Descubra ms en www.kawsarbd1.weebly.comDure ahorrado y corregido por Md.Kawsar Siddiqui 113Principios de la solucin directiva de las finanzasLorenzo J. Descripcin

de los RECURSOS de S

del INSTRUCTOR del riesgo yde la vuelta del CAPTULO 5 de Gitman' queeste captulo se centra en los fundamentales del riesgo y de la relacin de la vuelta de activos y de su valuacin. Parael solo activo sostenido en el aislamiento, el riesgo se mide con la distribucinde la probabilidad y su estadstica asociada:el medio, la desviacin de estndar, y el coeficiente de variacin. El concepto de ladiversificacin es examinadomidiendo el riesgo de una lista de los activos que se correlacionan perfectamente positivamente, correlacionado perfectamente negativamente,y los que sean sin correlacin. Despus, el captulo mira la diversificacin internacional y su efecto sobre riesgo.El modelo de tasacin de activo fijo (CAPM) entonces se presenta como herramientade la valuacin para las seguridades y como explicacingeneral del riesgo-vuelve la compensacin implicada en todos los tipos de transacciones financieras.Los asuntos de estecaptulo de PMF EL DISCO no se cubre en el profesor particular de PMF o el Problem-Solver de PMF.Las plantillas de la hoja de balancede las plantillas de PMF se proporcionan para los problemas siguientes:Autoprueba 2del anlisis de la lista de la autoprueba 1del asunto del problema beta y coeficientedel problema 5-7 de CAPM de lneadel mercado de seguridad del problema 5-26 de la variacin, riesgodel captulo 5 de SML y vueltaDescubra ms en www.kawsarbd1.weebly.comrrado y corregido por la gua del estudio de Md.KawsarSiddiqui 114

Dure aho

los ejemplos siguientes de la gua del estudio se sugieren para la presentacin de la sala de clase:

Asunto 4del ejemplo Actitudes 6del riesgo Determinacin grfica de 12beta El impacto del mercado cambia en el riesgode vuelta y la vuelta del captulo 5Descubra ms en www.kawsarbd1.weebly.comrrado y corregido por Md.Kawsar Siddiqui 115RESPUESTAS PARA REPASAR riesgo

Dure aho

de las PREGUNTAS 5-1 se define como la ocasin de la prdida financiera, segn lo medido por la variabilidad de las vueltas previstas asociadasa un activo dado. Un responsable debe evaluar una inversin midiendo la ocasin dela prdida, odel riesgo, y de comparar el riesgo previsto a la vuelta prevista. Algunos activos se consideran riesgo-libres;los ejemplos mas comunes son U. S. Ediciones del Hacienda.5-2 la vuelta en una inversin (aumento olquier excedente de las distribuciones deal perodo definido. Se expresa como porrodo. El frmulaes:[ ]La vuelta =(valor del conclusin - valor inicial) +del valor inicial

prdida total) es el cambio en valor ms cuaefectivociento de la inversin del comenzar-de--pe

vuelta observada

de la distribucin de efectivo requiere el activo ser comprada y vendido durante los perodos se mide la vuelta.La vuelta sin realizar es la vuelta que habra podido ser observada si el activo haba sido comprado y vendidodurante el perodo la vuelta fue medida.5-3 A. El encargado financiero riesgo-contrario requiere un aumento a cambio deun aumento dado en riesgo.b. El encargado riesgo-indiferente no requiere ningn cambio a cambio de un aumento en riesgo.c. El encargado riesgo-que busca acepta una disminucin a cambio de un aumento dado en riesgo.La mayora de los encargados financieros son riesgo-contrarios.5-4 el anlisis de la sensibilidad evala riesgo del activo usando ms que uno sistemaposible de vueltas para obtener un sentidode la variabilidad de resultados. The range is found by subtracting the pessimistic outcome from the optimisticoutcome. The larger the range, the more variability of risk associated with theasset.5-5 The decision maker can get an estimate of project risk by viewing a plot ofthe probability distribution,which relates probabilities to expected returns and shows the degree of dispersion of returns. The morespread out the distribution, the greater the variability or risk associated withthe return stream.

5-6 The standard deviation of a distribution of asset returns is an absolute measure of dispersion of risk aboutthe mean or expected value. A higher standard deviation indicates a greater project risk. With a largerstandard deviation, the distribution is more dispersed and the outcomes have a higher variability, resultingin higher risk.5-7 The coefficient of variation is another indicator of asset risk, measuring relative dispersion. It is calculatedby dividing the standard deviation by the expected value. The coefficient of variation may be a better basisthan the standard deviation for comparing risk of assets with differing expectedreturns.5-8 An efficient portfolio is one that maximizes return for a given risk level or minimizes risk for a given levelof return. Return of a portfolio is the weighted average of returns on the individual component assets:Chapter 5 Risk and ReturnFind out more at www.kawsarbd1.weebly.comsaved and edited by Md.Kawsar Siddiqui 116==n1jjjp kwk

Last

Where n = number of assets, wj = weight of individual assets, and = expected jkReturns.The standard deviation of a portfolio is not the weighted average of component standard deviations; therisk of the portfolio as measured by the standard deviation will be smaller. Itis calculated by applying thestandard deviation formula to the portfolio assets:kp iin k kn= =( )( )21 15 9 The correlation between aet return i important when evaluating the effect of a new aet on theportfolio' overall rik. Return on different aet moving in the ame direction are poitively correlated,while thoe moving in oppoite direction are negatively correlated. Aet wit

h high poitive correlationincreae the variability of portfolio return; aet with high negative correlation reduce the variability ofportfolio return. When negatively correlated aet are brought together through diverification, thevariability of the expected return from the reulting combination can be le than the variability or rik ofthe individual aet. When one aet ha high return, the other' return arelow and vice vera.Therefore, the reult of diverification i to reduce rik by providing a pattern of table return.Diverification of rik in the aet election proce allow the invetor to reduce overall rik by combiningnegatively correlated aet o that the rik of the portfolio i le than therik of the individual aet in it.Even if aet are not negatively correlated, the lower the poitive correlationbetween them, the lower thereulting rik.5 10 The incluion of foreign aet in a dometic company' portfolio reduce rik for two reaon. Whenreturn from foreign currency denominated aet are tranlated into dollar, the correlation of return ofthe portfolio' aet i reduced. Alo, if the foreign aet are in countriethat are le enitive to theU.S. buine cycle, the portfolio' repone to market movement i reduced.When the dollar appreciate relative to other currencie, the dollar value of aforeign currencydenominated portfolio decline and reult in lower return in dollar term. Ifthi appreciation i due tobetter performance of the U.S. economy, foreign currency denominated portfoliogenerally have lowerreturn in local currency a well, further contributing to reduced return.Political rik reult from poible action by the hot government that are harmful to foreign invetor orpoible political intability that could endanger foreign aet. Thi form ofrik i particularly high indeveloping countrie. Companie diverifying internationally may have aet eized or the return ofprofit blocked.5 11 The total rik of a ecurity i the combination of nondiverifiable rik and diverifiable rik. Diverifiablerik refer to the portion of an aet' rik attributable to firm pecific, random event (trike, litigation,lo of key contract, etc.) that can be eliminated by diverification. Nondiverifiable rik i attributable tomarket factor affecting all firm (war, inflation, political event, etc.). Some argue that nondiverifiablerik i the only relevant rik becaue diverifiable rik can be eliminated by creating a portfolio of aetwhich are not perfectly poitively correlated.5 12 Beta meaure nondiverifiable rik. It i an index of the degree of movement of an aet' return inrepone to a change in the market return. The beta coefficient for an aet can be found by plotting the

Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comLataved and edited by Md.Kawar Siddiqui 117aet' hitorical return relative to the return for the market. By uing tatitical technique, the"characteritic line" i fit to the data point. The lope of thi line i beta. Beta coefficient for activelytraded tock are publihed in Value Line Invetment Survey and in brokerage report. The beta of aportfolio i calculated by finding the weighted average of the beta of the individual component aet.5 13 The equation for the Capital Aet Pricing Model i: kj = RF+[bj x (kmRF)],Where:kj = the required (or expected) return on aet j.RF = the rate of return required on a rik free ecurity (a U.S. Treaury bill)bj = the beta coefficient or index of nondiverifiable (relevant) rik for aetjkm = the required return on the market portfolio of aet (the market return)The ecurity market line (SML) i a graphical preentation of the relationhip between the amount ofytematic rik aociated with an aet and the required return. Sytematic rik i meaured by beta and ion the horizontal axi while the required return i on the vertical axi.5 14 a. If there i an increae in inflationary expectation, the ecurity market line will how a parallel hiftupward in an amount equal to the expected increae in inflation. The required return for a given levelof rik will alo rie.b. The lope of the SML (the beta coefficient) will be le teep if invetor become le rik avere, anda lower level of return will be required for each level of rik.5 15 The CAPM provide financial manager with a link between rik and return.Becaue it wa developed toexplain the behavior of ecuritie price in efficient market and ue hitorical data to etimate requiredreturn, it may not reflect future variability of return. While tudie have upported the CAPM whenapplied in active ecuritie market, it ha not been found to be generally applicable to real corporateaet. However, the CAPM can be ued a a conceptual framework to evaluate therelationhip betweenrik and return.Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comLataved and edited by Md.Kawar Siddiqui 118SOLUTIONS TO PROBLEMS5 1 LG 1: Rate of Return:1tt1tttP)CPP(k +=

a.Invetment X: Return %50.12000,20$)500,1$000,20$000,21($ =+=Invetment Y: Return %36.12000,55$)800,6$000,55$000,55($ =+=b. Invetment X hould be elected becaue it ha a higher rate of return for the ame level of rik.5 2 LG 1: Return Calculation:1tt1tttP)CPP(k +=Invetment Calculation kt (%)ABCDE

($1,100 $800 $100) $800 25.00($118,000 $120,000 + $15,000) $120,000 10.83($48,000$45,000 + $7,000) $45,000 22.22($500 $600 + $80) $600 3.33($12,400$12,500 + $1,500) $12,500 11.20

5 3 LG 1: Rik Preferencea. The rik indifferent manager would accept Invetment X and Y becaue thee have higher return than the12% required return and the rik doent matter.b. The risk-averse manager would accept Investment X because it provides the highest return and has thelowest amount of risk. Investment X offers an increase in return for taking onmore risk than what the firmcurrently earns.c. The risk-seeking manager would accept Investments Y and Z because he or she is willing to take greaterrisk without an increase in return.d. Traditionally, financial managers are risk-averse and would choose InvestmentX, since it provides therequired increase in return for an increase in risk.

5-4 LG 2: Risk Analysisa. Expansion RangeA 24% - 16% = 8%B 30% - 10% = 20%

b. Project A is less risky, since the range of outcomes for A is smaller than the range for Project B.Chapter 5 Risk and ReturnFind out more at www.kawsarbd1.weebly.comLastsaved and edited by Md.Kawsar Siddiqui 119c. Since the most likely return for both projects is 20% and the initial investments are equal, the answerdepends on your risk preference.d. The answer is no longer clear, since it now involves a risk-return trade-off.Project B has a slightly higherreturn but more risk, while A has both lower return and lower risk.5-5 LG 2: Risk and Probabilitya. Camera RangeR 30% - 20% = 10%S 35% - 15% = 20%b. Possible Probability Expected Return WeightedOutcomes Pri ki Value (%)(ki x Pri)Camera R Pessimistic 0.25 20 5.00Most likely 0.50 25 12.50Optimistic 0.25 30 7.501.00 Expected Return 25.00Camera S Pessimistic 0.20 15 3.00Most likely 0.55 25 13.75Optimistic 0.25 35 8.751.00 Expected Return 25.50c. Camera S is considered more risky than Camera R because it has a much broaderrange of outcomes. Therisk-return trade-off is present because Camera S is more risky and also provides a higher return thanCamera R.

Chapter 5 Risk and ReturnFind out more at www.kawsarbd1.weebly.comsaved and edited by Md.Kawsar Siddiqui 1205-6 LG 2: Bar Charts and Riska.Bar Chart-Line J00.10.20.30.40.50.60.75 1.25 8.5 14.7Expected Return (%) 5 16.25

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Probability

Bar Chart-Line K

00.10.20.30.40.50.61 2. 155 8 13.5Expected Return (%)

Probability

b. WeightedMarket Probability Expected Return ValueAcceptance Pri ki (ki x Pri)Line J Very Poor 0.05 .0075 .000375Poor 0.15 .0125 .001875Average 0.60 .0850 .051000Good 0.15 .1475 .022125Excellent 0.05 .1625 .0081251.00 Expected Return .083500Chapter 5 Risk and ReturnFind out more at www.kawsarbd1.weebly.comsaved and edited by Md.Kawsar Siddiqui 121Line K Very Poor 0.05 .010 .000500Poor 0.15 .025 .003750Average 0.60 .080 .048000

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Good 0.15 .135 .020250Excellent 0.05 .150 .0075001.00 Expected Return .080000c. Line K appears less risky due to a slightly tighter distribution than line J,indicating a lower range ofoutcomes.5-7 LG 2: Coefficient of Variation:kCV k=a. A 3500.%20%7CVA ==B 4318.%22%5.9CVB ==C 3158.%19%6CVC ==D 3438.%16%5.5CVD ==b. Aet C ha the lowet coefficient of variation and i the leat riky relative to the other choice.

5 8 LG 2: Standard Deviation veru Coefficient of Variation a Meaure of Rika. Project A i leat riky baed on range with a value of .04.b. Project A i leat riky baed on tandard deviation with a value of .029. Standard deviation i not theappropriate meaure of rik ince the project have different return.c. A 2417.12.029.CVA ==B 2560.125.032.CVB ==C 2692.13.035.CVC ==D .2344128.030.CVD ==In thi cae project A i the bet alternative ince it provide the leat amount of rik for each percent ofreturn earned. Coefficient of variation i probably the bet meaure in thi in

tance ince it provide atandardized method of meauring the rik/return trade off for invetment withdiffering return.Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 1225 9 LG 2: Aeing Return and Rika. Project 2571. Range: 1.00

( .10) = 1.10

2. Expected return: irn1ii Pkk ==Rate of Return Probability Weighted Value Expected Returnki Pri ki x Pri irn1ii Pkk ==.10 .01 .001.10 .04 .004.20 .05 .010.30 .10 .030.40 .15 .060.45 .30 .135.50 .15 .075.60 .10 .060.70 .05 .035.80 .04 .0321.00 .01 .0101.00 .4503. Standard Deviation: ==n1ii )kk( 2 x Pri2 Pri )kk( i 2 x Priki k kki )kk( i .10 .450 .550 .3025 .01 .003025.10 .450 .350 .1225 .04 .004900.20 .450 .250 .0625 .05 .003125.30 .450 .150 .0225 .10 .002250.40 .450 .050 .0025 .15 .000375.45 .450 .000 .0000 .30 .000000.50 .450 .050 .0025 .15 .000375.60 .450 .150 .0225 .10 .002250.70 .450 .250 .0625 .05 .003125.80 .450 .350 .1225 .04 .0049001.00 .450 .550 .3025 .01 .003025..027350Project 257 = .027350 = .165378

Lat

4. 3675.450.165378.CV ==Project 4321. Range: .50

.10 = .40

2. Expected return: irn1ii Pkk ==Rate of Return Probability Weighted Value Expected ReturnChapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 123ki Pri ki x Pri irn1ii Pkk ==.10 .05 .0050.15 .10 .0150.20 .10 .0200.25 .15 .0375.30 .20 .0600.35 .15 .0525.40 .10 .0400.45 .10 .0450.50 .05 .02501.00 .300

3. Standard Deviation: ==n1ii )kk( 2 x Priki k kki )kk( i 2 P ri )kk( i 2 x Pri.10.15.20.25.30.35.40.45.50

.300 .20 .0400 .05 .002000.300 .15 .0225 .10 .002250.300 .10 .0100 .10 .001000.300 .05 .0025 .15 .000375.300 .00 .0000 .20 .000000.300 .05 .0025 .15 .000375.300 .10 .0100 .10 .001000.300 .15 .0225 .10 .002250.300 .20 .0400 .05 .002000.011250

Project 432 = .011250 = .1060664. 3536.

Lat

300.106066.CV ==

b. Bar ChartProject 257ProbabilityChapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 124

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c.Summary StatiticProject 257 Project 43200.050.10.150.20.250.310% 30% 40% 60% 70% 80% 100%Rate of ReturnProject 43210% 20% 45% 50%Range 1.100 .400ExpectedReturn ( k ) 0.450 .300StandardDeviation ( ) 0.165 .106 kCoefficient ofVariation (CV) 0.3675 .353600.050.150.20.250.320% 25% 35% 40% 45% 50%Probability0.110% 15% 30%Since Project 257 and 432 have differing expected value, the coefficient of variationhould be the criterion by which the rik of the aet i judged. Since Project

432 haa maller CV, it i the opportunity with lower rik.Rate of Return

5 10 LG 2: IntegrativeExpected Return, Standard Deviation, and Coefficient of Variationa. Expected return: ==n1iiri PkkRate of Return Probability Weighted Value Expected Returnki Pri ki x Pri irn1ii Pkk ==Aet F .40 .10 .04.10 .20 .02.00 .40 .00.05 .20 .01.10 .10 .01.04Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 125Aet G .35 .40 .14.10 .30 .03.20 .30 .06.11Aet H .40 .10 .04.20 .20 .04.10 .40 .04.00 .20 .00.20 .10 .02.10Aet G provide the larget expected return.b. Standard Deviation: ==n1i

Lat

ik )kk( 2 x Pri)kk( i )kk( i 2 P ri 2 kAet F .40 .04 = .36 .1296 .10 .01296.10 .04 = .06 .0036 .20 .00072.00 .04 = .04 .0016 .40 .00064.05 .04 = .09 .0081 .20 .00162.10 .04 = .14 .0196 .10 .00196.01790 .1338

)kk( i )kk( i 2 P ri 2 kAet G .35 .11 = .24 .0576 .40 .02304.10 .11 = .01 .0001 .30 .00003.20 .11 = .31 .0961 .30 .02883.05190 .2278Aet H .40 .10 = .30 .0900 .10 .009.20 .10 = .10 .0100 .20 .002.10 .10 = .00 .0000 .40 .000.00 .10 = .10 .0100 .20 .002.20 .10 = .30 .0900 .10 .009.022 .1483Baed on tandard deviation, Aet G appear to have the greatet rik, but it mut be meaured againt itexpected return with the tatitical meaure coefficient of variation, ince thethree aet have differingexpected value. An incorrect concluion about the rik of the aet could bedrawn uing only thetandard deviation.c.valueexpected)(deviation tandard=Variation oft Coefficien Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 126Aet F: 345.304.1338.CV ==

Lat

Aet G: 071.211.2278.CV ==Aet H: 483.110.1483.CV ==A meaured by the coefficient of variation, Aet F ha the larget relative rik.5 11 LG 2: Normal Probability Ditributiona. Coefficient of variation: CV = kk

Solving for tandard deviation: .75 = k .189k = .75 x .189 = .14175

b. 1. 58% of the outcome will lie between 1 tandard deviation from the expected value:+l = .189 + .14175 = .33075l = .189 .14175 = .047252. 95% of the outcome will lie between 2 tandard deviation from the expectedvalue:+2 = .189 + (2 x. 14175) = .47252 = .189 (2 x .14175) = .09453. 99% of the outcome will lie between 3 tandard deviation from the expectedvalue:+3 = .189 + (3 x .14175) = .614253 = .189 (3 x .14175) = .23625c.Probability DitributionChapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 12701020304050600.236 0.094 0.047 0.331 0.473 0.6140.189Return

Probability

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5 12 LG 3: Portfolio Return and Standard Deviationa. Expected Portfolio Return for Each Year: kp = (wL x kL) + (wM x kM)ExpectedAet L Aet M Portfolio ReturnYear (wL x kL) + (wM x kM) kp200420052006200720082009

(14%(14%(16%(17%(17%(19%

x.40x.40x.40x.40x.40x.40

======

5.6%)5.6%)6.4%)6.8%)6.8%)7.6%)

++++++

(20%(18%(16%(14%(12%(10%

xxxxxx

.60.60.60.60.60.60

======

12.0%) = 17.6%10.8%) = 16.4%9.6%) = 16.0%8.4%) = 15.2%7.2%) = 14.0%6.0%) = 13.6%

b. Portfolio Return:nkwkn1jjjp==%5.15467.1566.130.142.150.164.166.17kp ==+++++=c. Standard Deviation: kp iin k kn= =( )( )21 1Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 12816%)5.15%6.13(%)5.15%0.14(%)5.15%2.15(%)5.15%0.16(%)5.15%4.16(%)5.15%6.17(222222kp +++++=

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5%)9.1(%)5.1(%)3.0(%)5.0(%)9(.%)1.2(222222kp+++++=5%)61.3%25.2%09.0%25.0%81.0%41.4(kp+++++=51129.1284.2542.11kp ===d. The aet are negatively correlated.e. Combining thee two negatively correlated aet reduce overall portfolio rik.5 13 LG 3: Portfolio Analyia. Expected portfolio return:Alternative 1: 100% Aet F%5.174%19%18%17%16kp =+++=Alternative 2: 50% Aet F + 50% Aet GAet F Aet G Portfolio ReturnYear (wF x kF) + (wG x kG) kp2001200220032004

(16%(17%(18%(19%

xxxx

.50.50.50.50

====

8.0%)8.5%)9.0%)9.5%)

++++

(17%(16%(15%(14%

xxxx

.50.50.50.50

====

8.5%)8.0%)7.5%)7.0%)

====

16.5%16.5%16.5%16.5%

%5.16466kp ==Alternative 3: 50% Aet F + 50% Aet HAet F Aet H Portfolio ReturnYear (wF x kF) + (wH x kH) kp2001 (16% x .50 = 8.0%) + (14% x .50 = 7.0%) 15.0%2002 (17% x .50 = 8.5%) + (15% x .50 = 7.5%) 16.0%2003 (18% x .50 = 9.0%) + (16% x .50 = 8.0%) 17.0%

2004 (19% x .50 = 9.5%) + (17% x .50 = 8.5%) 18.0%Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 129%5.16466kp ==

b. Standard Deviation: kp iin k kn= =( )( )21 1(1)[ ]14%)5.17%0.19(%)5.17%0.18(%)5.17%0.17(%)5.17%0.16( 2222F +++=[ ]3%)5.1(%)5.0(%)5.0(%) 1.5( 2222F+++=3%)25.2%25.0%25.0%25.2(F+++=291.1667.135F ===(2) [ ]14%)5.16%5.16(%)5.16%5.16(%)5.16%5.16(%)5.16%5.16( 2222FG +++=[ ]3)0()0()0()0( 2222FG+++=

Lat

0FG =(3)[ ]FH = + + + ( . . ( . . ( . . ( . .150% 165%) 16 0% 165%) 17 0% 165%) 18 0% 165%)4 12 2 2 2[ ]3%)5.1(%)5.0(%)5.0(%)5.1( 2222FH+++=[ ]3)25.225.25.25.2(FH+++=Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 130

Lat

291.1667.135FH ===c. Coefficient of variation: CV = kk 0738.%5.17291.1CVF ==0%5.160CVFG ==0782.%5.16291.1CVFH ==d. Summary:kp: Expected Valueof Portfolio kp CVpAlternative 1 (F) 17.5% 1.291 .0738Alternative 2 (FG) 16.5% 0 .0Alternative 3 (FH) 16.5% 1.291 .0782Since the aet have different expected return, the coefficient of variation hould be ued to determinethe bet portfolio. Alternative 3, with poitively correlated aet, ha the highet coefficient of variationand therefore i the rikiet. Alternative 2 i the bet choice; it i perfectly negatively correlated andtherefore ha the lowet coefficient of variation.

5 14 LG 4: Correlation, Rik, and Returna. 1. Range of expected return: between 8% and 13%2. Range of the rik: between 5% and 10%b. 1. Range of expected return: between 8% and 13%2. Range of the rik: 0 < rik < 10%c. 1. Range of expected return: between 8% and 13%2. Range of the rik: 0 < rik < 10%5 15 LG 1, 4: International Invetment Returna. Returnpeo = %73.2020732.500,20250,4500,20500,20750,24 ===b. 84.225,2$hare000,122584.2$21.950.20dollarper Peopeoin Priceprice Purchae ===Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 13169.512,2$hare000,151269.2$85.975.24dollarper Peopeoin Priceprice aleS ===

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c. Returnpeo = %89.1212887.84.225,285.28684.225,284.225,269.512,2 ===d. The two return differ due to the change in the exchange rate between the peo and the dollar. The peohad depreciation (and thu the dollar appreciated) between the purchae date andthe ale date, cauing adecreae in total return. The anwer in part c i the more important of the tworeturn for Joe. An invetorin foreign ecuritie will carry exchange rate rik.5 16 LG 5: Total, Nondiverifiable, and Diverifiable Rika. and b.

c. Only nondiverifiable riki relevant becaue, ahown by the graph, diverifiable rik can be virtually eliminated through holding a portfolio of at leat 20ecuritie which are not poitively correlated. David Talbot' portfolio, auming diverifiable rik couldno longer be reduced by addition to the portfolio, ha 6.47% relevant rik.02468101214160 5 10 15 20Number of SecuritieDiverifiable NondiverifiablePortfolioRik(kp)(%)5 17 LG 5: Graphic Derivation of BetaChapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 132a. Derivation of Betab. To etimatebeta, the "rie overrun" method can beued:Beta =RieRun= YXTaking thepoint hown on thegraph:75.4348912 ==XY=A Beta =

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33.13410132226XY=B Beta ===128404812162024283216 12 8 4 0 4 8 12 16Aet BAet AMarket ReturnAet Return %b = lope = 1.33b = lope = .75A financial calculator with tatitical function can be ued to perform linearregreion analyi. The beta(lope) of line A i .79; of line B, 1.379.c. With a higher beta of 1.33, Aet B i more riky. It return will move 1.33time for each one point themarket move. Aet As return will move at a lower rate, as indicated by its beta coefficient of .75.5-18 LG 5: Interpreting BetaEffect of change in market return on asset with beta of 1.20:a. 1.20 x (15%) = 18.0% increaseb. 1.20 x (-8%) = 9.6% decreasec. 1.20 x (0%) = no changed. The asset is more risky than the market portfolio, which has a beta of 1. The higher beta makes thereturn move more than the market.5-19 LG 5: Betasa. and b.Increase in Expected Impact Decrease in Impact onAsset Beta Market Return on Asset Return Market Return Asset ReturnA 0.50 .10 .05 -.10 -.05B 1.60 .10 .16 -.10 -.16C - 0.20 .10 -.02 -.10 .02D 0.90 .10 .09 -.10 -.09

c. Asset B should be chosen because it will have the highest increase in return.d. Asset C would be the appropriate choice because it is a defensive asset, moving in opposition to themarket. In an economic downturn, Asset Cs return is increasing.5-20 LG 5: Betas and Risk Rankingsa. Stock BetaMost risky B 1.40A 0.80Chapter 5 Risk and ReturnFind out more at www.kawsarbd1.weebly.comsaved and edited by Md.Kawsar Siddiqui 133Least risky C -0.30

Last

b. and c. Increase in Expected Impact Decrease in Impact onAsset Beta Market Return on Asset Return Market Return Asset ReturnA 0.80 .12 .096 -.05 -.04B 1.40 .12 .168 -.05 -.07C - 0.30 .12 -.036 -.05 .015d. In a declining market, an investor would choose the defensive stock, stock C.While the market declines,the return on C increases.e. In a rising market, an investor would choose stock B, the aggressive stock.As the market rises one point,stock B rises 1.40 points.5-21 LG 5: Portfolio Betas: bp = =n1jjj bwa.Portfolio A Portfolio BAsset Beta wA wA x bA wB wB x bB12345

1.30 .10 .130 .30 .390.70 .30 .210 .10 .071.25 .10 .125 .20 .251.10 .10 .110 .20 .22.90 .40 .360 .20 .18bA = .935 bB = 1.11b. Portfolio A is slightly less risky than the market (average risk), while Portfolio B is more risky than themarket. Portfolio Bs return will move more than Portfolio As for a given increase or decrease in marketreturn. Portfolio B is the more risky.5-22 LG 6: Capital Asset Pricing Model (CAPM): kj = RF + [bj x (km - RF)]Case kj = RF + [bj x (km - RF)]ABCD

8.9% = 5% + [1.30 x (8% - 5%)]12.5% = 8% + [0.90 x (13% - 8%)]8.4% = 9% + [- 0.20 x (12% - 9%)]15.0% = 10% + [1.00 x (15% - 10%)]

E 8.4% = 6% + [0.60

x (10% - 6%)]

5-23 LG 6: Beta Coefficients and the Capital Asset Pricing ModelTo solve this problem you must take the CAPM and solve for beta. The resultingmodel is:FmFRkRkBeta =a. 4545.%11%5%5%16%5%10Beta ===b. 9091.%11%10%5%16%5%15Beta ===Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 134c. 1818.1%11%13%5%16%5%18Beta ===

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d. 3636.1%11%15%5%16%5%20Beta ===e. If Katherine i willing to take a maximum of average rik then he will be able to have an expected returnof only 16%. (k = 5% + 1.0(16%5%) = 16 %.)5 24 LG 6: Manipulating CAPM: kj = RF + [bj x (kma. kj = 8% + [0.90 x (12%kj = 11.6%b. 15% = RF + [1.25 x (14%RF = 10%c. 16% = 9% + [1.10 x (kmkm = 15.36%d. 15% = 10% + [bj x (12.5%bj = 2

8%)]RF)]

9%)]10%)

RF)]

5 25 LG 1, 3, 5, 6: Portfolio Return and Betaa. bp = (.20)(.80)+(.35)(.95)+(.30)(1.50)+(.15)(1.25) = .16+.3325+.45+.1875=1.13b. %8000,20$600,1$000,20$600,1$)000,20$000,20($kA ==+=%86.6000,35$400,2$000,35$400,1$)000,35$000,36($kB ==+=%15000,30$500,4$000,30$0)000,30$500,34($kC ==+=%5.12000,15$875,1$000,15$375$)000,15$500,16($kD ==+=c. %375.10000,100$375,10$000,100$375,3$)000,100$000,107($kP ==+=d. kA = 4% + [0.80 x (10%

4%)] = 8.8%

kB = 4% + [0.95 x (10%

4%)] = 9.7%

kC = 4% + [1.50 x (10%

4%)] = 13.0%

kD = 4% + [1.25 x (10% 4%)] = 11.5%Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.com135

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e. Of the four invetment, only C had an actual return which exceeded the CAPMexpected return (15%veru 13%). The underperformance could be due to any unytematic factor whichwould have cauedthe firm not do a well a expected. Another poibility i that the firm' characteritic may have changeduch that the beta at the time of the purchae overtated the true value of betathat exited during that year.A third explanation i that beta, a a ingle meaure, may not capture all of the ytematic factor thatcaue the expected return. In other word, there i error in the beta etimate.

5 26 LG 6: Security Market Line, SMLa., b., and d.Security Market Line02468101214160 0.2 0.4 0.6 0.8 1 1.2 1.4SRiAKBRik premium

Market RikRequired Rateof Return %

Nondiverifiablec. kj RF + [bj x (km

RF)]

Aet Akj = .09 + [0.80 x (.13 .09)]kj = .122Aet Bkj = .09 + [1.30 x (.13 .09)]kj = .142d. Aet A ha a maller required return than Aet B becaueAet A veru 1.30 for Aet B. The market rik premiumlower than Aet B' (14.2% 9% = 5.2%).Rik (Beta) aved and edited by Md.Kawar Siddiquiit i le riky, baed on the beta of 0.80 forfor Aet A i 3.2% (12.2% 9%), which iChapter 5 Rik and ReturnFind out m w.kawarbd1.weebly.com

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d edited by Md.Kawar Siddiqui 1365 27 LG 6: Shift in the Security Market Linea., b., c., d.Security Market Lineb. kj = RF + [bj x (kmore at ww

RF)]

kA = 8% + [1.1 x (12%8%)]kA =8%+ 4.4%kA =12.4%c. kA = 6% + [1.1kA = 6% + 4.4% 02481012141618200 0.2 0.4 0.6 0.8Aet AAet ASMLdSMLaSMLcRequiredReturn(%)6kA = 10.4%Nondiverifiabled. kA = 8% + [1.1kA = 8% + 5.5%kA = 13.5%

x (10%

6%)]

1 1.2 1.4 1.6 1.8 2

Rik (Beta)x (13% 8%)]

e. 1. A decreae in inflationary expectation reduce the required return a hown in the parallel downwardhift of the SML.2. Increaed rik averion reult in a teeper lope, ince a higher return would be required for each levelof rik a meaured by beta.

5 28 LG 5, 6: Integrative Rik, Return, and CAPMa. Project kj = RF + [bj x (km

RF)]

ABCDE

kjkjkjkjkj

=====

9%9%9%9%9%

+++++

[1.5[.75[2.0[ 0[( .5)

x (14%x (14%x (14%x (14%x (14%

9%)] = 16.5%9%)] = 12.75%9%)] = 19.0%9%)] = 9.0%9%)] = 6.5%

b. and d.Security Market LineSMLbSMLdRequiredRate ofReturn(%)Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 137c. Project A i 150% a reponivea the market.Project B i 75% a reponive athe market.Project C i twice a reponivea the market.Project D i unaffected by marketmovement.Project E i only half areponive a the market, butmove in the oppoite direction athe market.

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d. See graph for new SML.kA = 9% + [1.5 x (12% 9%)]kB = 9% + [.75 x (12% 9%)]kC = 9% + [2.0 x (12% 9%)]kD = 9% + [0x (12%9%)] = 9.00%kE = 9% + [ .5 x (12% 9%)]024681012141618200.5 0 0.5 1 1.5 2Nondiverifiable Rik (Beta)e. The teeper lope of SMLb indicate a higher rik premium than SMLd for theemarket condition. Wheninvetor rik averion decline, invetor require lower return for any given rik level (beta).Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comLataved and edited by Md.Kawar Siddiqui 138Chapter 5 Cae

Analyzing Rik and Return on Charger Product' InvetmentThi cae require tudent to review and apply the concept of the rik return trade off by analyzing two poibleaet invetment uing tandard deviation, coefficient of variation, and CAPM.a.Expected rate of return:1tt1tttP)CPP(k +=Aet X:Cah Ending Beginning Gain/ Annual RateYear Flow (Ct) Value (Pt) Value (Pt 1) Lo of Return1994199519961997199819992000200120022003

$1,000 $22,000 $20,000 $2,000 15.00%1,500 21,000 22,0001,000 2.271,400 24,000 21,000 3,000 20.951,700 22,000 24,000 2,000 1.251,900 23,000 22,000 1,000 13.181,600 26,000 23,000 3,000 20.001,700 25,000 26,0001,000 2.692,000 24,000 25,000 1,000 4.002,100 27,000 24,000 3,000 21.252,200 30,000 27,000 3,000 19.26

Average expected return for Aet X = 11.74%Aet Y:Cah Ending Beginning Gain/ Annual RateYear Flow (Ct) Value (Pt) Value (Pt 1) Lo of Return1994199519961997199819992000200120022003

$1,500 $20,000 $20,000 $0 7.50%1,600 20,000 20,000 0 8.001,700 21,000 20,000 1,000 13.501,800 21,000 21,000 0 8.571,900 22,000 21,000 1,000 13.812,000 23,000 22,000 1,000 13.642,100 23,000 23,000 0 9.132,200 24,000 23,000 1,000 13.912,300 25,000 24,000 1,000 13.752,400 25,000 25,000 0 9.60

Average expected return for Aet Y = 11.14%b.k = =n1i2i )1n()kk(

Aet X:Return AverageYear ki Return, k )kk( i )kk( i 2Chapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comaved and edited by Md.Kawar Siddiqui 1391994 15.00% 11.74% 3.26% 10.63%1995 2.27 11.74 9.47 89.681996 20.95 11.74 9.21 84.8219971.25 11.74 12.99 168.741998 13.18 11.74 1.44 2.071999 20.00 11.74 8.26 68.232000 2.69 11.74 9.05 81.902001 4.00 11.74 7.74 59.912002 21.25 11.74 9.51 90.442003 19.26 11.74 7.52 56.55712.97%90.822.7911097.712x ===76.%74.1190.8CV ==Aet YReturn AverageYear ki Return, k )kk( i )kk( i 21994 7.50% 11.14% 3.64% 13.25%1995 8.00 11.14 3.14 9.861996 13.50 11.14 2.36 5.571997 8.57 11.14 2.57 6.601998 13.81 11.14 2.67 7.131999 13.64 11.14 2.50 6.252000 9.13 11.14 2.01 4.042001 13.91 11.14 2.77 7.672002 13.75 11.14 2.61 6.812003 9.60 11.14 1.54 2.3769.55%78.273.711055.69Y ===25.%14.1178.2CV ==c. Summary Statitic:Aet X Aet YExpected Return 11.74% 11.14%Standard Deviation 8.90% 2.78%Coefficient of Variation .76 .25

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Comparing the expected return calculated in part a, Aet X provide a return of 11.74 percent, onlylightly above the return of 11.14 percent expected from Aet Y. The higher tandard deviation andcoefficient of variation of Invetment X indicate greater rik. With jut thiinformation, it i difficult toChapter 5 Rik and ReturnFind out more at www.kawarbd1.weebly.comLataved and edited by Md.Kawar Siddiqui 140determine whether the .60 percent difference in return i adequate compenationfor the difference in rik.Baed on thi information, however, Aet Y appear to be the better choice.d. Uing the capital aet pricing model, the required return on each aet i a follow:Capital Aet Pricing Model: kj = RF + [bj x (kmAet RF + [bj x (kmX 7% + [1.6 x (10%Y 7% + [1.1 x (10%

RF)]

RF)] = kj7%)] = 11.8%7%)] = 10.3%

From the calculation in part a, the expected return for Aet X i 11.74%, compared to it required returnof 11.8%. On the other hand, Aet Y ha an expected return of 11.14% and a required return of only10.8%. Thi make Aet Y the better choice.e. In part c, we concluded that it would be difficult to make a choice between Xand Y becaue the additionalreturn on X may or may not provide the needed compenation for the extra rik.In part d, by calculating arequired rate of return, it wa eay to reject X and elect Y. The required return on Aet X i 11.8%, butit expected return (11.74%) i lower; therefore Aet X i unattractive. For Aet Y the revere i true,and it i a good invetment vehicle.Clearly, Charger Product i better off uing the tandard deviation and coefficient of variation, rather thana trictly ubjective approach, to ae invetment rik. Beta and CAPM, however, provide a linkbetween rik and return. They quantify rik and convert it into a required return that can be compared tothe expected return to draw a definitive concluion about invetment acceptability. Contrating theconcluion in the repone to quetion c and d above hould clearly demontrate why Junior i better offuing beta to ae rik.f. (1) Increae in rik free rate to 8 % and market return to 11 %:Aet RF + [bj x (kmX 8% + [1.6 x (11%Y 8% + [1.1 x (11%

RF)] = kj8%)] = 12.8%8%)] = 11.3%

(2) Decreae in market return to 9 %:

Aet RF + [bj x (km

RF)] = kj

X 7% + [1.6 x (9% 7%)] = 10.2%Y 7% + [1.1 x (9% 7%)] = 9.2%In ituation (1), the required return rie for both aet, and neither ha anexpected return above the firm'required return.With ituation (2), the drop in market rate caue the required return to decreae o that the expectedreturn of both aet are above the required return. However, Aet Y providea larger return comparedto it required return (11.14 9.20 = 1.94), and it doe o with le rik thanAet X.