VaR 3.1 VaR 3.2 VaR

D 1

1. 2 2.1 2.2 2.3 2.4 2.5 3. VaR 3.1 VaR 3.2 VaR 3.3 4. 2

VaR VaR a-garch VaR Black-Scholes 1., 1998 VaR VaR-covered porfolio insurance 3

Upside Capure 2 Perold and Sharpe 1988 Rubinsein 1985 Black and Scholes 1973 opion-based porfolio insurance OBPI proecive pu synheic pu buy-and-hold consan proporion porfolio insurance CPPI ime-invarian porfolio proecion TIPP sop-loss sraegy consan mix, 4

2.1 Bird Demnis & Tippe 1988 5

2.2 Black & Scholes1973 rt qt P = Ke N d Se 2 N d1 1 2 ln S / K + r q + σ / 2 T d 1 = σ T d 2 = 2 ln S / K + rq σ / 2 T = d1 σ T σ T S K r σ N d 1 = T = q = = e q T [ N d1 1] 2 Dela 1 6

7 2.3 Rubinsein & Leland 1981 Black & Scholes 1 2 1 2 1 2 1 2 1 ] [1 ] [1 ] [ T r T q T r T q T r T q T r T q Ke d N Se d N Ke d N Se d N Ke d N Se d N Ke d N Se d N S P S + = + = + = + + = + = 3 3 Nd 1 Se -q 1-Nd 2 Ke -r S

T K Nd 1 1- Nd 1 S Nd 1 d 1 Nd 1 Self-financing 2.4 8

Black, Jones & Perold1986 M : E = M * A-F E M A F M=1 M>1 1/M 9

Andre F. Perold & William F. Sharpe1988 0 0 1 Esep & Krizman1988 TIPP CPPI TIPP : F ' = MaxA*f F f 90% F TIPP CPPI 2.5 10

1973 Black Scholes 1981 Rubinsein Leland 11

CPPI TIPP CPPI TIPP 3. VaR 3.1 VaR VaR VaR W 0 EW * * W δ R δ µ VaR=EW-W * =W 0 1+µ-W 0 1+R * =W 0 µ-r * =-W 0 R * -µ 4 R f R * δ R * < = P R R f R dr = δ R 2 N µ, σ R * = µ + sσ s δ VaR 12

VaR= W sσ 5 0 Gauss-VaR VaR * R R VaR J.P.Morgan RiskMerics, GARCH Hisorical Simulaion, Mone Carlo Simulaion Tail index VaR, VaR Pownall R.A. Koedijk,K.G. 1999 α α Huisman e al. 1998 α θ = s / α 2 s α Gauss-VaR s θ Garch 1 1 σ VaR = W θσ 6 0 α σ Garch a-garch VaR VaR 13

a-garch VaR 3.2 VaR VaR VaR VaR A r w V VaR A w[ e r T w = [ e 1] = A1 w V r T VT + V T 1] T 7 w A1-w V VaR ' V = Max{0,[ V Max0, AR ]} AR T- T T T VaR T 14

T- AR VaR VaR T VaR VaR VaR VaR 10 VaR 3.3 VaR CPPI A 1 90% 90% 10% 2 3 VaR 95% 10 VaR 10 VaR 10 4 CPPI M=1 15

5 90 6 7 B 2000 5 10 2001 5 10 2001 5 10 2002 5 10 2002 5 10 2002 12 10 1 16

1 CPPI VaR 0.000239 0.000111 0.000291 0.000269 0.000481 0.001302 0.001632 0.008578 0.002935 0.009045 0.057273 0.026700 0.069833 0.064580 0.115408 D 0.625000 0.604167 0.595833 0.700000 0.591667 0.000154 0.000050-0.000559 0.000247-0.001212 0.001821 0.000444 0.006519 0.004063 0.017065 0.036646 0.011902-0.132925 0.058782-0.288456 17

D 0.537815 0.869748 0.491597 0.621849 0.470588-0.000123 0.000031-0.000751 0.000501-0.001195 0.001512 0.000946 0.012031 0.007798 0.013450-0.017989 0.004548-0.109714 0.073170-0.174483 D 0.479452 0.554795 0.452055 0.561644 0.445205 D VaR 12 6 2000-5-10 2001-5-10 VaR 2001-5-10 2002-5-10 VaR 2002-5-10 2002-12-10 VaR D CPPI VaR 18

VaR VaR VaR 4. VaR VaR VaR VaR VaR a-garch VaR Black-Scholes 19

VaR VaR VaR 1. [M] 1998 6. 2. Black, Fischer and Rober Jones, 1987, Simplifying Porfolio Insurance [J]. Journal of Porfolio Managemen, 48-51. 3. Black, Fisher and Myron Scholes, 1973, The Pricing of Opions and 20

Corporae Liabiliies [J]. Journal of Poliical Economy, 637-659. 4. Bird Demnis & Tippe 1988 A Sop Loss Approach o Porfolio Insurance [J]. Journal of Porfolio Managemen, Fall, 35-40. 5. Bollerslev, T. Generalized Auoregressive Condiional Heeroskedasiciy [J]. Journal of Economerics 1986 31: 307 327. 6. Brennan, J. Michael and Eduardo S. Schwarz, 1988, Time-Invarian Porfolio Insurance Sraegies [J]. Journal of Finance, 283-299. 7. Choie, Kenneh S. and Eric J. Seff, 1989, TIPP: Insurance wihou complexiy: Commen [J]. Journal of Porfolio Managemen, 107-108. 8. Campbell,R., Huisman,R., Koedijk,K. Opimal porfolio selecion in a Value a Risk framework [J]. Journal of banking & Finance, 2001,25,1789-1804. 9. Esep,Tony and Mark Krizman,1986,TIPP:Insurance wihou Complexiy [J]. Journal of Porfolio Managemen,Fall,59-62. 10. Huisman, R.Koedijk, K.G., Pownall, R.A.. VaR-x: fa ails in financial risk managemen [J]. Journal of Risk, fall, 1998. 11. Jansen,D.W.K,Koedijk,K.G.,de Vries,C.G. Porfolio selecion wih limied downside risk[j]. Journal of Empirical Finance, 2000,7,247-269. 12. JP Morgan. RiskMerics echnology documen [M].4 h ediion, RiskMerics Group,New York,1996. 13. Perold, Andre F. and William F. Sharpe, 1988, Dynamic Sraegies 21

for Asse Allocaion [J]. Financial Analyss Journal, 16-28. 14. Pownall,R.A.,Koedijk,K.G. Capuring downside risk in financial markes: he case of he Asian Crisis [J]. Journal of Inernaional Money and Finance 1999,18,853-870. 15. Rubinsein, Mark, 1985, Alernaive Pahs o Porfolio Insurance[J]. Financial Analyss Journal, 42-52. 16. Rubinsein,Mark,and Hayne E.Leland,1981,Replicaing Opions wih Posiion in Sock and Cash[J]. Financial Analyss Journal, July-Aug,63-72. 22