it is likel% to pa% aO+.94 dividend ne#t %ear. Since anal%sts estimate accar will have a 11.+E &rowth rate,what is its reuired return!

?se euation 10.9< EAA.1818AA.011+.010.=O

94.+O

0

1==+=+= g

P

Di

LG= 10*19 Re(uire% Return?niversal :orest's current stock price o ?niversal :orest isO28.00 and it is likel% to pa% a O0.+ dividend ne#t %ear. Since anal%sts estimate?niversal :orest will have a 10.0E &rowth rate, what is its reuired return!

?se euation 10.9< E8.10108.010.000.28O

+.0O

0

1==+=+= g

P

Di

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/ntermediateroblems 10*1= E"#e$te% Return Ris):or the same economic state probabilit% distribution in

roblem 10.1, determine the standard deviation o the e#pected return.

LG1

E$ono!i$

St&te

Prob&biit' Return

:ast Growth 0. 80E

Slow Growth 0.2 10E

Kecession 0.+ 3+2E

?se euation 10.+ and e#pected return rom roblem 10.1 o 1+E

MBA711 - Chapter 10 - Answers to All Questions

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