재무관리(2판) 추록

663,000 3 285,000 0 50,000 25,000 30% 10% NPV 2011 1 0 1 2 3-663,000-25,000 25,000 285,000_1-0.3 285,000_1-0.3 285,000_1-0.3 Dep_t 221,000_0.3 221,000_0.3 221,000_0.3 50,000-50,000_0.3-688,000 265,800 265,800 325,800 265,800 265,800 325,800 NPV = -688,000 + 11124 + 11124 + 11124 = 18,084 1.1 1.1 1.1 115.2 NPV = -100 + 11111111 = 0 IRR = 15.2% > 15% 1+ IRR

EBIT 0 Q p CFC v Dep IC EBIT = Qp - v - CFC - Dep =0 CFC + Dep Q = 111112 p - v OCF = EBIT1-t + Dep = Dep 0% OCF 0 OCF ={Qp - v - CFC - Dep}1-t + Dep =0 Qp - v1-t- CFC1-t + Dept =0 CFC1-t- Dept Q = 11111111123 p - v1-t -100%

0 NPV =[{Qp - v - CFC - Dep}1-t + Dep]_PVIFA - IC =0 IC Qp - v1-t- CFC1-t + Dept = 1113 PVIFA IC CFC1-t- Dept + 1113 PVIFA Q = 1111111112111123 p - v1-t 0 0 0 < < EBIT <0 EBIT =0 EBIT >0 NPV NPV <0 NPV <0 NPV =0 OCF =0 OCF = Dep OCF > Dep = < IRR = -100% IRR =0 IRR = A 10 5 1,000 5,000 2 2 20% 10%

EBIT = Q_10-5 - 1,000-2,500 = 0 Q = 700 OCF ={Q_10-5 - 1,000-2,500}1-0.2 + 2,500 = 0 Q =75 1 1 PVIFA10% 2 = 12 + 124 = 1.7355 1.1 1.1 NPV =[{Q10-5 - 1,000-2,500}1-0.2 + 2,500]_1.7355-5,000 = 0 Q = 795 10% 3,000 10 3 5 1,000 0 3 10% 2.48692013 1 0% + 442

-100% 0 A B A 10 1 2 B 14 7 3 12% 2012 1 A 11.69 B 15.68 A equivalent annual cost 6.92 B equivalent annual cost 5.53 A equivalent annual cost B equivalent annual cost 1 1 PVÅ = 10 + 123 + 113 = 10 + 1_1.69 = 11.69 1.12 1.12 0.7 0.7 0.7 PVı = 14 + 123 + 113 + 113 = 14 + 0.7_2.4 = 15.68 1.12 1.12 1.12 11.69 EACÅ = 112 = 6.92 1.69 15.68 EACı = 112 = 6.53 2.4

13% 10% 20% 15% 2013 1-1 0.4 0.6 0.2 10% 0.8 10% A B efficient A B 0.15 + 0.1_0.15 w = 111111111111 = 0.6w = 0.4 0.1 + 0.15 + 2_0.1_0.15 10% q < 114 = 0.67 0.67 10% 15% 0.67 10% 2

CAPM 5.0% 15.0% 5.0%A 2.0A 12.5% CML SML 2011 1 a CML SML trade-off b A 2.0 A c A 1.0 SML CML d CML reward to variability ratio e SML abc abd ace bce bde a CML SML b c A 10% A 0.8= 10% 12.5% d CML e SML

A B A 45% B 55% Sharpe ratio 0.2 risk free rate 2012 1 A B 6.50% 8.50% 0.10 0.15 0.06 ERπ = 0.45_6.5% + 0.55_8.5% = 7.6% VarRπ = 0.45 _0.1 + 0.55 _0.15 + 2_0.45_0.55_0.06 = 0.095325 rπ = '0ƒ.0953ß2ß5 = 30.875% 0.076 - Rƒ 0.2 = 11111 Rƒ = 1.43% 0.30875 CAPM A B 18% 08% 35% 22% 0 A B 68% 32% 2013 1

ERµ = 18%_0.68 + 8%_0.32 = 14.8% råµ 0.68_0.35 bå = 124 = 1111111111124 = 1.3523 r µ 0.68 _0.35 + 0.32 _0.22 18% = ERΩ + {14.8% - ERΩ}_1.3523 ERΩ = 5.72% Fama Franch 3 R = a + b m R m + b SMB SMB + b HML HML + e SMB = - HML = - PBR PBR APT 8 Eugene FFama and Kenneth RFrenchThe Cross Section of Expected Stock ReturnsJournal of Finance 47 1992

irrationality PER PER active investment passive investment 20% 20% 7%p

50 50 50 50

ROE capital gains account momentum

a b loss aversion S U U DW W a b

1,000 1,000 50% A 100% 500 B U = ' W 2,000 1,000 50% A 100% 500 B 1,000 1,000 50% A 100% 500 B DW>0 U = ' D W DW<0 U =-' D W 2,000 1,000 50% A 500 B EWÅ = 2,000_0.5 + 1,000_0.5 = 1,500 EWı = 1,500 EUÅ = 'ƒ2,000_0.5 + 'ƒ1,000_0.5 = 38.1721 EUı = 'ƒ1,500 = 38.7298 B EWÅ = 1,000_0.5 + 2,000_0.5 = 1,500 EWı = 1,500 EUÅ = 'ƒ1,000_0.5 + 'ƒ2,000_0.5 = 38.1721 EUı = 'ƒ1,500 = 38.7298 B EDWÅ = 1,000_0.5 + 0_0.5 = 500 EDWı =500 EUÅ = 'ƒ1,000_0.5 + '0_0.5 = 15.8114

EUı = ' 50å0 = 22.3607 B EDWÅ = -1,000_0.5 + 0_0.5 = -500 EDWı = -500 EUÅ =-'ƒ -1, 00ß0å _0.5 - '0_0.5 = -15.8114 EUı =-'ƒ 500å = -22.3607 A A reflection effect Kahneman and Tversky1979 prospect Certainty effect 80% 4,000 A 100% 3,000 B B 20% 4,000 C 25% 3,000 D

C CD AB 1/4 CD C A B 80% 4,000 20% 4,000 A C 20% 0 80% 0 100% 3,000 25% 3,000 B 0% 0 D 75% 0 a b Reflection effect AB A 80% 4,000 A' 100% 3,000 B' A' loss aversion 80% 4,000 80% -4,000 A A' 20% 0 20% 0 100% 3,000 100% -3,000 B 0% 0 B' 0% 0 a b

Isolation effect 80% 4,000 C' 3,000 D' D' C' 4,000 20% D' 3,000 25% CD CD C C' D' D' AB 80% 4,000 3,000 1,000 50% 1,000 E 100% 500 F F 2,000

50% 1,000 E' 100% 500 F' E' reference point A 80% 20% 4,000 0 C 20% 80% 4,000 0 C' 80% 25% 75% 0 20% 4,000 0 B 100% 0% 3,000 0 D 25% 75% 3,000 0 D' 25% 100% 3,000 75% 0 aab bcd cc'd'

A 1 10% 30% 20% 11,000 Bº = 11121 = 9,167 1 + 20% 11,000_0.9 + 7,700_0.1 Bº = 111111111113 = 9,167 ER = 16.4% 1+ER = YTM - ER = 20% - 16.4% = 3.6% 1 20,000 40% 13% 40% 13%DP 2006 1

DP { -2,000 DP =0 DP } 2,000-2,000 < DP <0 0 < DP < 2,000 NPVGO 20,000 = 111 = 153,846 13% 20,000_1-0.4 = 11111111 = 153,846 13% - 0.4_0.13 A B 10% 5% Constant Growth Dividend Discount Model 2013 1 ROE A 15% 12% 100 0.5 B 9% 20% 100 0.4 A B ROE

100_1-0.12 kå = 5% + 10%_0.5 = 10% gå = 0.12_0.15 = 1.8% PÅ = 11111114 = 1,073 10% - 1.8% 100_1-0.2 kı = 5% + 10%_0.4 = 9% gı = 0.12_0.09 = 1.8% Pı = 1111112 = 1,111 9% - 1.8% B ROE ROE NPV 3.21 8,560 300,000 10,000 1 2011 1 1 8 160 9,840 160 153,120 160 1,771,200 3.21 = 1111 = 37,500 8,560 300,000 1 = 1112 =8 37,500 300,000_10,000 + 321,000,000 = 11111111111112 = 9,840 300,000 + 37,500 = 10,000-9,840 = 160

160 = 124_8,560 = 171,200 8 = 9,840_160+20 = 1,771,200 AB 2011 1 At=1 2,500 2t=23 25% 4t=4 5% 15% 10% B 3,200 80% 5% b 1.20 2.5% 6.0% 2,500_1.25 _1.05 111111113 2,500 2,500_1.25 2,500_1.25 10%-5% VÅ = 1124 + 111114 + 1111135 + 1111111134 = 61,042 1.15 1.15 1.15 1.15 3,200_0.8_1.05 Vı = 111111111113 = 57,191 2.5% + 6%_1.2-5% = 61,042-57,191 = 3,851 A W U DW DW } 0 UDW = ' D W DW <0 UDW =-' D W

DW 10 50% -15 DW = -15 50% -5 DW =-5 prospect theory loss aversion 5 U DW EDW = -15_0.5 + -5_0.5 = -10 UDW =-' 15_0.5 - '5_0.5 = -3.0545 UDCEQ = -3.0545 -'ƒd C E Q = -3.0545 DCEQ = -9.3300 RP =-10--9.33 = -0.67

free cash flow FCF 25% 2012 1 100 85 50 40 200 165 120 110 130 100 300 250 300 250 500 220 180 24 76 12 64 16 48 FCF { 20 20 < FCF { 40 40 < FCF { 60 60 < FCF { 80 FCF >80 DNWC = 100-50- 85-40 =5 DFA =200-165=35 FCF = 76_1-0.25 +24-5+35+24 =17

2,500 3,400 degree of operational leveragedol 2012 1 DOL { 1.5 1.5 < DOL { 2.5 2.5 < DOL { 3.5 3.5 < DOL { 4.5 DOL > 4.5 2,500_p - v - F =0 F = 2,500_p - v = 3,400_p - v = 3,400_p - v - 2,500_p - v= 900_p - v 3,400_p - v DOL = 11111123 = 3.78 900_p - v

b Å = b Í = bòå b Å = b Í bòí = b Í + b Í - bı;sb; bòå = bòí 13 S + bı 13 B VÒ VÒ bòí bòå q = Rƒ +{ERµ - Rƒ}bÒÍ kò = Rƒ +{ERµ - Rƒ}bÒÍ kòº = Rƒ +{ERµ - Rƒ}bÒÅ q = k kò kòº q = kòº V = 111 EBIT q VÒ = 111 EBIT kòº V = VÒ V VÒ b Å = b Í V Bt bòå = b Í 13 + bı 13 VÒ VÒ bòí = b Í + b Í-bı1-t;sB; bòå = bòí 13 S + bı 13 B VÒ VÒ bòí bòå q = Rƒ +{ERµ - Rƒ}b Í kò = Rƒ +{ERµ - Rƒ}bÒÍ kòº = Rƒ +{ERµ - Rƒ}bÒÅ q = k kò = q + q-k 1-t;sB; kòº = kò 13 S + k 13 B VÒ VÒ kò kòº kòº = q{1-t13} B VÒ kòº = kò 13 S + k 1-t13 B VÒ VÒ kòº V = 111114 EBIT1-t q EBIT1-t EBIT1-t+It VÒ = 111114 VÒ = 11111115 kòº kòº V VÒ = V + Bt VÒ

quick ratioq 1 365 2012 1 120 140 150% 10 60 365 = 123 = 6.0833 = 1123 = 730 60 120 730 = 11112 =10 =73 = 11112 = 150% = 210 140 210-73 = 1111112 = 97.86% 140 1,200 1010 250 10 35% 9% 0 10 9% 6.4177 5.85% 7.4127 2013 1 NPV = 1,200 - {L_1-0.35 + 120_0.35}_7.4127 = 0 L = 184.44

1 510 1 510_100 +40_100_1-0.3 = 53,800 1 55,000 53,800 1 510_100 + 40,000_10% = 55,000 1 55,000 1 510_100+ 40,000_9% = 54,600 1 55,000 54,600 1 550_100 +400-200,000-200,000_10% = 55,000 1,000 2011 1 500 400,000 255,000 145,000 800,000 10% 1,000 295,000 65,000 100 4,000 150 850 620,000 1,000 100 1,000 80,000 720

440,000 295,000 65,000 500 100 1 5 800 5 4,000 800_850 = 680,000 800 80 720 A B B 5% 7% A B 1,350 A NPV 2011 1 A 1,000 150,000 50,000 1,500 B 650 58,500 29,250 900 29,250 dpsº = 11223 =45 650 45_1.05 = 1122323 = 900 k = 10.25% k -5% 45_1.07 = 1122323113 = 1,481.5 10.25% - 7% = 1,481.5-900_650 = 377,975 = 1,350-900_650 = 292,500 = 377,975-292,500 = 85,475

2011 1 delta + - theta gamma + 0 C S K PVK 2012 1 0 + C } maxs-pvk0 +

out of the money at the money 0 C { S-K 0 Cº { Sº Cº } Sº-PVK Cº } 0 1 1

= Dπ + = 1 + 1 = 1 + Dπ + = 1+Dπ + = Dç + A 10,000 6 70% 20% 30% 20% A 14% A 1 10,000 A 2,000 1 10,000

10,000 12,000 18,000 14,400 19,600 16,400 485.4 1,121.5 1,345.8 3,400 3,400 3,600 a b 1.07-0.8 p = 1213123 = 0.675 1.2-0.8 0_0.675 + 400_0.325 P = 1213111123121 = 121.5 1.07 400_0.675 + 3,600_0.325 P = 121311112312111 = 1,345.8 1.07 121.5_0.675 + 1,345.8_0.325 Pº = 12131111231211113 = 485.4 1.07 2,000 10,000 2,000 = 2,000_485.4 = 970,800 121.5-1,345.8 Dπ = 1112213123 = -0.3061 Dç = 1-0.3061 = 0.6939 12,000-8,000 0.6939 2,000 69.39% = _Dç = 20,000,000_69.39% = 13,878,000 = - = 20,000,000-13,878,000 = 6,122,000 Pº = -0.3061Sº + 3,546.4 = 485.4 2,000 2,000 = 2,000_Sº + 2,000_Pº = 2,000_Sº + 2,000_-0.3061Sº + 3,546.4 = 2,000_1-0.3061Sº + 2,000_3,546.4 = 1,387.8_Sº + 7,092,800

2,000 97.08 = _Dç = 20,000,000_69.39% = 13,878,000 = - + = 20,000,000-13,878,000 + 970,800 = 7,092,800 2,000 612.2 2,000 97.08 = 2,000_Sº + 2,000_Pº - 970,800 = 2,000_Sº + 2,000_-0.3061Sº + 3,546.4-970,800 = 2,000_1-0.3061Sº + 2,000_3,546.4-970,800 = 1,387.8_Sº + 6,122,000 1 V 605 28.8% 10% 5% 1 500 605 Vº = 132 = 550 1.1 ln550500 + 0.05 + 0.5_0.288 _1 d = 1321111111111111113 = 0.6485 0.288_'1 d = 0.6485-0.288_'1 = 0.3605

Nd = 0.7417 Nd = 0.6408 500 C = 0.7417_550-0.6408_ 11 = 103.16 500 P = -550 + 103.16 + 11 = 28.78 e 0.05 e 0.05 = 550 + 28.78 = 578.78 100 1 20 17 5 20% 15% 12% 11 2 1 5,000 1 ln1720 + 0.12 + 0.5_0.15 _1 d = 13211111111111111 = -0.2085 0.15_'1 d = -0.2085-0.15_'1 = -0.3585 Nd = 0.4174 Nd = 0.3600 20 C = 0.4174_17-0.3600_ 11 = 0.71 1.5 S' = 17-11 = 15.67 e 0.12 e 0.12 ln15.6720 + 0.12 + 0.5_0.15 _1 d = 1321111111111111113 = -0.7516 0.15_'1 d = -0.7516-0.15_'1 = -0.9016 Nd = 0.2262

Nd = 0.1836 20 C = 0.2262_15.67-0.1836_ 11 = 0.29 e 0.12 5 t=0 30 1 t=1 PV 40 25 60% 40% 10% 1 20 1 t=1 PV 70 35 1 real option t=0 PV 5% 40 30 max30-20 0 V V NPV 25 10 max10-20 0 a b cnpvnpv 40_0.6 + 25_0.4 NPV = -30 + 1223111111 = 0.91 1.1 10_0.6 + 0_0.4 NPV = 1223111112 = 5.45 1.1 1 1 PV 30 = 70-40 20 1 PV 10= 35-25 20 NPV = 0.91 + 5.45 = 6.36

40_0.6 + 25_0.4 = 1223111111 = 30.91 1.1 40_p + 25_1-p 30.91 = 1211111111 = 0.497 1.05 30_0.497 + 10_0.503 = 122311111111 = 18.99 1.05 30-20_0.497 + 0_0.503 NPV Cº = 1223111111111123 = 4.73 1.05 NPV 1 20 NPV = 0.91 + 4.73 = 5.64 DH 3 DH 20% 0 1 2 3-300 120 120 120 = 20% 3 =500 3 =480 = 40% = 10% =5% 1 NPV 2 NPV

120 120 120 NPV = -300 + 11 + 11 + 11 = -47.22 1.2 1.2 1.2 480 S = 11 = 360.63 1.1 ln360.63500 + 0.05 + 0.5_0.4 _3 d = 13211111111111111133 = 0.0913 0.4_'3 d = 0.0913-0.4_'3 = -0.6015 Nd = 0.5364 Nd = 0.2737 500 C = 0.5364_360.63-0.2737_ 1123 = 75.62 NPV = -47.22 + 75.62 = 28.4 e 0.05_3 downside loss upside potential 2013 1

PVX + C = S + P + 100 PV 100 3 1 PV 100 95 90 88 30% real option option to delay timing option 2011 1 5.46 5.92 10.0 12.0 15.23 0 NPV =100-100=0 100-95 1 NPV = 11112 = 3.85 1.3 100-90 2 NPV = 11112 = 5.92 1.3 100-88 3 NPV = 11112 = 5.46 1.3 =5.92-0=5.92

= + (» 3 \ { 3 \ 93 = + (» 3 \ { 3 \ 93

HRHedge Ratio 1 1.2 1 1.2 1 100Qƒ 1,000Qß 1,200HR` `Qß 12N Qß N = HR 14 Qƒ perfect hedge target date = imperfect hedge partial hedge 4 =

< basis risk > rolling hedge forward 6 3 3 3 6 rollover risk 2012 1 A 1 9 A 1 3 9 2012 1 2012 3 2012 6 2012 9 20,000 21,000 18,000 15,000 2012 3 20,100 21,000 2012 6 21,200 18,000 2012 9 17,500 15,000 = 15,000-20,000 = -5,000 3 = 20,100-21,000 = -900 6 = 21,200-18,000 = 3,200

9 = 17,500-15,000 = 2,500 = -5,000 + -900 + 3,200 + 2,500 = -200 1 1 Qß Qß Qß N = HR _ 14 = -1_ 14 = -14 Qƒ Qƒ Qƒ Qß Qß N = HR _ 14 =-1+dˇ _ 14 Qƒ Qƒ 1 1 Fº=Sº1+Rƒˇ

Dƒ 1 Sº F Fº Dƒ = 12 =1+Rƒˇ = 13 S Sº N 1 1 HR =- 14 =-111232 Dƒ 1+Rƒˇ 1 Qß 1 Qß N =- 14 14 =-111232 14 Dƒ Qƒ 1+Rƒˇ Qƒ Sº Qß Vß N =- 13 14 =-14 Fº Qƒ Vƒ d 1 Fº= 11123 Sº_1+Rƒˇ 1+dˇ F 1+Rƒ Fº Dƒ = 12 ={ 1114}ˇ = 13 S 1+d Sº 5 1 Fº - F F fº fº = 123111 =Sº - 123111 Dƒ = 123 =1 1+Rƒˇ 1+Rƒˇ Sº fº fº = Fº - F = Sº1+Rƒˇ - F Dƒ = 123 =1+Rƒˇ Sº 1

A 10% 2001 12001 22002 A 1,000 1,600 700 2002 A 500 2 1 A 10 1 10% 1 8% 7% 1 1% Fº = 1,000_1 + 10% = 1,210 Qß 500 N = HR 14 =-1_ 1122 =-50 Qƒ 10 1 1 2 500 500 1 10 50 2 1,210 2 1 1 Dƒ = 1 + 10% = 1.21 HR = - 14 = - 1424 = -0.8264 Dƒ 1.21

Qß 500 N = HR 14 = -0.8264_ 1122 = -41.3 Qƒ 10 41.3 1 1 1 Dƒ = 1+8% = 1.08 HR = - 14 = - 11 = -0.9259 Dƒ 1.08 Qß 500 N = HR 14 = -0.9259_ 1122 = -46.3 Qƒ 10 41.3 5 46.3 2 1 Dƒ = 1+Rƒ =1 HR =- 14 =- 1 =-1 Dƒ Qß 500 N = HR 14 =-1_ 1122 =-50 Qƒ 10 41.3 50 1 + 10% 1 1 Dƒ = { 1424113}2 = 1.0569 HR = - 14 = - 14241 = -0.9462 1+7% Dƒ 1.0569 Qß 500 N = HR 14 = -0.9462_ 1122 = -47.3 Qƒ 10 1 1+8% 1 1 Dƒ = { 1424123}1 = 1.0693 HR = - 14 = - 14241 = -0.9352 1+1% Dƒ 1.0693 Qß 500 N = HR 14 = -0.9352_ 1122 = -46.8 Qƒ 10 47.3 0.5 46.8 2 1+Rƒ 1 Dƒ = { 142413}0 =1 HR =- 14 =- 1 =-1 1+d Dƒ

Qß 500 N = HR 14 =-1_ 1122 =-50 Qƒ 10 1 Vƒ 1 Fº 1 Qƒ 1 2 Vƒ = 1,000_1.1 _10 = 12,100 500,000 N =-1112 = -41.3 12,100 Vƒ = 1,600_1.08_10 = 17,280 800,000 N =-1112 = -46.3 17,280 Vƒ = 700_10 = 7,000 350,000 N =-1112 = -50 7,000 Vƒ = 1,000_1.11.07 _10 = 10,569 500,000 N =-1112 = -47.3 10,569 Vƒ = 1,600_1.081.01_10 = 17,109 800,000 N =-1112 = -46.8 17,109 Vƒ = 700_10 = 7,000 350,000 N =-1112 = -50 7,000 1 HR r Ó = VarDS + HR_DF r Ó = VarDS + HR VarDF +2HR CovDS DF r Ó HR 0

`r Ó 13423 =2HR VarDF +2CovDS DF =0 HR CovDS DF ríï rí HR =- 1342311123 =- 134 =-14 qíï VarDF r Ï rï r Ó MVP = r Í - q ÍÏ r Í = 1-q ÍÏr Í 1 r Í 100% q ÍÏ% hedge effectiveness % rï IR = {HR_ 14}2= q ÍÏ rí DS = a + bíï` `DF + e CovDSDF bíï = 11111324 HR =-bíï VarDF DS r DS r DF DS CovDS DF HR =- 124 =- 1111124 =- qíï N = HR 13 Qß 12 DF VarDF Qƒ DF

RÏ RÍ RÍ = a + bíï RÏ + e CovRÍRÏ rß bíï = 1111323 = 14q߃ VarRÏ rƒ bíï 1% % DS DF Cov{ 134 133} Sº Fº CovDSDF Fº Fº bíï = 1111211342 = 11111324_ 14 =-HR 14 DF VarDF Sº Sº Var{ 133} Fº Sº HR =-bíï 14 Fº Qß Sº Qß SºQß Vß N = HR 14 =-{bíï 14} 14 =-bíï 114 =-bíï 14 Qƒ Fº Qƒ FºQƒ Vƒ bíï 1 bíï =1

RÍ CovRÍ RÏ Sº Qß bíï = 111114 = 12 q߃ HR =-bíï13 N = HR 13 VarRÏ r RÏ Fº Qƒ RÏ r RÍ N =-bíï Vß 13 Vƒ 1,000 20,000 1 5 400 450 0.9 5% 6% 0.99 1 23,000 rí 400 HR =-13 qíï = - 123_0.9 = -0.8 rï 450 1,000 N = -0.8_ 12311 = -160 5 IR = 0.9 = 81% r Ó = 400 + -0.8 _450 +2_-0.8_400_450_0.9 r Ó = 1-0.9 _400 = 30,400 ró = 'ƒ3ƒ0,400 = 174.36 rß 5% bíï = 13 q߃ = 123_0.99 = 0.825 rƒ 6%

Vß 1,000_20,000 N =-bíï 13 = -0.825_ 12311112 = -143.78 Vƒ 5_23,000 Sº 20,000 HR =-bíï 13 = -0.825_ 13123 = -0.7174 Fº 23,000 1,000 N =-0.7174_ 131233 = -143.48 5 1,000kg 1g 20,000 1 5kg 1 400g500 g 0.9 2 5%g8%g 0.92 1g 23,000 optimal hedge ratio cross hedge

A S N Hº = Aº + Nfº DH DA DF 123 = 123 +N 123 =0 DS DS DS DH DAAº Aº DFFº Fº 123 = 123123_ 13 +N 123123_ 13 =0 DS DSSº Sº DSSº Sº 1 båí_aº + N_ 12_Fº =0 bíï Aº N =-båí_{bíï_ 13} Fº CovRÅRÍ CovRÍRÏ båí = 111311 bíï = 111311 VarRÍ VarRÏ A 20,000 2,000 1.5 B 40,000 1,000 1.2 C 10,000 2,000 0.8 200 KOSPI 200 naive hedge ratio 100% minimum variance hedge ratio

11 KOSPI 200 1 50 2013 1 0.8 0.9 1.0 1.2 1.5 Vß = 20,000_2,000 + 40,000_1,000 + 10,000_2,000 = 10,000 bí = 1.5_0.4 + 1.2_0.4 + 0.8_0.2 = 1.24 10,000 N =- 111122 =-1 200_50 10,000 N = -1.24_ 111122 = -1.24 200_50 K A K A 5.0% 6.5% 3.1% 3.8% K A K 0.2%p

= 6.5% - 5.0% - 3.8% - 3.1% = 0.8%p K -5% +5%-2.7% -3.1%+0.4% = -2.7% A -3.8% -5%+2.7% -5%-1.1% K 5% 2.7% K K -5% +5%-2.8% -3.1%+0.3% = -2.8% A -3.8% -6.2%+3.8% -6.5%+0.3% = -6.2% 1.2% 1%