利率期货在 金融风险管理中的运用 http:// aronge.net aronge@xmu.edu.cn CFA-Eurex
1...40 50 1005 4% 2
Section 1 3
5%6% or or 3 or 30 or 4
P c1 c2 c3 c4 = + + + + ( 1+ r ) ( 1+ r ) ( 1+ r ) ( 1+ r ) t t t t 1 2 3 4 1 2 3 4... 1 2 5
P P c1 c2 c3 c4 = + + + +... ( 1+ r ) ( 1+ r ) ( 1+ r ) ( 1+ r ) t t t t 1 2 3 4 1 2 3 4 c1 c2 c3 c4 = + + + +... ( 1+ y) ( 1+ y) ( 1+ y) ( 1+ y) t t t t 1 2 3 4 Yield to Maturity YTM P PYTM YTMYTM 6
// = 7
YTM or P 96111 1233%4% 5% 2.5%8% P P 2.5 2.5 102.5 = + +» 96 YTM» 3.89% ( 1+ 3% ) ( 1+ 4% ) ( 1+ 3.9% ) 1 2 3 8 8 108 = + +» 111 YTM» 3.89% ( 1+ 3% ) ( 1+ 4% ) ( 1 + 3.9% ) 1 2 3 8
D YTM dpt 1 ΔPt D = D Δy dy P P t t t t t t $DYTM dpt $ D = D P = ΔP $ D Δy dy t t t t t t t BPV DV01 1 BPV t = $ D 0.0001 t 9
2 n dpt 1 d Pt 2 1 d Pt n dpt = ( dy) + 2 ( dy) +... + ( dy) +... n dy 2! dy n! dy YTM 10
effective duration D t 1P t P P+ Pt 1 P P+ + = 2 Δy Δ y P 2 P Δy t t t t t 11
1 1 = = + n i t i i t c P y m ( ) 1 1 1 1 1 1 = + = = + n i i i i t t t t t t t c t t P y dp D dy P m y m 12
1 13
14
A 100 6% 5 1 B 100 9% 5 1 C 100 6% 6 1 YTM5.83% YTM=6.85% YTM=4.83% A 100.00 95.63-4.37% 104.56 +4.56% B 112.62 107.9-4.19% 117.57 +4.4% C 99.98 94.92-5.06% 105.36 +5.38% 15
$ D = P $ D D P j V = j D V j P j j 16
17
(BPV) (BPV) (BPV) Note 1 Note 2 Note 3 18
(HR) dv = dv + HR dv HR t 1t t 2t t dv1 t dy $ D D V = = = dv $ D D V dy t 1t 1t 1t 2t 2t 2t 2t D 1 D 1 * t HR t D D V = D V * 1t 1t 1t 2t 2t 19
Section 2 20
1 BPVCTDBPVCF 2 CTD QBPV 21
1 1A CF BPV A 100.5313 101.2220 1.1013 4.67 CTD 103.4238 104.1830 0.9734 5.65 106.2500 5.65 4.67 101.222 1 000 000 = 47270.67 10 000 5.65 104.1830 = 0.05886 10 000 0.05886 10000 = 604.7195 0.9734 HR HR 1 2 47270.67 = = 78.2 78份 604.7195 101 222 000 4.67 = = 78.7 79份 1062500 5.65 22
2 F=SFCTD 1 F AI Q = = CF 1 S 1 $D Q = = $D y y CF y CF 2 D Q F AI Q 1 = = CF 1 S 1 S 1 = DS = yq y F AI ys AI ys CF S 23
2 F S 1BPVCTDBPV CF F AI Q = = CF 1 F 1 $D Q = = $D y y CF y CF rt ( t) (( S I) e ) ( S I) rt ( t) S rt ( t) rt ( t) F $D F = = =- e = e = $DSe y y y y 2CTD $D Q $DF CF F D = = = D D Q CF F AI F AI rt ( t) rt ( t) $D F $DSe DS S e DF = = = DS F F F Q F F ( ) F= S I e F ( ) rt t 24
HR CTD 20-25bp 25
3RP Repo Repo Δ RP=0.000314+0.094878 Δ YTM+ε, R 2 = 0.000431 ( 0.147966) ( 0.79935) 26
RPYTM 1 $D $D Q F æf - AIö ç ç Q CF çè ø 1 F 1 =- =- =- = y y CF y CF $D rt ( -t) (( S I) e ) ( S I) ( ) F - - rt-t rt-t =- =- =- e -( S -I) e T -t y y y ( S -I) 1 rt ( -t) =- ( S -I) e -F( T -t) y S -I» F D -F S ( T - t) = F éd - S ( T -t) ù êë ûú F ( ) ( ) 2 D Q ( ) F éd - T -t ù = = = ë û Q CF Q CF $D Q $DF 1 ê S ú 1 F = éd - -» S F - AI ëê ûú ( T t) ù D - ( T - t) S F - AI CF 27
YTMRP YTM RP RP RPRP 28
4 beta 29
beta betactdytm1 YTM y = a+ β y + ε ( CTD) ( ) Δ y = a+ β Δ y + ε Δ y = a+ β Δ y + ε ( D ) Δ y = a+ β Δ y + ε σ S y S D S CTD 7 5 = a+ b D+ ε CTD 30
betahr HR β 原投资组合的 BPV = 每份国债期货的 BPV β beta Beta CTDYTM 31
5CTD 32
33
CTD CTDBPV YTM BPVYTM BPV D t 1P t P P+ Pt 1 P P+ + = 2 Δy Δ y P 2 P Δy t t t t t 34
Section 3 35
BPVBPV HR CTD beta RP 36
511 4% 5 1 3.5% CTD63.8% 1.2203 37
CTD 4.47BPV 45789.88CTD5.30 BPV0.05381YTM RP 1 45789.88 0.05381 10000 1.2203 104 份 38
102.2575 83.4999 1 3.45% 102.4868 83.7214-229273.00 226729.10-2543.88 2 3.52% 102.1660 83.4129 91528.06-90485.80 1042.26 39
1 5161 15 3.5% 6CTD6 3.8%1.2203 40
611 5 0.01% 10 ( 1 3.51% ) i= 1 + 8 i = 45137.74元 45137.74 0.05381 10000 1.2203 102 份 41
4050 25 8.254 6.825 683362.1468 42
BPV 40 8.254 0.0001 = 0.033016亿元 50 6.825 0.0001 = 0.034125亿元 BPV 8 ( 0.034125-0.033016) 10 68366 2.1467 0.0001» 7559份 43
100 58% 5 7.5% 4.81 1 024 359.36 44
1,024,359.368% 5 1 9.5% 930664.35 944907.92-93695.01-79451.44 14243.58 2 8.5% 976276.32 983648.06-48083.04-40711.30 7371.74 3 7.5% 1024359.36 1024359.36 0.00 0.00 0.00 4 6.5% 1075060.21 1067155.25 50700.86 42795.90-7904.96 5 5.5% 1128535.14 1112156.38 104175.78 87797.03-16378.76 45
6.510% 4.85 1 9.5% 930664.35 930778.02-93695.01-93581.33 113.67 2 8.5% 976276.32 976144.50-48083.04-48214.86-131.82 3 7.5% 1024359.36 1024359.36 0.00 0.00 0.00 4 6.5% 1075060.21 1075624.93 50700.86 51265.58 564.72 5 5.5% 1128535.14 1130159.30 104175.78 105799.94 1624.16 46
47
HR 48
The End.