Chapter 5 Risk and return

Transcription

1 Chapter 5 Rsk and return Instructor s resources Overvew Ths chapter focuses on the fundamentals of the rsk and return relatonshp of assets and ther valuaton. For the sngle asset held n solaton, rsk s measured wth the probablty dstrbuton and ts assocated statstcs: the mean, the standard devaton, and the coeffcent of varaton. The concept of dversfcaton s examned by measurng the rsk of a portfolo of assets that are perfectly postvely correlated, perfectly negatvely correlated, and those that are uncorrelated. Next, the chapter looks at nternatonal dversfcaton and ts effect on rsk. The Captal Asset Prcng Model (CAPM) s then presented as a valuaton tool for securtes and as a general explanaton of the rsk return tradeoff nvolved n all types of fnancal transactons. Chapter 5 hghlghts the mportance of understandng the relatonshp of rsk and return when makng professonal and personal decsons. Study Gude The followng Study Gude examples are suggested for classroom presentaton: Example Topc 4 Rsk atttudes 6 Graphc determnaton of beta 12 Impact of market changes on return Suggested answer to chapter openng crtcal thnkng queston Venture captal s a form of prvate equty n whch captal s rased n prvate markets as opposed to the publc markets. How can the venture captalsts eventually captalse on ther nvestments? Venture captal frms nvestng n new and promsng technologes and start-up companes must fnd a buyer n order to captalse on ther nvestment. The ext or sellng out s often acheved va an ntal publc offerng (IPO). Another opton s to sell ther stake n the company to another venture captal frm or prvate-equty frm. Answers to Revew Questons 1. Rsk s defned as the chance of fnancal loss, as measured by the varablty of expected returns assocated wth a gven asset. A decson-maker should evaluate an nvestment by measurng the chance of loss, or rsk, and comparng the expected rsk to the expected return. Some assets are consdered rsk free; the most ordnary examples are RSA Treasury ssues.

2 110 Gtman Prncples of Manageral Fnance, Twelfth Edton 2. The return on an nvestment (total gan or loss) s the change n value plus any cash dstrbutons over a defned tme perod. It s expressed as a percent of the begnnng-of-the-perod nvestment. The formula s: [(endng value ntal value) cash dstrbuton] Return ntal value Realsed return requres the asset to be purchased and sold durng the tme perods the return s measured. Unrealsed return s the return that could have been realsed f the asset had been purchased and sold durng the tme perod the return was measured. 3. a. The rsk-averse fnancal manager requres an ncrease n return for a gven ncrease n rsk. b. The rsk-ndfferent manager requres no change n return for an ncrease n rsk. c. The rsk-seekng manager accepts a decrease n return for a gven ncrease n rsk. Most fnancal managers are rsk averse. 4. Scenaro analyss evaluates asset rsk by usng more than one possble set of returns to obtan a sense of the varablty of outcomes. The range s found by subtractng the pessmstc outcome from the optmstc outcome. The larger the range, the greater the rsk assocated wth the asset. 5. The decson-maker can get an estmate of project rsk by vewng a plot of the probablty dstrbuton, whch relates probabltes to expected returns and shows the degree of dsperson of returns. The more spread out the dstrbuton, the greater the varablty or rsk assocated wth the return stream. 6. The standard devaton of a dstrbuton of asset returns s an absolute measure of dsperson of rsk around the mean or expected value. A hgher standard devaton ndcates a greater project rsk. Wth a larger standard devaton, the dstrbuton s more dspersed and the outcomes have a hgher varablty, resultng n hgher rsk. 7. The coeffcent of varaton s another ndcator of asset rsk, however ths measures relatve dsperson. It s calculated by dvdng the standard devaton by the expected value. The coeffcent of varaton may be a better bass than the standard devaton for comparng rsk of assets wth dfferng expected returns. 8. An effcent portfolo s one that maxmses return for a gven rsk level or mnmses rsk for a gven level of return. Return of a portfolo s the weghted average of returns on the ndvdual component assets: where: n number of assets, w j weght of ndvdual assets, k ˆj expected returns. n rˆ w rˆ p j j j1

3 Chapter 5 Rsk and return 111 The standard devaton of a portfolo s not the weghted average of component standard devatons; the rsk of the portfolo as measured by the standard devaton wll be smaller. It s calculated by applyng the standard devaton formula to the portfolo assets: rp n 1 ( r r) ( n 1) 2 9. The correlaton between asset returns s mportant when evaluatng the effect of a new asset on the portfolo s overall rsk. Returns on dfferent assets movng n the same drecton are postvely correlated, whle those movng n opposte drectons are negatvely correlated. Assets wth hgh postve correlaton ncrease the varablty of portfolo returns; assets wth hgh negatve correlaton reduce the varablty of portfolo returns. When negatvely correlated assets are brought together through dversfcaton, the varablty of the expected return from the resultng combnaton can be less than the varablty or rsk of the ndvdual assets. When one asset has hgh returns, the other s returns are low and vce versa. Therefore, the result of dversfcaton s to reduce rsk by provdng a pattern of stable returns. Dversfcaton of rsk n the asset selecton process allows the nvestor to reduce overall rsk by combnng negatvely correlated assets so that the rsk of the portfolo s less than the rsk of the ndvdual assets n t. Even f assets are not negatvely correlated, the lower the postve correlaton between them, the lower ther resultng portfolo return varablty. 10. The ncluson of foregn assets n a domestc company s portfolo reduces rsk for two reasons. When returns from foregn-currency-denomnated assets are translated nto rands, the correlaton of returns of the portfolo s assets s reduced. Also, f the foregn assets are n countres that are less senstve to the RSA busness cycle, the portfolo s response to market movements s reduced. When the rand apprecates relatve to other currences, the rand value of a foregn-currencydenomnated portfolo declnes and results n lower returns n rand terms. If ths apprecaton s due to better performance of the RSA economy, foregn-currency-denomnated portfolos generally have lower returns n local currency as well, further contrbutng to reduced returns. Poltcal rsks result from possble actons by the host government that are harmful to foregn nvestors or possble poltcal nstablty that could endanger foregn assets. Ths form of rsk s partcularly hgh n developng countres. Companes dversfyng nternatonally may have assets sezed or the return of profts blocked. 11. The total rsk of a securty s the combnaton of nondversfable rsk and dversfable rsk. Dversfable rsk refers to the porton of an asset s rsk attrbutable to frm-specfc, random events (strkes, ltgaton, loss of key contracts, etc.) that can be elmnated by dversfcaton. Nondversfable rsk s attrbutable to market factors affectng all frms (war, nflaton, poltcal events, etc.). Some argue that nondversfable rsk s the only relevant rsk because dversfable rsk can be elmnated by creatng a portfolo of assets that s not perfectly postvely correlated. 12. Beta measures nondversfable rsk. It s an ndex of the degree of movement of an asset s return n response to a change n the market return. The beta coeffcent for an asset can be found by plottng the asset s hstorcal returns relatve to the returns for the market. By usng statstcal technques, the characterstc lne s ft to the data ponts. The slope of ths lne s beta. Beta coeffcents for actvely traded shares are publshed n the Value Lne Investment Survey, n brokerage reports, and several onlne stes. The beta of a portfolo s calculated by fndng the weghted average of the betas of the ndvdual component assets.

4 112 Gtman Prncples of Manageral Fnance, Twelfth Edton 13. The equaton for the captal asset prcng model s: r j R F [b j (r m R F )], where: r j the requred (or expected) return on asset j R F the rate of return requred on a rsk-free securty (a U.S. Treasury bll) b j the beta coeffcent or ndex of nondversfable (relevant) rsk for asset j r m the requred return on the market portfolo of assets (the market return) The securty market lne (SML) s a graphcal presentaton of the relatonshp between the amount of systematc rsk assocated wth an asset and the requred return. Systematc rsk s measured by beta and s on the horzontal axs whle the requred return s on the vertcal axs. 14. a. If there s an ncrease n nflatonary expectatons, the securty market lne wll show a parallel shft upward n an amount equal to the expected ncrease n nflaton. The requred return for a gven level of rsk wll also rse. b. The slope of the SML (the beta coeffcent) wll be less steep f nvestors become less rskaverse, and a lower level of return wll be requred for each level of rsk. 15. The CAPM provdes fnancal managers wth a lnk between rsk and return. Because t was developed to explan the behavour of securtes prces n effcent markets and uses hstorcal data to estmate requred returns, t may not reflect future varablty of returns. Whle studes have supported the CAPM when appled n actve securtes markets, t has not been found to be generally applcable to real corporate assets. However, the CAPM can be used as a conceptual framework to evaluate the relatonshp between rsk and return. Suggested answer to crtcal thnkng queston for Focus on Practce There s a dfference between nternatonal mutual funds and global mutual funds. How mght that dfference affect ther correlaton wth U.S. equty mutual funds? The dfference between global funds and nternatonal funds s that global funds can nvest n shares and bonds around the world, ncludng U.S. securtes, whereas nternatonal funds nvest n shares and bonds around the world but not U.S securtes. Therefore, global funds are more lkely to be correlated wth U.S. equty mutual funds, snce a sgnfcant porton of ther portfolos are lkely to be U.S. equtes. An nvestor seekng ncreased nternatonal dversfcaton n a portfolo should consder nternatonal funds over global funds or ncrease the porton of the portfolo devoted to global funds f seekng dversfcaton through global funds. Suggested answer to crtcal thnkng queston for Focus on Ethcs Is httng the numbers an approprate goal, gven the Chapter 1 contrast of proft and shareholder wealth maxmsaton? If not, why do executves emphasse t? The presentaton n Chapter 1 of our textbook s clear (and see also the moral mperatve n the Chapter 1 ethcs focus box): managers are to maxmse shareholder wealth, not profts. Shareholder wealth encompasses cash flow amount, tmng, and rsk all of whch are mssed by an earnngs per share (EPS) focus. Further, to the extent that managers focus on proft, they should target long-run economc proft, not

5 Chapter 5 Rsk and return 113 next quarter s EPS. Really, there are only two justfcatons for management attenton on EPS: (1) profts are a large and a necessary part of operatng cash flows (thnk of the ndrect approach to the statement of cash flows, n the operatng secton); and (2) nvestors may use EPS changes to enable reevaluaton of the company s busness strategy and trend lne. (In Chapter 7, you wll be presented wth the prce-earnngs multple approach to share valuaton.) Answers to Warm-up exercses E5-1. Answer: Total annual return C1 P1 P0 $0 $12,000,000 $10,000,000 K1 20% P $10,000,000 0 Logstcs, Ltd doubled the annual rate of return predcted by the analyst. The negatve net ncome s rrelevant to the problem. E5-2. Answer: Expected return E5-3. Analyst Probablty Return Weghted value % 1.75% % 0.25% % 2.0% % 1.2% Total 1.00 Expected return 4.70% Comparng the rsk of two nvestments Answer: CV CV Based solely on standard devatons, Investment 2 has lower rsk than Investment 1. Based on coeffcents of varaton, Investment 2 s stll less rsky than Investment 1. Snce the two nvestments have dfferent expected returns, usng the coeffcent of varaton to assess rsk s better than smply comparng standard devatons because the coeffcent of varaton consders the relatve sze of the expected returns of each nvestment. E5-4. Answer: Computng the expected return of a portfolo r ( ) ( ) ( ) p (0.0171) (0.0496) ( ) % The portfolo s expected to have a return of approxmately 9.3%. E5-5. Answer: Calculatng a portfolo beta Beta ( ) ( ) ( ) ( ) ( )

6 114 Gtman Prncples of Manageral Fnance, Twelfth Edton E5-6. Answer: Calculatng the requred rate of return a. Requred return = ( ) = = 0.14 b. Requred return = ( ) = = c. Although the rsk-free rate does not change, as the market return ncreases, the requred return on the asset rses by 180% of the change n the market s return. Solutons to Problems P5-1. ( Pt Pt 1 Ct ) LG 1: Rate of return: r= Basc a. Investment X: Return Investment Y: Return t Pt 1 (R21, 000 R20, 000 R1,500) 12.50% R20, 000 (R55, 000 R55, 000 R6,800) 12.36% R55, 000 b. Investment X should be selected because t has a hgher rate of return for the same level of rsk. P5-2. LG 1: Return calculatons: Basc ( P P C ) r= t t t1 t Pt 1 Investment Calculaton r t (%) A (R1,100 R800 R100) R B (R118,000 R120,000 R15,000) R120, C (R48,000 R45,000 R7,000) R45, D (R500 R600 R80) R E (R12,400 R12,500 R1,500) R12, P5-3. LG 1: Rsk preferences Intermedate a. The rsk-ndfferent manager would accept Investments X and Y because these have hgher returns than the 12% requred return and the rsk doesn t matter. b. The rsk-averse manager would accept Investment X because t provdes the hghest return and has the lowest amount of rsk. Investment X offers an ncrease n return for takng on more rsk than what the frm currently earns. c. The rsk-seekng manager would accept Investments Y and Z because he or she s wllng to take greater rsk wthout an ncrease n return. d. Tradtonally, fnancal managers are rsk averse and would choose Investment X, snce t provdes the requred ncrease n return for an ncrease n rsk.

7 Chapter 5 Rsk and return 115 P5-4. LG 2: Rsk analyss Intermedate a. Expanson Range A 24% 16% 8% B 30% 10% 20% b. Project A s less rsky, snce the range of outcomes for A s smaller than the range for Project B. c. Snce the most lkely return for both projects s 20% and the ntal nvestments are equal, the answer depends on your rsk preference. d. The answer s no longer clear, snce t now nvolves a rsk return tradeoff. Project B has a slghtly hgher return but more rsk, whle A has both lower return and lower rsk. P5-5. LG 2: Rsk and probablty Intermedate a. Camera Range R 30% 20% 10% S 35% 15% 20% b Possble Outcomes Probablty P r Expected Return r Weghted value (%)(r P r ) Camera R Pessmstc Most lkely Optmstc Expected return Camera S Pessmstc Most lkely Optmstc Expected return c. Camera S s consdered more rsky than Camera R because t has a much broader range of outcomes. The rsk return tradeoff s present because Camera S s more rsky and also provdes a hgher return than Camera R.

8 116 Gtman Prncples of Manageral Fnance, Twelfth Edton P5-6. LG 2: Bar charts and rsk Intermedate a.

9 Chapter 5 Rsk and return 117 b. Market acceptance Probablty P r Expected return r Weghted value (r P r ) Lne J Very poor Poor Average Good Excellent Expected return Lne K Very poor Poor Average Good Excellent Expected return c. Lne K appears less rsky due to a slghtly tghter dstrbuton than lne J, ndcatng a lower range of outcomes. r P5-7. LG 2: Coeffcent of varaton: CV r Basc a. A B C 7% CVA % 9.5% CVB % 6% CVC % 5.5% D CVD % b. Asset C has the lowest coeffcent of varaton and s the least rsky relatve to the other choces. P5-8. LG 2: Standard devaton versus coeffcent of varaton as measures of rsk Basc a. Project A s least rsky based on range wth a value of b. Project A s least rsky based on standard devaton wth a value of Standard devaton s not the approprate measure of rsk snce the projects have dfferent returns.

10 118 Gtman Prncples of Manageral Fnance, Twelfth Edton c. A B CVA CVB C CVC D CVD In ths case Project D s the best alternatve snce t provdes the least amount of rsk for each percent of return earned. Coeffcent of varaton s probably the best measure n ths nstance snce t provdes a standardsed method of measurng the rsk return tradeoff for nvestments wth dfferng returns. P5-9. LG 2: Personal fnance: Rate of return, standard devaton, coeffcent of varaton Challenge a. Share prce Varance Year Begnnng End Returns (Return Average Return) % % 11.73% 26.83% b. Average return 72.31% c. Sum of varances Sample dvsor (n 1) Varance 86.97% Standard devaton d Coeffcent of varaton e. The share prce of Idon has defntely gone through some major prce changes over ths tme perod. It would have to be classfed as a volatle securty havng an upward prce trend over the past four years. Note how comparng securtes on a CV bass allows the nvestor to put the share n proper perspectve. The share s rsker than what Mke normally buys but f he beleves that Idon wll contnue to rse then he should nclude t.

11 Chapter 5 Rsk and return 119 P5-10. LG 2: Assessng return and rsk Challenge a. Project 257 (1) Range: 1.00 (.10) 1.10 (2) Expected return: Rate of return r n r =1 r r P Probablty P r Weghted value r P r (3) Standard devaton: ( r r ) P n 1 r r r Expected return n r r P r 2 r ( r r) P r ( r r) 2 P r Project r

12 120 Gtman Prncples of Manageral Fnance, Twelfth Edton (4) CV b. Project 432 (1) Range: (2) Expected return: Rate of return r n r r P 1 r Probablty P r Weghted value r P r Expected return n r r P = r 2 (3) Standard devaton: ( r r ) P r r r n 1 r 2 r ( r r) P r ( r r) 2 P r Project (4) CV

13 Chapter 5 Rsk and return 121 c. Bar Charts d. Summary statstcs Project 257 Project 432 Range Expected return ( r ) Standard devaton ( r ) Coeffcent of varaton (CV) Snce Projects 257 and 432 have dfferng expected values, the coeffcent of varaton should be the crteron by whch the rsk of the asset s judged. Snce Project 432 has a smaller CV, t s the opportunty wth lower rsk.

14 122 Gtman Prncples of Manageral Fnance, Twelfth Edton P5-11. LG 2: Integratve expected return, standard devaton, and coeffcent of varaton Challenge a. Expected return: n r r P 1 r Rate of return r Probablty P r Weghted value r P r Asset F Asset G Asset H Expected return n r r P r Asset G provdes the largest expected return.

15 Chapter 5 Rsk and return b. Standard devaton: ( r r ) xp n 1 r r 2 r ( r r) P r 2 r Asset F Asset G Asset H Based on standard devaton, Asset G appears to have the greatest rsk, but t must be measured aganst ts expected return wth the statstcal measure coeffcent of varaton, snce the three assets have dfferng expected values. An ncorrect concluson about the rsk of the assets could be drawn usng only the standard devaton. c. standard devaton ( ) Coeffcent of varaton = expected value Asset F: Asset G: CV CV Asset H: CV As measured by the coeffcent of varaton, Asset F has the largest relatve rsk.

16 124 Gtman Prncples of Manageral Fnance, Twelfth Edton P5-12. LG 2: Normal probablty dstrbuton Challenge a. Coeffcent of varaton: CV r r Solvng for standard devaton: 0.75 r r b. (1) 68% of the outcomes wll le between 1 standard devaton from the expected value: c (2) 95% of the outcomes wll le between 2 standard devatons from the expected value: ( ) ( ) (3) 99% of the outcomes wll le between 3 standard devatons from the expected value: ( ) ( )

17 Chapter 5 Rsk and return 125 P5-13. LG 3: Personal fnance: Portfolo return and standard devaton Challenge a. Expected portfolo return for each year: r p (w L r L ) (w M r M ) Year Asset L (w L r L ) Asset M (w M r M ) Expected portfolo return 2010 (14% %) (20% %) 17.6% 2011 (14% %) (18% %) 16.4% 2012 (16% %) (16% %) 16.0% 2013 (17% %) (14% %) 15.2% 2014 (17% %) (12% %) 14.0% 2015 (19% %) (10% %) 13.6% r p b. Portfolo return: r p r p n j1 w j n r j % 6 c. Standard devaton: rp n 1 ( r r) 2 ( n 1) rp rp rp (17.6% 15.5%) (16.4% 15.5%) (16.0% 15.5%) (15.2% 15.5%) (14.0% 15.5%) (13.6% 15.5%) (2.1%) (0.9%) (0.5%) ( 0.3%) ( 1.5%) ( 1.9%) 5 ( ) rp % % 5 d. The assets are negatvely correlated. e. Combnng these two negatvely correlated assets reduces overall portfolo rsk.

18 126 Gtman Prncples of Manageral Fnance, Twelfth Edton P5-14. LG 3: Portfolo analyss Challenge a. Expected portfolo return: Alternatve 1: 100% Asset F r p 16% 17% 18% 19% 17.5% 4 Alternatve 2: 50% Asset F 50% Asset G Year Asset F (w F r F ) Asset G (w G r G ) Portfolo return r p 2010 (16% %) (17% %) 16.5% 2011 (17% %) (16% %) 16.5% 2012 (18% %) (15% %) 16.5% 2013 (19% %) (14% %) 16.5% r p 16.5% 16.5% 16.5% 16.5% 16.5% 4 Alternatve 3: 50% Asset F 50% Asset H Year Asset F (w F r F ) Asset H (w H r H ) Portfolo return r p 2010 (16% %) (14% %) 15.0% 2011 (17% %) (15% %) 16.0% 2012 (18% %) (16% %) 17.0% 2013 (19% %) (17% %) 18.0% r p 15.0% 16.0% 17.0% 18.0% 16.5% 4 b. Standard devaton: (1) F F F rp n 1 ( r r) 2 ( n 1) [(16.0% 17.5%) (17.0% 17.5%) (18.0% 17.5%) (19.0% 17.5%) ] [( 1.5%) ( 0.5%) (0.5%) (1.5%) ] 3 ( ) F % 3

19 Chapter 5 Rsk and return 127 (2) (3) FG FG 0 FG FH FH FH [(16.5% 16.5%) (16.5% 16.5%) (16.5% 16.5%) (16.5% 16.5%) ] [(0) (0) (0) (0) ] [(15.0% 16.5%) (16.0% 16.5%) (17.0% 16.5%) (18.0% 16.5%) ] [( 1.5%) ( 0.5%) (0.5%) (1.5%) ] 3 [( )] FH % 3 c. Coeffcent of varaton: CV r r 1.291% CVF % 0 CVFG % 1.291% CVFH % d. Summary: r p : Expected value of portfolo rp CV p Alternatve 1 (F) 17.5% 1.291% Alternatve 2 (FG) 16.5% Alternatve 3 (FH) 16.5% 1.291% Snce the assets have dfferent expected returns, the coeffcent of varaton should be used to determne the best portfolo. Alternatve 3, wth postvely correlated assets, has the hghest coeffcent of varaton and therefore s the rskest. Alternatve 2 s the best choce; t s perfectly negatvely correlated and therefore has the lowest coeffcent of varaton.

20 128 Gtman Prncples of Manageral Fnance, Twelfth Edton P5-15. LG 4: Correlaton, rsk, and return Intermedate a. (1) Range of expected return: between 8% and 13% (2) Range of the rsk: between 5% and 10% b. (1) Range of expected return: between 8% and 13% (2) Range of the rsk: 0 rsk 10% c. (1) Range of expected return: between 8% and 13% (2) Range of the rsk: 0 rsk 10% P5-16. LG 1, 4: Personal fnance: Internatonal nvestment returns Intermedate a) Pt(1000 x 24.75) 24,750 Pt-1(1000 x 20.50)20,500/20,500 = 20,73% b) Pt = 24,750 Mt / 2.85 = R8,684 Pt-1 = 20,500 Mt / 2.40 = R8,542 c) R8,684 R8,542/R8,542 = 1,66% d. The two returns dffer due to the change n the exchange rate between the metcal and the rand. The metcal had deprecaton (and thus the rand apprecated) between the purchase date and the sale date, causng a decrease n total return. The answer n part (c) s the more mportant of the two returns for Themba. An nvestor n foregn securtes wll carry exchange-rate rsk. P5-17. LG 5: Total, nondversfable, and dversfable rsk Intermedate a and b

21 Chapter 5 Rsk and return 129 c. Only nondversfable rsk s relevant because, as shown by the graph, dversfable rsk can be vrtually elmnated through holdng a portfolo of at least 20 securtes that are not postvely correlated. Davd Randall s portfolo, assumng dversfable rsk could no longer be reduced by addtons to the portfolo, has 6.47% relevant rsk. P5-18. LG 5: Graphc dervaton of beta Intermedate a. b. To estmate beta, the rse over run method can be used: Takng the ponts shown on the graph: Y Beta A 0.75 X Rse Y Beta Run X Y Beta B 1.33 X A fnancal calculator wth statstcal functons can be used to perform lnear regresson analyss. The beta (slope) of lne A s 0.79; of lne B, c. Wth a hgher beta of 1.33, Asset B s more rsky. Its return wll move 1.33 tmes for each one pont the market moves. Asset A s return wll move at a lower rate, as ndcated by ts beta coeffcent of P5-19. LG 5: Interpretng beta Basc Effect of change n market return on asset wth beta of 1.20: a (15%) 18.0% ncrease b (8%) 9.6% decrease c (0%) no change d. The asset s more rsky than the market portfolo, whch has a beta of 1. The hgher beta makes the return move more than the market.

22 130 Gtman Prncples of Manageral Fnance, Twelfth Edton P5-20. LG 5: Betas Basc a and b Asset Beta Increase n market return Expected mpact on asset return Decrease n market return Impact on asset return A B C D c. Asset B should be chosen because t wll have the hghest ncrease n return. d. Asset C would be the approprate choce because t s a defensve asset, movng n opposton to the market. In an economc downturn, Asset C s return s ncreasng. P5-21. LG 5: Personal fnance: Betas and rsk rankngs Intermedate a. b and c Share Beta Most rsky B 1.40 A 0.80 Least rsky C 0.30 Asset Beta Increase n market return Expected mpact on asset return Decrease n market return Impact on asset return A B C d. In a declnng market, an nvestor would choose the defensve share, Share C. Whle the market declnes, the return on C ncreases. e. In a rsng market, an nvestor would choose Share B, the aggressve share. As the market rses one pont, Share B rses 1.40 ponts.

23 Chapter 5 Rsk and return 131 P5-22. LG 5: Portfolo betas: b p Intermedate a. n j1 w j b Portfolo A j Portfolo B Asset Beta w A w A b A w B w B b B b A b B 1.11 b. Portfolo A s slghtly less rsky than the market (average rsk), whle Portfolo B s more rsky than the market. Portfolo B s return wll move more than Portfolo A s for a gven ncrease or decrease n market return. Portfolo B s the more rsky. P5-23. LG 6: Captal asset prcng model (CAPM): r j R F [b j (r m R F )] Basc Case r j R F [b j (r m R F )] A 8.9% 5% [1.30(8% 5%)] B 12.5% 8% [0.90(13% 8%)] C 8.4% 9% [0.20(12% 9%)] D 15.0% 10% [1.00(15% 10%)] E 8.4% 6% [0.60(10% 6%)] P5-24. LG 5, 6: Personal fnance: Beta coeffcents and the captal asset prcng model Intermedate To solve ths problem you must take the CAPM and solve for beta. The resultng model s: r RF Beta r R m F a. 10% 5% 5% Beta % 5% 11% b. 15% 5% 10% Beta % 5% 11% c. 18% 5% 13% Beta % 5% 11% d. 20% 5% 15% Beta % 5% 11% e. If Katherne s wllng to take a maxmum of average rsk then she wll be able to have an expected return of only 16%. (r 5% 1.0(16% 5%) 16%.)

24 132 Gtman Prncples of Manageral Fnance, Twelfth Edton P5-25. LG 6: Manpulatng CAPM: r j R F [b j (r m R F )] Intermedate a. r j 8% [0.90(12% 8%)] r j 11.6% b. 15% R F [1.25(14% R F )] R F 10% c. 16% 9% [1.10(r m 9%)] r m 15.36% d. 15% 10% [b j (12.5% 10%) b j 2 P5-26. LG 1, 3, 5, 6: Personal fnance: Portfolo return and beta Challenge a. b p (0.20)(0.80) (0.35)(0.95) (0.30)(1.50) (0.15)(1.25) b. r A r B r C r D c. r P (R20,000 R20,000) R1,600 R1,600 8% R20,000 R20,000 (R36,000 R35,000) R1,400 R2, % R35,000 R35,000 (R34,500 R30, 000) 0 R4,500 15% R30, 000 R30, 000 (R16,500 R15,000) R375 R1, % R15,000 R15,000 (R107,000 R100,000) R3,375 R10, % R100,000 R100,000 d. r A 4% [0.80(10% 4%)] 8.8% r B 4% [0.95(10% 4%)] 9.7% r C 4% [1.50(10% 4%)] 13.0% r D 4% [1.25(10% 4%)] 11.5% e. Of the four nvestments, only C (15% versus 13%) and D (12.5% versus 11.5%) had actual returns that exceeded the CAPM expected return (15% versus 13%). The underperformance could be due to any unsystematc factor that would have caused the frm not to do as well as expected. Another possblty s that the frm s characterstcs may have changed such that the beta at the tme of the purchase overstated the true value of beta that exsted durng that year. A thrd explanaton s that beta, as a sngle measure, may not capture all of the systematc factors that cause the expected return. In other words, there s error n the beta estmate.

25 Chapter 5 Rsk and return 133 P5-27. LG 6: Securty market lne, SML Intermedate a, b, and d c. r j R F [b j (r m R F )] Asset A r j 0.09 [0.80( )] r j Asset B r j 0.09 [1.30( )] r j d. Asset A has a smaller requred return than Asset B because t s less rsky, based on the beta of 0.80 for Asset A versus 1.30 for Asset B. The market rsk premum for Asset A s 3.2% (12.2% 9%), whch s lower than Asset B s market rsk premum (14.2% 9% 5.2%). P5-28. LG 6: Shfts n the securty market lne Challenge a, b, c, d

26 134 Gtman Prncples of Manageral Fnance, Twelfth Edton b. r j R F [b j (r m R F )] r A 8% [1.1(12% 8%)] r A 8% 4.4% r A 12.4% c. r A 6% [1.1(10% 6%)] r A 6% 4.4% r A 10.4% d. r A 8% [1.1(13% 8%)] r A 8% 5.5% r A 13.5% e. (1) A decrease n nflatonary expectatons reduces the requred return as shown n the parallel downward shft of the SML. (2) Increased rsk averson results n a steeper slope, snce a hgher return would be requred for each level of rsk as measured by beta. P5-29. LG 6: Integratve-rsk, return, and CAPM Challenge a. b and d Project r j R F [b j (r m R F )] A r j 9% [1.5(14% 9%)] 16.5% B r j 9% [0.75(14% 9%)] 12.75% C r j 9% [2.0(14% 9%)] 19.0% D r j 9% [0(14% 9%)] 9.0% E r j 9% [(0.5)(14% 9%)] 6.5%

27 Chapter 5 Rsk and return 135 c. Project A s 150% as responsve as the market. Project B s 75% as responsve as the market. Project C s twce as responsve as the market. Project D s unaffected by market movement. Project E s only half as responsve as the market, but moves n the opposte drecton as the market. d. See graph for new SML. r A 9% [1.5(12% 9%)] 13.50% r B 9% [0.75(12% 9%)] 11.25% r C 9% [2.0(12% 9%)] 15.00% r D 9% [0(12% 9%)] 9.00% r E 9% [0.5(12% 9%)] 7.50% e. The steeper slope of SML b ndcates a hgher rsk premum than SML d for these market condtons. When nvestor rsk averson declnes, nvestors requre lower returns for any gven rsk level (beta). P5-30. Ethcs problem Intermedate One way s to ask how the canddate would handle a hypothetcal stuaton. One may gan nsght nto the moral/ethcal framework wthn whch decsons are made. Another approach s to use a pencl-and-paper honesty test these are surprsngly accurate, despte the obvous noton that the job canddate may attempt to game the exam by gvng the rght versus the ndvdually accurate responses. Before even admnsterng the stuatonal ntervew queston or the test, ask the canddate to lst the preference attrbutes of the type of company he or she aspres to work for, and see f character and ethcs terms emerge n the descrpton. Some companes do credt hstory checks, after ganng the canddates approval to do so. Usng all four of these technques allows one to trangulate toward a vald and defensble apprasal of a canddate s honesty and ntegrty. Case Analysng rsk and return on Chargers Products nvestments Ths case requres students to revew and apply the concept of the rsk return tradeoff by analysng two possble asset nvestments usng standard devaton, coeffcent of varaton, and CAPM. ( Pt Pt 1 Ct ) 1. Expected rate of return: rt P Asset X: Year Cash flow (C t ) t1 Endng value (P t ) Begnnng value (P t 1 ) Gan/ Loss Annual rate of return 2000 R1,000 R22,000 R20,000 R2, % ,500 21,000 22,000 1, ,400 24,000 21,000 3, ,700 22,000 24,000 2,

28 136 Gtman Prncples of Manageral Fnance, Twelfth Edton Asset X: (contnued) Year Cash flow (C t ) Endng value (P t ) Begnnng value (P t 1 ) Gan/ Loss Annual rate of return ,900 23,000 22,000 1, ,600 26,000 23,000 3, ,700 25,000 26,000 1, ,000 24,000 25,000 1, ,100 27,000 24,000 3, ,200 30,000 27,000 3, Average expected return for AssetX 11.74% Asset Y: Year Cash flow (C t ) 2000 R1,50 0 Endng value (P t ) R20,00 0 Begnnng value (P t 1 ) Gan/ Loss Annual rate of return R20,000 R % ,600 20,000 20, ,700 21,000 20,000 1, ,800 21,000 21, ,900 22,000 21,000 1, ,000 23,000 22,000 1, ,100 23,000 23, ,200 24,000 23,000 1, ,300 25,000 24,000 1, ,400 25,000 25, Average expected return for Asset Y 11.14% n 2 2. r ( r r ) ( n 1) 1 Asset X: Year Return r Average return, r ( r r) ( r r) % 11.74% 3.26%

29 Chapter 5 Rsk and return 137 Asset X: (contnued) Return Average 2 Year r return, r ( r r) ( r r) x % % CV % Asset Y: Year Return r Average return, r ( r r) ( r r) % 11.14% 3.64% Y % % CV %

30 138 Gtman Prncples of Manageral Fnance, Twelfth Edton 3. Summary statstcs: Asset X Asset Y Expected return 11.74% 11.14% Standard devaton 8.90% 2.78% Coeffcent of varaton Comparng the expected returns calculated n part (a), Asset X provdes a return of 11.74%, only slghtly above the return of 11.14% expected from Asset Y. The hgher standard devaton and coeffcent of varaton of Investment X ndcates greater rsk. Wth just ths nformaton, t s dffcult to determne whether the 0.60% dfference n return s adequate compensaton for the dfference n rsk. Based on ths nformaton, however, Asset Y appears to be the better choce. 4. Usng the captal asset prcng model, the requred return on each asset s as follows: Captal asset prcng model: r j R F [b j (r m R F )] Asset R F [b j (r m R F )] r j X 7% [1.6(10% 7%)] 11.8% Y 7% [1.1(10% 7%)] 10.3% From the calculatons n part (a), the expected return for Asset X s 11.74%, compared to ts requred return of 11.8%. On the other hand, Asset Y has an expected return of 11.14% and a requred return of only 10.8%. Ths makes Asset Y the better choce. 5. In part c, we concluded that t would be dffcult to make a choce between X and Y because the addtonal return on X may or may not provde the needed compensaton for the extra rsk. In part d, by calculatng a requred rate of return, t was easy to reject X and select Y. The requred return on Asset X s 11.8%, but ts expected return (11.74%) s lower; therefore Asset X s unattractve. For Asset Y the reverse s true, and t s a good nvestment vehcle. Clearly, Charger Products s better off usng the standard devaton and coeffcent of varaton, rather than a strctly subjectve approach, to assess nvestment rsk. Beta and CAPM, however, provde a lnk between rsk and return. They quantfy rsk and convert t nto a requred return that can be compared to the expected return to draw a defntve concluson about nvestment acceptablty. Contrastng the conclusons n the responses to Questons c and d above should clearly demonstrate why Allster s better off usng beta to assess rsk. 6. a. Increase n rsk-free rate to 8% and market return to 11%: Asset R F [b j (r m R F )] r j X 8% [1.6(11% 8%)] 12.8% Y 8% [1.1(11% 8%)] 11.3% b. Decrease n market return to 9%: Asset R F [b j (r m R F )] r j X 7% [1.6(9% 7%)] 10.2% Y 7% [1.1(9% 7%)] 9.2%

31 Chapter 5 Rsk and return 139 In Stuaton 1, the requred return rses for both assets, and nether has an expected return above the frm s requred return. Wth Stuaton 2, the drop n market rate causes the requred return to decrease so that the expected returns of both assets are above the requred return. However, Asset Y provdes a larger return compared to ts requred return ( ), and t does so wth less rsk than Asset X. Spreadsheet Exercse The answer to Chapter 5 s share portfolo analyss spreadsheet problem s located n the Instructor s Resource Center at Group exercses Ths exercse uses current nformaton from several webstes regardng the recent performance of each group s shadow frm. Ths nformaton s then compared to a relevant ndex. The tme perods for comparson are 1- and 5-years. Calculated annual returns and basc graphcal analyss begn the process of comparson. Correlaton between the frm and the market s nvestgated further through the use of the frm s beta, and the rsk-free rate as represented by the 3-month Treasury rate. Lastly, the group s asked to graph the frm s SML usng the data they calculated. Accurate and tmely nformaton s the frst message of ths assgnment. Students are encouraged to look at several stes and also to search for others. The nformaton content of the dfferent stes can then be compared. Ths nformaton s then used to get students to see how basc share market analyss s done. As always, parts of ths exercse can be modfed or dropped at the adopter s dscreton. One suggeston s to add other companes to the comparson(s). Also, some of the more complex calculatons could be elmnated.

32 140 Gtman Prncples of Manageral Fnance, Twelfth Edton Integratve Case 5: Cont Furnture Integratve Case 5, Cont Furnture, nvolves evaluatng workng captal management of a furnture manufacturer. Operatng cycle, cash converson cycle, and negotated fnancng needed are determned and compared wth ndustry practces. The student then analyses the mpact of changng the frm s credt terms to evaluate ts management of trade recevables before makng a recommendaton. 1. Operatng cycle (OC) average age of nventory average collecton perod 110 days 75 days 185 days Cash converson cycle(ccc) OCaverage payment perod 185 days30 days 155 days Resources needed Total annual outlays CCC 365 days R26,500, [R1] R11,253, Industry OC 83 days 75 days 158 days Industry CCC 158 days39 days 119 days 365 Industry resources needed R8,639, Cont Furnture Negotated fnancng R11,253,425 Less: Industry resources needed 8,639,726 R2,613,699 Cost of neffcency: R2,613, R392, a. Offerng 3/10 net 60: Reducton n collecton perod 75 days (1 0.4) 45 days OC CCC Resources needed Addtonal savngs R26,500, days 45 days 128 days 128 days39 days 89 days R26,500, R6,461, days R8,639,726R6,461,644 R2,178,082

33 Chapter 5 Rsk and return 141