Solutions to Problems

Transcription

1 Solutos to Problems ( Pt Pt + Ct) P5-. LG : Rate of retur: rt Pt Basc ($,000 $0,000 + $,500) a. Ivestmet X: Retur.50% $0,000 Ivestmet Y: Retur ($55,000 $55,000 + $6,800).36% $55,000 b. Ivestmet X should be selected because t has a hgher rate of retur for the same level of rsk. ( Pt Pt + Ct) P5-. LG : Retur calculatos: r t P Basc Ivestmet Calculato r t (%) A ($,00 $800 $00) $ B ($8,000 $0,000 + $5,000) $0, C ($48,000 $45,000 + $7,000) $45,000. D ($500 $600 + $80) $ E ($,400 $,500 + $,500) $,500.0 t P5-3. P5-4. LG : Rsk prefereces Itermedate The rsk-averse maager would accept Ivestmet X because t provdes the hghest retur ad has the lowest amout of rsk. Ivestmet X offers a crease retur for takg o more rsk tha what the frm curretly ears. LG : Rsk aalyss Itermedate a. Expaso Rage A 4% 6% 8% B 30% 0% 0% b. Project A s less rsky, sce the rage of outcomes for A s smaller tha the rage for Project B. c. Sce the most lkely retur for both projects s 0% ad the tal vestmets are equal, the aswer depeds o your rsk preferece. d. The aswer s o loger clear, sce t ow volves a rsk retur tradeoff. Project B has a slghtly hgher retur but more rsk, whle A has both lower retur ad lower rsk.

2 Chapter 5 Rsk ad Retur 9 P5-5. LG : Rsk ad probablty Itermedate a. Camera Rage R 30% 0% 0% S 35% 5% 0% b. Possble Outcomes Probablty P r Expected Retur r Weghted Value (%)(r P r ) Camera R Pessmstc Most lkely Optmstc Expected retur 5.00 Camera S Pessmstc Most lkely Optmstc Expected retur 5.50 c. Camera S s cosdered more rsky tha Camera R because t has a much broader rage of outcomes. The rsk retur tradeoff s preset because Camera S s more rsky ad also provdes a hgher retur tha Camera R. P5-6. LG : Bar charts ad rsk Itermedate a.

3 9 Gtma Prcples of Maageral Face, Bref Ffth Edto b. Market Acceptace Probablty P r Expected Retur r Weghted Value (r P r ) Le J Very Poor Poor Average Good Excellet Expected retur Le K Very Poor Poor Average Good Excellet Expected retur c. Le K appears less rsky due to a slghtly tghter dstrbuto tha Le J, dcatg a lower rage of outcomes. σ r P5-7. LG : Coeffcet of varato: CV r Basc a. A 7% CV A % B 9.5% CV B % C 6% CV C % D 5.5% CV D % b. Asset C has the lowest coeffcet of varato ad s the least rsky relatve to the other choces.

4 Chapter 5 Rsk ad Retur 93 P5-8. LG : Persoal face: Rate of retur, stadard devato, coeffcet of varato Challege a. Stock Prce Varace Year Begg Ed Returs (Retur Average Retur) % % % % b. Average retur.3% c. Sum of varaces.69 3 Sample dvsor ( ) Varace 86.97% Stadard devato d..0 Coeffcet of varato e. The stock prce of Apple has deftely goe through some major prce chages over ths tme perod. It would have to be classfed as a volatle securty havg a upward prce tred over the past 4 years. Note how comparg securtes o a CV bass allows the vestor to put the stock proper perspectve. The stock s rsker tha what Mke ormally buys but f he beleves that Apple wll cotue to rse the he should clude t. P5-9. LG : Assessg retur ad rsk Challege a. Project 57 () Rage:.00 ( 0.0).0 () Expected retur: r r Pr Rate of Retur r Probablty P r Weghted Value r P r Expected Retur r r P r

5 94 Gtma Prcples of Maageral Face, Bref Ffth Edto (3) Stadard devato: σ ( r r) P r r r r r ( r r) P r ( r ) r Pr σ Project (4) CV b. Project 43 () Rage: () Expected retur: r r P r Rate of Retur r Probablty P r Weghted Value r P r Expected Retur r r P r

6 Chapter 5 Rsk ad Retur 95 (3) Stadard devato: σ ( r r) P r (4) c. Bar Charts r r r r ( r ) r P r ( r r ) P r σ Project CV

7 96 Gtma Prcples of Maageral Face, Bref Ffth Edto d. Summary statstcs Project 57 Project 43 Rage Expected retur ( r ) Stadard devato ( σ r ) Coeffcet of varato (CV) Sce Projects 57 ad 43 have dfferg expected values, the coeffcet of varato should be the crtero by whch the rsk of the asset s judged. Sce Project 43 has a smaller CV, t s the opportuty wth lower rsk. P5-0. LG : Itegratve expected retur, stadard devato, ad coeffcet of varato Challege a. Expected retur: r r P r Rate of Retur r Probablty P r Weghted Value r P r Asset F Asset G Asset H Expected Retur r r P r Asset G provdes the largest expected retur.

8 Chapter 5 Rsk ad Retur 97 b. Stadard devato: σ ( r r) xp r r r ( r r) P r σ σ r Asset F Asset G Asset H c. Based o stadard devato, Asset G appears to have the greatest rsk, but t must be measured agast ts expected retur wth the statstcal measure coeffcet of varato, sce the three assets have dfferg expected values. A correct cocluso about the rsk of the assets could be draw usg oly the stadard devato. stadard devato ( σ ) Coeffcet of varato expected value Asset F: CV Asset G: 0.78 CV Asset H: CV As measured by the coeffcet of varato, Asset F has the largest relatve rsk.

9 98 Gtma Prcples of Maageral Face, Bref Ffth Edto P5-. LG 3: Persoal face: Portfolo retur ad stadard devato Challege a. Expected portfolo retur 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 Retur r p 00 (4% %) + (0% %) 7.6% 0 (4% %) + (8% %) 6.4% 0 (6% %) + (6% %) 6.0% 03 (7% %) + (4% %) 5.% 04 (7% %) + (% %) 4.0% 05 (9% %) + (0% %) 3.6% b. Portfolo retur: r p j w j r j Retur r p % 6 c. Stadard devato: σ rp σ rp σ rp ( r r) ( ) (7.6% 5.5%) + (6.4% 5.5%) + (6.0% 5.5%) (5.% 5.5%) (4.0% 5.5%) (3.6% 5.5%) (.%) + (0.9%) + (0.5%) + ( 0.3%) + (.5%) + (.9%) 5 s rp ( ) σ rp % % 5 d. The assets are egatvely correlated. e. Combg these two egatvely correlated assets reduces overall portfolo rsk.

10 Chapter 5 Rsk ad Retur 99 P5-. LG 3: Portfolo aalyss Challege a. Expected portfolo retur: Alteratve : 00% Asset F rp 6% + 7% + 8% + 9% 7.5% 4 Alteratve : 50% Asset F + 50% Asset G Asset F Year (w F r F ) + Asset G (w G r G ) Portfolo Retur r p 00 (6% %) + (7% %) 6.5% 0 (7% %) + (6% %) 6.5% 0 (8% %) + (5% %) 6.5% 03 (9% %) + (4% %) 6.5% r p 6.5% + 6.5% + 6.5% + 6.5% 6.5% 4 Alteratve 3: 50% Asset F + 50% Asset H Asset F Year (w F r F ) + Asset H (w H r H ) Portfolo Retur r p 00 (6% %) + (4% %) 5.0% 0 (7% %) + (5% %) 6.0% 0 (8% %) + (6% %) 7.0% 03 (9% %) + (7% %) 8.0% 5.0% + 6.0% + 7.0% + 8.0% r p 6.5% 4 b. Stadard devato: ( r r) () σ rp ( ) σ F σ F σ F [(6.0% 7.5%) + (7.0% 7.5%) + (8.0% 7.5%) + (9.0% 7.5%) ] 4 [(.5%) + ( 0.5%) + (0.5%) + (.5%) ] 3 ( ) σ F % 3

11 00 Gtma Prcples of Maageral Face, Bref Ffth Edto [(6.5% 6.5%) + (6.5% 6.5%) + (6.5% 6.5%) + (6.5% 6.5%) ] () σ FG 4 [(0) + (0) + (0) + (0) ] σ FG 3 σ FG 0 [(5.0% 6.5%) + (6.0% 6.5%) + (7.0% 6.5%) + (8.0% 6.5%) ] (3) σ FH 4 σ FH [(.5%) + ( 0.5%) + (0.5%) + (.5%) ] 3 σ FH [( )] σ FH % 3 c. Coeffcet of varato: d. Summary: CV σ r r.9% CVF % 0 CVFG 0 6.5%.9% CVFH % r p : Expected Value of Portfolo σ rp CV p Alteratve (F) 7.5%.9% Alteratve (FG) 6.5% Alteratve 3 (FH) 6.5%.9% Sce the assets have dfferet expected returs, the coeffcet of varato should be used to determe the best portfolo. Alteratve 3, wth postvely correlated assets, has the hghest coeffcet of varato ad therefore s the rskest. Alteratve s the best choce; t s perfectly egatvely correlated ad therefore has the lowest coeffcet of varato.

12 Chapter 5 Rsk ad Retur 0 P5-3. LG 4: Correlato, rsk, ad retur Itermedate a. () Rage of expected retur: betwee 8% ad 3% () Rage of the rsk: betwee 5% ad 0% b. () Rage of expected retur: betwee 8% ad 3% () Rage of the rsk: 0 < rsk < 0% c. () Rage of expected retur: betwee 8% ad 3% () Rage of the rsk: 0 < rsk < 0% P5-4. LG, 4: Persoal face: Iteratoal vestmet returs Itermedate a. Retur pesos 4,750 0,500 4, % 0,500 0,500 b. Prce pesos 0.50 Purchase prce $.584,000 shares $,5.84 Pesos per dollar 9. Prce pesos 4.75 Sales prce $.569,000 shares $,5.69 Pesos per dollar 9.85 c. Retur pesos,5.69, %,5.84,5.84 d. The two returs dffer due to the chage the exchage rate betwee the peso ad the dollar. The peso had deprecato (ad thus the dollar apprecated) betwee the purchase date ad the sale date, causg a decrease total retur. The aswer Part (c) s the more mportat of the two returs for Joe. A vestor foreg securtes wll carry exchage-rate rsk. P5-5. LG 5: Total, odversfable, ad dversfable rsk Itermedate a. ad b. c. Oly odversfable rsk s relevat because, as show by the graph, dversfable rsk ca be vrtually elmated through holdg a portfolo of at least 0 securtes that are ot postvely correlated. Davd Talbot s portfolo, assumg dversfable rsk could o loger be reduced by addtos to the portfolo, has 6.47% relevat rsk.

13 0 Gtma Prcples of Maageral Face, Bref Ffth Edto P5-6. LG 5: Graphc dervato of beta Itermedate a. b. To estmate beta, the rse over ru method ca be used: Rse ΔY Beta Ru Δ X Takg the pots show o the graph: ΔY 9 3 Beta A 0.75 ΔX ΔY 6 4 Beta B.33 ΔX A facal calculator wth statstcal fuctos ca be used to perform lear regresso aalyss. The beta (slope) of Le A s 0.79; of Le B,.379. c. Wth a hgher beta of.33, Asset B s more rsky. Its retur wll move.33 tmes for each oe pot the market moves. Asset A s retur wll move at a lower rate, as dcated by ts beta coeffcet of P5-7. LG 5: Iterpretg beta Basc Effect of chage market retur o asset wth beta of.0: a..0 (5%) 8.0% crease b..0 ( 8%) 9.6% decrease c..0 ( 0%) o chage d. The asset s more rsky tha the market portfolo, whch has a beta of. The hgher beta makes the retur move more tha the market.

14 Chapter 5 Rsk ad Retur 03 P5-8. LG 5: Betas Basc a. ad b. Asset Beta Icrease Market Retur Expected Impact o Asset Retur Decrease Market Retur Impact o Asset Retur A B C D c. Asset B should be chose because t wll have the hghest crease retur. d. Asset C would be the approprate choce because t s a defesve asset, movg opposto to the market. I a ecoomc dowtur, Asset C s retur s creasg. P5-9. LG 5: Persoal face: Betas ad rsk rakgs Itermedate a. Stock Beta Most rsky B.40 A 0.80 Least rsky C 0.30 b. ad c. Asset Beta Icrease Market Retur Expected Impact o Asset Retur Decrease Market Retur Impact o Asset Retur A B C d. I a declg market, a vestor would choose the defesve stock, Stock C. Whle the market decles, the retur o C creases. e. I a rsg market, a vestor would choose Stock B, the aggressve stock. As the market rses oe pot, Stock B rses.40 pots.

15 04 Gtma Prcples of Maageral Face, Bref Ffth Edto P5-0. LG 5: Portfolo betas: b p Itermedate a. j w j b j Portfolo A Portfolo B Asset Beta w A w A b A w B w B b B b A b B. b. Portfolo A s slghtly less rsky tha the market (average rsk), whle Portfolo B s more rsky tha the market. Portfolo B s retur wll move more tha Portfolo A s for a gve crease or decrease market retur. Portfolo B s the more rsky. P5-. LG 6: Captal asset prcg 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% + [.30 (8% 5%)] B.5% 8% + [0.90 (3% 8%)] C 8.4% 9% + [ 0.0 (% 9%)] D 5.0% 0% + [.00 (5% 0%)] E 8.4% 6% + [0.60 (0% 6%)] P5-. LG 5, 6: Persoal face: Beta coeffcets ad the captal asset prcg model Itermedate To solve ths problem you must take the CAPM ad solve for beta. The resultg model s: r RF Beta r R m F a. 0% 5% 5% Beta % 5% % b. 5% 5% 0% Beta % 5% % c. 8% 5% 3% Beta.88 6% 5% % d. 0% 5% 5% Beta % 5% % e. If Kathere s wllg to take a maxmum of average rsk the she wll be able to have a expected retur of oly 6%. (r 5% +.0(6% 5%) 6%.)

16 Chapter 5 Rsk ad Retur 05 P5-3. LG 6: Mapulatg CAPM: r j R F + [b j (r m R F )] Itermedate a. r j 8% + [0.90 (% 8%)] r j.6% b. 5% R F + [.5 (4% R F )] R F 0% c. 6% 9% + [.0 (k m 9%)] r m 5.36% d. 5% 0% + [b j (.5% 0%) b j P5-4. LG, 3, 5, 6: Persoal face: Portfolo retur ad beta Challege a. b p (0.0)(0.80) + (0.35)(0.95) + (0.30)(.50) + (0.5)(.5) ($0,000 $0,000) + $,600 $,600 b. r A 8% $0,000 $0,000 r B r C r D c. r P ($36,000 $35,000) + $,400 $, % $35,000 $35,000 ($34,500 $30,000) + 0 $4,500 5% $30,000 $30,000 ($6,500 $5,000) + $375 $,875.5% $5,000 $5,000 ($07,000 $00,000) + $3,375 $0, % $00,000 $00,000 d. r A 4% + [0.80 (0% 4%)] 8.8% r B 4% + [0.95 (0% 4%)] 9.7% r C 4% + [.50 (0% 4%)] 3.0% r D 4% + [.5 (0% 4%)].5% e. Of the four vestmets, oly C (5% versus 3%) ad D (.5% versus.5%) had actual returs that exceeded the CAPM expected retur (5% versus 3%). The uderperformace could be due to ay usystematc factor that would have caused the frm ot do as well as expected. Aother possblty s that the frm s characterstcs may have chaged such that the beta at the tme of the purchase overstated the true value of beta that exsted durg that year. A thrd explaato s that beta, as a sgle measure, may ot capture all of the systematc factors that cause the expected retur. I other words, there s error the beta estmate.

17 06 Gtma Prcples of Maageral Face, Bref Ffth Edto P5-5. LG 6: Securty market le, SML Itermedate a. b. ad d. c. r j R F + [b j (r m R F )] Asset A r j [0.80 ( )] r j 0. Asset B r j [.30 ( )] r j 0.4 d. Asset A has a smaller requred retur tha Asset B because t s less rsky, based o the beta of 0.80 for Asset A versus.30 for Asset B. The market rsk premum for Asset A s 3.% (.% 9%), whch s lower tha Asset B s market rsk premum (4.% 9% 5.%). P5-6. LG 6: Itegratve-rsk, retur, ad CAPM Challege a. Project r j R F + [b j (r m R F )] A r j 9% + [.5 (4% 9%)] 6.5% B r j 9% + [0.75 (4% 9%)].75% C r j 9% + [.0 (4% 9%)] 9.0% D r j 9% + [0 (4% 9%)] 9.0% E r j 9% + [( 0.5) (4% 9%)] 6.5%

18 Chapter 5 Rsk ad Retur 07 b. ad d. c. Project A s 50% as resposve as the market. Project B s 75% as resposve as the market. Project C s twce as resposve as the market. Project D s uaffected by market movemet. Project E s oly half as resposve as the market, but moves the opposte drecto as the market. P5-7. Ethcs problem Itermedate Oe way s to ask how the caddate would hadle a hypothetcal stuato. Oe may ga sght to the moral/ethcal framework wth whch decsos are made. Aother approach s to use a pecl-ad-paper hoesty test these are surprsgly accurate, despte the obvous oto that the job caddate may attempt to game the exam by gvg the rght versus the dvdually accurate resposes. Before eve admsterg the stuatoal tervew questo or the test, ask the caddate to lst the preferred attrbutes of the type of compay he or she aspres to work for, ad see f character ad ethcs terms emerge the descrpto. Some compaes do credt hstory checks, after gag the caddates approval to do so. Usg all four of these techques allows oe to tragulate toward a vald ad defesble apprasal of a caddate s hoesty ad tegrty.

19 08 Gtma Prcples of Maageral Face, Bref Ffth Edto Case Aalyzg Rsk ad Retur o Chargers Products Ivestmets Ths case requres studets to revew ad apply the cocept of the rsk retur tradeoff by aalyzg two possble asset vestmets usg stadard devato, coeffcet of varato, ad CAPM. ( Pt Pt + Ct). Expected rate of retur: rt P Asset X: Year Cash Flow (C t ) t Edg Value (P t ) Begg Value (P t ) Ga/ Loss Aual Rate of Retur 000 $,000 $,000 $0,000 $, % 00,500,000,000, ,400 4,000,000 3, ,700,000 4,000, ,900 3,000,000, ,600 6,000 3,000 3, ,700 5,000 6,000, ,000 4,000 5,000, ,00 7,000 4,000 3, ,00 30,000 7,000 3, Average expected retur for Asset X.74% Asset Y: Year Cash Flow (C t ) Edg Value (P t ) Begg Value (P t ) Ga/ Loss Aual Rate of Retur 000 $,500 $0,000 $0,000 $ % 00,600 0,000 0, ,700,000 0,000, ,800,000, ,900,000,000, ,000 3,000,000, ,00 3,000 3, ,00 4,000 3,000, ,300 5,000 4,000, ,400 5,000 5, Average expected retur for Asset Y.4%

20 Chapter 5 Rsk ad Retur 09. σ r ( r r) ( ) Asset X: Year Retur r Average Retur, r ( r r ) ( r r) %.74% 3.6% σ x % % CV % Asset Y: Average Year Retur r Retur, r ( r r) ( r r) %.4% 3.64%

21 0 Gtma Prcples of Maageral Face, Bref Ffth Edto 3. Summary statstcs: σ Y % 0.78% CV 0.5.4% Asset X Asset Y Expected retur.74%.4% Stadard devato 8.90%.78% Coeffcet of varato Comparg the expected returs calculated Part (a), Asset X provdes a retur of.74%, oly slghtly above the retur of.4% expected from Asset Y. The hgher stadard devato ad coeffcet of varato of Ivestmet X dcates greater rsk. Wth just ths formato, t s dffcult to determe whether the 0.60% dfferece retur s adequate compesato for the dfferece rsk. Based o ths formato, however, Asset Y appears to be the better choce. 4. Usg the captal asset prcg model, the requred retur o each asset s as follows: Captal asset prcg model: r j R F + [b j (r m R F )] Asset R F + [b j (r m R F )] r j X 7% + [.6 (0% 7%)].8% Y 7% + [. (0% 7%)] 0.3% From the calculatos Part (a), the expected retur for Asset X s.74%, compared to ts requred retur of.8%. O the other had, Asset Y has a expected retur of.4% ad a requred retur of oly 0.8%. Ths makes Asset Y the better choce. 5. I Part c, we cocluded that t would be dffcult to make a choce betwee X ad Y because the addtoal retur o X may or may ot provde the eeded compesato for the extra rsk. I Part (d), by calculatg a requred rate of retur, t was easy to reject X ad select Y. The requred retur o Asset X s.8%, but ts expected retur (.74%) s lower; therefore Asset X s uattractve. For Asset Y the reverse s true, ad t s a good vestmet vehcle. Clearly, Charger Products s better off usg the stadard devato ad coeffcet of varato, rather tha a strctly subjectve approach, to assess vestmet rsk. Beta ad CAPM, however, provde a lk betwee rsk ad retur. They quatfy rsk ad covert t to a requred retur that ca be compared to the expected retur to draw a deftve cocluso about vestmet acceptablty. Cotrastg the coclusos the resposes to Questos c ad d above should clearly demostrate why Juor s better off usg beta to assess rsk.

22 Chapter 5 Rsk ad Retur 6. a. Icrease rsk-free rate to 8% ad market retur to %: Asset R F + [b j (r m R F )] r j X 8% + [.6 (% 8%)].8% Y 8% + [. (% 8%)].3% b. Decrease market retur to 9%: Asset R F + [b j (r m R F )] r j X 7% + [.6 (9% 7%)] 0.% Y 7% + [. (9% 7%)] 9.% I Stuato, the requred retur rses for both assets, ad ether has a expected retur above the frm s requred retur. Wth Stuato, the drop market rate causes the requred retur to decrease so that the expected returs of both assets are above the requred retur. However, Asset Y provdes a larger retur compared to ts requred retur ( ), ad t does so wth less rsk tha Asset X. Spreadsheet Exercse The aswer to Chapter 5 s stock portfolo aalyss spreadsheet problem s located the Istructor s Resource Ceter at A Note o Web Exercses A seres of chapter-relevat assgmets requrg Iteret access ca be foud at the book s Compao Webste at I the course of completg the assgmets studets access formato about a frm, ts dustry, ad the macro ecoomy, ad coduct aalyses cosstet wth those foud each respectve chapter.