Answers to Warm-Up Exercises

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1 Aswes to Wam-Up Execses E8-1. Total aual etu Aswe: ($0 $1,000 $10,000) $10,000 $,000 $10,000 0% Logstcs, Ic. doubled the aual ate of etu pedcted by the aalyst. The egatve et come s elevat to the poblem. E8-. Aswe: Expected etu E8-3. Aalyst Pobablty Retu Weghted Value % 1.75% % 0.5% %.0% % 1.% Total 1.00 Expected etu 4.70% Compag the sk of two vestmets Aswe: CV CV E8-4. Based solely o stadad devatos, Ivestmet has lowe sk tha Ivestmet 1. Based o coeffcets of vaato, Ivestmet s stll less sky tha Ivestmet 1. Sce the two vestmets have dffeet expected etus, usg the coeffcet of vaato to assess sk s bette tha smply compag stadad devatos because the coeffcet of vaato cosdes the elatve sze of the expected etus of each vestmet. Computg the expected etu of a potfolo Aswe: p ( ) ( ) ( ) (0.0171) (0.049) ( % The potfolo s expected to have a etu of appoxmately 9.%. E8-5. Aswe: E8-6. Aswe: Calculatg a potfolo beta Beta ( ) ( ) ( ) ( ) ( ) Calculatg the equed ate of etu a. Requed etu ( ) b. Requed etu ( ) c. Although the sk-fee ate does ot chage, as the maket etu ceases, the equed etu o the asset ses by 180% of the chage the maket s etu.

2 Solutos to Poblems P8-1. ( Pt Pt 1 Ct ) Rate of etu: = t P LG 1; Basc t 1 a. Ivestmet X: Retu Ivestmet Y: Retu ($1,000 $0,000 $1,500) $0,000 ($55,000 $55,000 $6,800) $55, % 1.36% b. Ivestmet X should be selected because t has a hghe ate of etu fo the same level of sk. P8-. Retu calculatos: LG 1; Basc ( Pt Pt 1 Ct ) = t P t 1 Ivestmet Calculato t (%) A ($1,100 $800 $100) $ B ($118,000 $10,000 $15,000) $10, C ($48,000 $45,000 $7,000) $45,000. D ($500 $600 $80) $ E ($1,400 $1,500 $1,500) $1, P8-3. Rsk pefeeces LG 1; Itemedate a. The sk-eutal maage would accept Ivestmets X ad Y because these have hghe etus tha the 1% equed etu ad the sk does t matte. b. The sk-avese maage would accept Ivestmet X because t povdes the hghest etu ad has the lowest amout of sk. Ivestmet X offes a cease etu fo takg o moe sk tha what the fm cuetly eas. c. The sk-seekg maage would accept Ivestmets Y ad Z because he o she s wllg to take geate sk wthout a cease etu. d. Tadtoally, facal maages ae sk avese ad would choose Ivestmet X, sce t povdes the equed cease etu fo a cease sk.

3 P8-4. Rsk aalyss LG ; Itemedate a. Expaso Rage A 4% 16% 8% B 30% 10% 0% b. Poject A s less sky, sce the age of outcomes fo A s smalle tha the age fo Poject B. c. Sce the most lkely etu fo both pojects s 0% ad the tal vestmets ae equal, the aswe depeds o you sk pefeece. d. The aswe s o loge clea, sce t ow volves a sk-etu tadeoff. Poject B has a slghtly hghe etu but moe sk, whle A has both lowe etu ad lowe sk. P8-5. Rsk ad pobablty LG ; Itemedate a. Camea Rage R 30% 0% 10% S 35% 15% 0% b. Possble Outcomes Pobablty P Expected Retu Weghted Value (%)( P ) Camea R Pessmstc % Most lkely % Optmstc % 1.00 Expected etu 5.00% Camea S Pessmstc % Most lkely % Optmstc % 1.00 Expected etu 5.50% c. Camea S s cosdeed moe sky tha Camea R because t has a much boade age of outcomes. The sk-etu tadeoff s peset because Camea S s moe sky ad also povdes a hghe etu tha Camea R.

4 P8-6. Ba chats ad sk LG ; Itemedate a. b. Maket Acceptace Pobablty P Expected Retu Weghted Value ( P ) Le J Vey Poo Poo Aveage Good Excellet Expected etu Le K Vey Poo Poo Aveage Good Excellet Expected etu c. Le K appeas less sky due to a slghtly tghte dstbuto tha le J, dcatg a lowe age of outcomes.

5 P8-7. Coeffcet of vaato: CV LG ; Basc a. A B C CV A CV B CV C 7% 0% % % % 19% % D CV D % b. Asset C has the lowest coeffcet of vaato ad s the least sky elatve to the othe choces. P8-8. Stadad devato vesus coeffcet of vaato as measues of sk LG ; Basc a. Poject A s least sky based o age wth a value of b. The stadad devato measue fals to take to accout both the volatlty ad the etu of the vestmet. Ivestos would pefe hghe etu but less volatlty, ad the coeffcet of vaato povces a measue that takes to accout both aspects of vestos pefeeces. Poject D has the lowest CV, so t s the least sky vestmet elatve to the etu povded. c. A B CV A CV B C CV C D CV D I ths case Poject D s the best alteatve sce t povdes the least amout of sk fo each pecet of etu eaed. Coeffcet of vaato s pobably the best measue ths stace sce t povdes a stadadzed method of measug the sk-etu tadeoff fo vestmets wth dffeg etus.

6 P8-9. Pesoal face: Rate of etu, stadad devato, coeffcet of vaato LG ; Challege a. Stock Pce Vaace Yea Begg Ed Retus (Retu Aveage Retu) % 00.60% 11.73% 6.83% b. Aveage etu 7.31% c. Sum of vaaces.69 3 Sample dvso ( 1) Vaace 86.97% Stadad devato d. 1.0 Coeffcet of vaato e. The stock pce of H-Tech, Ic. has deftely goe though some majo pce chages ove ths tme peod. It would have to be classfed as a volatle secuty havg a upwad pce ted ove the past 4 yeas. Note how compag secutes o a CV bass allows the vesto to put the stock pope pespectve. The stock s ske tha what Mke omally buys but f he beleves that H-Tech, Ic. wll cotue to se the he should clude t. The coeffcet of vaato, howeve, s geate tha the 0.90 taget. P8-10. Assessg etu ad sk LG ; Challege a. Poject 57 (1) Rage: 1.00 (.10) 1.10 () Expected etu: Rate of Retu P =1 Pobablty P Weghted Value P Expected Retu P

7 (3) Stadad devato: ( ) P 1 ( ) P ( ) P (4) CV Poject Poject 43 (1) Rage: () Expected etu: Rate of Retu P 1 Pobablty P Weghted Value P Expected Retu P =

8 (3) Stadad devato: ( ) P 1 ( ) P ( ) P Poject (4) CV b. Ba Chats

9 c. Summay statstcs Poject 57 Poject 43 Rage Expected etu ( ) Stadad devato ( ) Coeffcet of vaato (CV) Sce Pojects 57 ad 43 have dffeg expected values, the coeffcet of vaato should be the cteo by whch the sk of the asset s judged. Sce Poject 43 has a smalle CV, t s the oppotuty wth lowe sk. P8-11. Itegatve expected etu, stadad devato, ad coeffcet of vaato LG ; Challege a. Expected etu: P 1 Rate of Retu Pobablty P Weghted Value P Asset F Expected Retu P

10 Asset G Asset H Cotued Asset G povdes the lagest expected etu. b. Stadad devato: ( ) xp 1 ( ) P Asset F Asset G Asset H Based o stadad devato, Asset G appeas to have the geatest sk, but t must be measued agast ts expected etu wth the statstcal measue coeffcet of vaato, sce the thee assets have dffeg expected values. A coect cocluso about the sk of the assets could be daw usg oly the stadad devato.

11 c. stadad devato ( ) Coeffcet of vaato = expected value Asset F: Asset G: CV CV Asset H: CV As measued by the coeffcet of vaato, Asset F has the lagest elatve sk. P8-1. Nomal pobablty dstbuto LG ; Challege a. Coeffcet of vaato: CV Solvg fo stadad devato: b. (1) 68% of the outcomes wll le betwee 1 stadad devato fom the expected value: () 95% of the outcomes wll le betwee stadad devatos fom the expected value: ( ) ( ) c. (3) 99% of the outcomes wll le betwee 3 stadad devatos fom the expected value: ( ) ( ) 0.365

12 P8-13. Pesoal face: Potfolo etu ad stadad devato LG 3; Challege a. Expected potfolo etu fo each yea: p (w L L ) (w M M ) Yea Asset L (w L L ) Asset M (w M M ) Expected Potfolo Retu p 013 (14% %) (0% %) 17.6% 014 (14% %) (18% %) 16.4% 015 (16% %) (16% %) 16.0% 016 (17% %) (14% %) 15.% 017 (17% %) (1% %) 14.0% 018 (19% %) (10% %) 13.6% b. Potfolo etu: p p c. Stadad devato: j 1 w j j % p 1 ( ) ( 1) p p p (17.6% 15.5%) (16.4% 15.5%) (16.0% 15.5%) (15.% 15.5%) (14.0% 15.5%) (13.6% 15.5%) (.1%) (0.9%) (0.5%) 6 1 ( 0.3%) ( 1.5%) ( 1.9%) 5 ( ) p % % 5 d. The assets ae egatvely coelated. e. Combg these two egatvely coelated assets educes oveall potfolo sk.

13 P8-14. Potfolo aalyss LG 3; Challege a. Expected potfolo etu: Alteatve 1: 100% Asset F p 16% 17% 18% 19% 17.5% 4 Alteatve : 50% Asset F Yea Asset F (w F F ) 50% Asset G Asset G (w G G ) Potfolo Retu p 013 (16% %) (17% %) 16.5% 014 (17% %) (16% %) 16.5% 015 (18% %) (15% %) 16.5% 016 (19% %) (14% %) 16.5% p 16.5% 16.5% 16.5% 16.5% 16.5% 4 Alteatve 3: 50% Asset F Yea Asset F (w F F ) 50% Asset H Asset H (w H H ) Potfolo Retu p 013 (16% %) (14% %) 15.0% 014 (17% %) (15% %) 16.0% 015 (18% %) (16% %) 17.0% 016 (19% %) (17% %) 18.0% p 15.0% 16.0% 17.0% 18.0% 16.5% 4 b. Stadad devato: (1) F F F F p 1 ( ) ( 1) [(16.0% 17.5%) (17.0% 17.5%) (18.0% 17.5%) (19.0% 17.5%) ] 4 1 [( 1.5%) ( 0.5%) (0.5%) (1.5%) ] 3 ( ) %

14 () (3) FG FG FG FH FH FH FH 0 [(16.5% 16.5%) (16.5% 16.5%) (16.5% 16.5%) (16.5% 16.5%) ] 4 1 [(0) (0) (0) (0) ] 3 [(15.0% 16.5%) (16.0% 16.5%) (17.0% 16.5%) (18.0% 16.5%) ] 4 1 [( 1.5%) ( 0.5%) (0.5%) (1.5%) ] 3 [( )] c. Coeffcet of vaato: CV % CV F CV FG 1.91% 17.5% % % CV FH % d. Summay: p : Expected Value of Potfolo p CV p Alteatve 1 (F) 17.5% 1.91% Alteatve (FG) 16.5% Alteatve 3 (FH) 16.5% 1.91% Sce the assets have dffeet expected etus, the coeffcet of vaato should be used to deteme the best potfolo. Alteatve 3, wth postvely coelated assets, has the hghest coeffcet of vaato ad theefoe s the skest. Alteatve s the best choce; t s pefectly egatvely coelated ad theefoe has the lowest coeffcet of vaato.

15 P8-15. Coelato, sk, ad etu LG 4; Itemedate a. (1) Rage of expected etu: betwee 8% ad 13% () Rage of the sk: betwee 5% ad 10% b. (1) Rage of expected etu: betwee 8% ad 13% () Rage of the sk: 0 sk 10% c. (1) Rage of expected etu: betwee 8% ad 13% () Rage of the sk: 0 sk 10% P8-16. Pesoal face: Iteatoal vestmet etus LG 1, 4; Itemedate a. Retu pesos b. 4,750 0,500 4,50 0,500 0, % Pce pesos 0.50 Puchase pce $.584 1,000 shaes $,5.84 Pesos pe dolla 9.1 Pce pesos 4.75 Sales pce $ ,000 shaes $,51.69 Pesos pe dolla 9.85 c. Retu pesos,51.69, ,5.84, % d. The two etus dffe due to the chage the exchage ate betwee the peso ad the dolla. The peso had depecato (ad thus the dolla appecated) betwee the puchase date ad the sale date, causg a decease total etu. The aswe pat c s the moe mpotat of the two etus fo Joe. A vesto foeg secutes wll cay exchage-ate sk. P8-17. Total, odvesfable, ad dvesfable sk LG 5; Itemedate a. ad b. c. Oly odvesfable sk s elevat because, as show by the gaph, dvesfable sk ca be vtually elmated though holdg a potfolo of at least 0 secutes that ae ot postvely coelated. Davd Talbot s potfolo, assumg dvesfable sk could o loge be educed by addtos to the potfolo, has 6.47% elevat sk.

16 P8-18. Gaphc devato of beta LG 5; Itemedate a. b. To estmate beta, the se ove u method ca be used: Beta Rse Y Ru X Takg the pots show o the gaph: Beta A Y X Beta B Y 6 4 X A facal calculato wth statstcal fuctos ca be used to pefom lea egesso aalyss. The beta (slope) of le A s 0.79; of le B, c. Wth a hghe beta of 1.33, Asset B s moe sky. Its etu wll move 1.33 tmes fo each oe pot the maket moves. Asset A s etu wll move at a lowe ate, as dcated by ts beta coeffcet of P8-19. Gaphcal devato ad tepetato of beta LG 5; Itemedate a. Wth a etu age fom 60% to 60%, Botech Cues, exhbted Pael B, s the moe sky stock. Retus ae wdely dspesed ths etu age egadless of maket codtos. By compaso, the etus of Pael A s Cyclcal Idustes Icopoated oly age fom about 40% to 40%. Thee s less dspeso of etus wth ths etu age. b. The etus o Cyclcal Idustes Icopoated s stock ae moe closely coelated wth the maket s pefomace. Hece, most of Cyclcal Idustes etus ft aoud the upwad slopg least-squaes egesso le. By compaso, Botech Cues has eaed etus appoachg 60% dug a peod whe the oveall maket expeeced a loss. Eve f the maket s up, Botech Cues has lost almost half of ts value some yeas. c. O a stadaloe bass, Botech Cues Copoato s ske. Howeve, f a vesto was seekg to dvesfy the sk of the cuet potfolo, the uque, osystematc pefomace of Botech Cues Copoato makes t a good addto. Othe cosdeatos would be the mea etu fo both (hee Cyclcal Idustes has a hghe etu whe the oveall maket etu s zeo), expectatos egadg the oveall maket pefomace, ad level to whch oe ca use hstoc etus to accuately foecast stock pce behavo.

17 P8-0. Itepetg beta LG 5; Basc Effect of chage maket etu o asset wth beta of 1.0: a. 1.0 (15%) 18.0% cease b. 1.0 ( 8%) 9.6% decease c. 1.0 (0%) o chage d. The asset s moe sky tha the maket potfolo, whch has a beta of 1. The hghe beta makes the etu move moe tha the maket. P8-1. Betas LG 5; Basc a. ad b. Asset Beta Icease Maket Retu Expected Impact o Asset Retu Decease Maket Retu Impact o Asset Retu A B C D c. Asset B should be chose because t wll have the hghest cease etu. d. Asset C would be the appopate choce because t s a defesve asset, movg opposto to the maket. I a ecoomc dowtu, Asset C s etu s ceasg. P8-. Pesoal face: Betas ad sk akgs LG 5; Itemedate a. b. ad c. Stock Beta Most sky B 1.40 A 0.80 Least sky C 0.30 Asset Beta Icease Maket Retu Expected Impact o Asset Retu Decease Maket Retu Impact o Asset Retu A B C d. I a declg maket, a vesto would choose the defesve stock, Stock C. Whle the maket decles, the etu o C ceases. e. I a sg maket, a vesto would choose Stock B, the aggessve stock. As the maket ses oe pot, Stock B ses 1.40 pots.

18 P8-3. Pesoal face: Potfolo betas: b p w j 1 LG 5; Itemedate a. Potfolo A j b j Potfolo B Asset Beta w A w A b A w B w B b B b A b B 1.11 b. Potfolo A s slghtly less sky tha the maket (aveage sk), whle Potfolo B s moe sky tha the maket. Potfolo B s etu wll move moe tha Potfolo A s fo a gve cease o decease maket etu. Potfolo B s the moe sky. P8-4. Captal asset pcg model (CAPM): j R F [b j ( m R F )] LG 6; Basc Case j R F [b j ( m R F )] A 8.9% 5% [1.30 (8% 5%)] B 1.5% 8% [0.90 (13% 8%)] C 8.4% 9% [ 0.0 (1% 9%)] D 15.0% 10% [1.00 (15% 10%)] E 8.4% 6% [0.60 (10% 6%)] P8-5. Pesoal face: Beta coeffcets ad the captal asset pcg model LG 5, 6; Itemedate To solve ths poblem you must take the CAPM ad solve fo beta. The esultg model s: RF Beta R m F a. Beta 10% 5% 5% 16% 5% 11% b. Beta 15% 5% 10% 16% 5% 11% c. Beta 18% 5% 13% 16% 5% 11% d. Beta 0% 5% 15% 16% 5% 11% e. If Kathee s wllg to take a maxmum of aveage sk the she wll be able to have a expected etu of oly 16%. ( 5% 1.0(16% 5%) 16%.)

19 P8-6. Mapulatg CAPM: j R F [b j ( m R F )] LG 6; Itemedate a. j 8% [0.90 (1% 8%)] j 11.6% b. 15% R F [1.5 (14% R F )] R F 10% c. 16% 9% [1.10 ( m 9%)] m 15.36% d. 15% 10% [b j (1.5% 10%) b j P8-7. Pesoal face: Potfolo etu ad beta LG 1, 3, 5, 6: Challege a. b p (0.0)(0.80) (0.35)(0.95) (0.30)(1.50) (0.15)(1.5) b. A ($0,000 $0,000) $1,600 $1,600 $0,000 $0,000 8% B C D c. P ($36,000 $35,000) $1,400 $, % $35,000 $35,000 ($34,500 $30,000) 0 $4,500 15% $30,000 $30,000 ($16,500 $15,000) $375 $1, % $15,000 $15,000 ($107,000 $100,000) $3,375 $10, % $100,000 $100,000 d. A 4% [0.80 (10% 4%)] 8.8% B 4% [0.95 (10% 4%)] 9.7% C 4% [1.50 (10% 4%)] 13.0% D 4% [1.5 (10% 4%)] 11.5% e. Of the fou vestmets, oly C (15% vs. 13%) ad D (1.5% vs. 11.5%) had actual etus that exceeded the CAPM expected etu (15% vs. 13%). The udepefomace could be due to ay usystematc facto that would have caused the fm ot do as well as expected. Aothe possblty s that the fm s chaactestcs may have chaged such that the beta at the tme of the puchase ovestated the tue value of beta that exsted dug that yea. A thd explaato s that beta, as a sgle measue, may ot captue all of the systematc factos that cause the expected etu. I othe wods, thee s eo the beta estmate.

20 P8-8. Secuty maket le, SML LG 6; Itemedate a, b, ad d. c. j R F [b j ( m R F )] Asset A j 0.09 [0.80 ( )] j 0.1 Asset B j 0.09 [1.30 ( )] j 0.14 d. Asset A has a smalle equed etu tha Asset B because t s less sky, based o the beta of 0.80 fo Asset A vesus 1.30 fo Asset B. The maket sk pemum fo Asset A s 3.% (1.% 9%), whch s lowe tha Asset B s maket sk pemum (14.% 9% 5.%). P8-9. Shfts the secuty maket le LG 6; Challege a, b, c, d.

21 b. j R F [b j ( m R F )] A 8% [1.1 (1% 8%)] A 8% 4.4% A 1.4% c. A 6% [1.1 (10% 6%)] A 6% 4.4% A 10.4% d. A 8% [1.1 (13% 8%)] A 8% 5.5% A 13.5% e. (1) A decease flatoay expectatos educes the equed etu as show the paallel dowwad shft of the SML. () Iceased sk aveso esults a steepe slope, sce a hghe etu would be equed fo each level of sk as measued by beta. P8-30. Itegatve sk, etu, ad CAPM LG 6; Challege a. Poject j R F [b j ( m R F )] A j 9% [1.5 (14% 9%)] 16.5% B j 9% [0.75 (14% 9%)] 1.75% C j 9% [.0 (14% 9%)] 19.0% D j 9% [0 (14% 9%)] 9.0% E j 9% [( 0.5) (14% 9%)] 6.5% b. ad d. c. Poject A s 150% as esposve as the maket.

22 Poject B s 75% as esposve as the maket. Poject C s twce as esposve as the maket. Poject D s uaffected by maket movemet. Poject E s oly half as esposve as the maket, but moves the opposte decto as the maket. d. See gaph fo ew SML. A 9% [1.5 (1% 9%)] 13.50% B 9% [0.75 (1% 9%)] 11.5% C 9% [.0 (1% 9%)] 15.00% D 9% [0 (1% 9%)] 9.00% E 9% [ 0.5 (1% 9%)] 7.50% e. The steepe slope of SML b dcates a hghe sk pemum tha SML d fo these maket codtos. Whe vesto sk aveso decles, vestos eque lowe etus fo ay gve sk level (beta). P8-31. Ethcs poblem LG 1; Itemedate Ivestos expect maages to take sks wth the moey, so t s clealy ot uethcal fo maages to make sky vestmets wth othe people s moey. Howeve, maages have a duty to commucate tuthfully wth vestos about the sk that they ae takg. Potfolo maages should ot take sks that they do ot expect to geeate etus suffcet to compesate vestos fo the etu vaablty.