Introduction to pair trading -Based on cointegration- Shinichi Takayanagi Kohta Ishikawa

Transcription

1 Inroducion o pair rading -Based on coinegraion- Shinichi Takayanagi Koha Ishikawa 1

2 Topics 1. Wha is pair rading? 2. Wha is coinegraion? 3. Idea of pair rading based on coinegraion 4. Simulaion by R language 5. Summary & concluding remarks 2

3 1. Wha is pair rading? 3

4 Pair rading was pioneered by Gerry Bamberger and Nunzio Taraglia Quaniaive group a Morgan Sanley Around 1980s D.E. Shaw & Co. is famous for his sraegy 4

5 Pair rading is Marke neural rading sraegy 5

6 Pair rading belongs o Saisical Arbirage 6

7 Basic idea of pair rading Selec wo socks which move similarly 7

8 Basic idea of pair rading Sell high priced sock Buy low priced sock 8

9 Basic idea of pair rading Sock A : Sock B : Sell Sock A Sell Sock B Buy Sock B Buy Sock A 9

10 Basic idea of pair rading Usually, monior he difference beween wo sock prices 10

11 Basic idea of pair rading he difference beween wo sock prices Sell Sock A Sell Sock B Buy Sock B Buy Sock A 11

12 2. Wha is coinegraion? 12

13 Coinegraion is Pioneered by Engle and Granger Saisical propery of ime series Around 1990s 13

14 Coinegraion is No correlaion 14

15 Coinegraion and correlaion Correlaion Specify co-movemen of reurn Shor erm relaionship Coinegraion Specify co-movemen of price Long erm relaionship 15

16 (weak) Saionary ime series No depend on ime E X var X 2 cov X, X s s 16

17 Example of saionary ime series Whie noise E 0 var 2 cov, 0, s s 17

18 Non saionary ime series Depend on ime E X var X 2 cov X, X, s s 18

19 Example of non saionary ime series Brownian moion E W 0 var W cov W, W s s 19

20 Lag operaor L LX X 1 1 L X X X 1 X 20

21 Inegraed of order P X : non saionary 1 Lp X : saionary X ~I p 21

22 Example of inegrae Z Z 1 : Random walk : Whie noise Calculae difference Z Z Z Z ~I 1 1 :Saionary 22

23 X and Y are coinegraed if u Y X u : ~I 0, saionary process X, Y : ~I 1 *This is a special version of general coinegraion for I(1) 23

24 Example of coinegraed ime series X : Y : Y X u X u :100 2 Normal brownian moion :3Gaussian noise 24

25 Example of coinegraed ime series Plo : u = Y 0.5 X 25

26 u seems o be Saionary & Mean reversion 26

27 Quesion Can we apply his idea o rading sraegy? 27

28 3. Idea of pair rading based on coinegraion 28

29 Geomeric brownian moion The mos widely used model of sock price ds S d dw S : Sock price : Average reurn : Volailiy W : Brownian moion 29

30 From Io s lemma d log S d dw 2 2 Log price follow Brownian moion 30

31 Brownian moion(log price) is I(1) * Random walk can be considered as discreizaion of Brownian moion 31

32 Then, we can apply Coinegraion idea o log sock price 32

33 Log price spread(*) is Saionary & Mean reversion Spread Y logx, X, Y :sock price : log 33

34 Simple rading idea if Spread very hish : Buy X, Sell Y if Spread very low : Buy Y, Sell X Spread log Y logx X, Y :sock price 34

35 4. Simulaion by R language 35

36 Process 1. Find wo likely coinegraed socks 2. Esimae spreads 3. Check saionariy 4. Creae rading signal 5. Run back-es 36

37 1.Find wo likely coinegraed socks > library(pairtrading) > #load sample sock price daa > daa(sock.price) > #selec 2 socks > price.pair <- sock.price[,1:2][" ::"] > head(price.pair) * Jus load sample daa in his case. 37

38 2. Esimae spreads > reg <- EsimaeParameers(price.pair, mehod = lm) > sr(reg) Lis of 3 $ spread :An xs objec from o conaining: Daa: num [1:635, 1] ar(*, "dimnames")=lis of 2..$ : NULL..$ : chr "B" Indexed by objecs of class: [Dae] TZ: xs Aribues: NULL $ hedge.raio: num $ premium : num

39 2. Esimae spreads > plo(reg$spread, main = "Spread ) Spread log Y logx, X, Y :sock price 39

40 3. Check saionariy > PP.es(as.numeric(reg$spread)) Phillips-Perron Uni Roo Tes daa: as.numeric(reg$spread) Dickey-Fuller = , Truncaion lag parameer = 6, p-value = > adf.es(as.numeric(reg$spread)) Augmened Dickey-Fuller Tes daa: as.numeric(reg$spread) Dickey-Fuller = , Lag order = 8, p-value = alernaive hypohesis: saionary 40

41 4. Creae rading signal > params <- EsimaeParameersHisorically(price.pair, period = 180) > signal <- Simple(params$spread, 0.05) > barplo(signal,col="blue",space = 0, border = "blue",xax="n",yax="n",xlab="",ylab="") > par(new=true) > plo(params$spread, ype="l", col = "red", lwd = 3, main = "Spread & Signal") 41

42 4. Creae rading signal 42

43 5. Run back-es > reurn.pairrading <- Reurn(price.pair, lag(signal), lag(params$hedge.raio)) > plo(100 * cumprod(1 + reurn.pairrading), main = "Performance of pair rading") 43

44 5. Run back-es 44

45 5. Summary & concluding remarks 45

46 Summary & concluding remarks Pair rading is simple quaniaive rading sraegy Coinegraion is long erm relaion ship of ime series Idea of coinegraion may give a chance o make a profi from financial marke by pair rading Nex sep. Sophisicae parameer esimaion & rading rule Make a simulaion close o real 46

47 Reference Pairs rade(hp://en.wikipedia.org/wiki/pairs_rade) Coinegraion(hp://en.wikipedia.org/wiki/Coinegraion) Andrew Neil Burgess, A Compuaional Mehodology for Modeling he Dynamics of Saisical Arbirage Russell Wojcik, Pairs Trading: A Professional Approach Daniel Herlemon, Pairs rading, convergence rading, coinegraion Paul Teeor, Using R o Tes Pairs of Securiies for Coinegraion (hp://quanrader.info/public/esforcoin.hml) Ganapahy Vidyamurhy, Pairs Trading: Quaniaive Mehods and Analysis 47