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比不依尔根觉罗
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1 利率期货在金融风险管理中的运用 aronge.net CFA-Eurex

2 % 2

3 Section 1 3

4 5%6% or or 3 or 30 or 4

5 P c1 c2 c3 c4 = ( 1+ r ) ( 1+ r ) ( 1+ r ) ( 1+ r ) t t t t

6 P P c1 c2 c3 c4 = ( 1+ r ) ( 1+ r ) ( 1+ r ) ( 1+ r ) t t t t c1 c2 c3 c4 = ( 1+ y) ( 1+ y) ( 1+ y) ( 1+ y) t t t t Yield to Maturity YTM P PYTM YTMYTM 6

7 // = 7

8 YTM or P %4% 5% 2.5%8% P P = + +» 96 YTM» 3.89% ( 1+ 3% ) ( 1+ 4% ) ( % ) = + +» 111 YTM» 3.89% ( 1+ 3% ) ( 1+ 4% ) ( % )

9 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 t 9

10 2 n dpt 1 d Pt 2 1 d Pt n dpt = ( dy) + 2 ( dy) ( dy) +... n dy 2! dy n! dy YTM 10

11 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

12 1 1 = = + n i t i i t c P y m ( ) = + = = + 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

13 1 13

14 14

15 A 100 6% 5 1 B 100 9% 5 1 C 100 6% 6 1 YTM5.83% YTM=6.85% YTM=4.83% A % % B % % C % % 15

16 $ D = P $ D D P j V = j D V j P j j 16

17 17

18 (BPV) (BPV) (BPV) Note 1 Note 2 Note 3 18

19 (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

20 Section 2 20

21 1 BPVCTDBPVCF 2 CTD QBPV 21

22 1 1A CF BPV A CTD = = = HR HR = = 份 = = 份

23 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

24 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

25 HR CTD 20-25bp 25

26 3RP Repo Repo Δ RP= Δ YTM+ε, R 2 = ( ) ( ) 26

27 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

28 YTMRP YTM RP RP RPRP 28

29 4 beta 29

30 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

31 betahr HR β 原投资组合的 BPV = 每份国债期货的 BPV β beta Beta CTDYTM 31

32 5CTD 32

33 33

34 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

35 Section 3 35

36 BPVBPV HR CTD beta RP 36

37 511 4% % CTD63.8%

38 CTD 4.47BPV CTD5.30 BPV YTM RP 份 38

39 % %

40 % 6CTD6 3.8%

41 % 10 ( % ) i= i = 元份 41

43 BPV = 亿元 = 亿元 BPV 8 ( ) » 7559份 43

44 100 58% 5 7.5%

45 1,024, % % % % % %

46 6.510% % % % % %

47 47

48 HR 48

49 The End.