1. introduction
Connection and data
The quest
Final Comments
Trading Strategies using R
The quest for the holy grail
Eran Raviv
Econometric Institute - Erasmus University,
http://eranraviv.com
April 02, 2012
Eran Raviv Trading Strategies using R April 02, 2012
2. introduction
Connection and data
The quest
Final Comments
Outline for section 1
1 introduction
2 Connection and data
3 The quest
Sign Prediction
Filtering
Time Series Analysis
Pairs Trading
4 Final Comments
Eran Raviv Trading Strategies using R April 02, 2012
3. Cumulative Returns
introduction
Connection and data
The quest
0.2 Final Comments
(very) Limited Success
Decision was
0.15 made to reduce
volume
0.1
cumsum 0.05
0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
-0.05
Eran Raviv Trading Strategies using R April 02, 2012
4. introduction
Connection and data
The quest
Final Comments
Outline for section 2
1 introduction
2 Connection and data
3 The quest
Sign Prediction
Filtering
Time Series Analysis
Pairs Trading
4 Final Comments
Eran Raviv Trading Strategies using R April 02, 2012
5. introduction
Connection and data
The quest
Final Comments
For Inter-day, yahoo is fine
nam = c ( 'AON ' , 'M C' , ' AKS ' , 'BAC ' , . . . ) ; t c k r = s o r t (nam)
M
# Most r e c e n t 252 days :
end<− f o r m a t ( Sys . Date ( ) , ”%Y m −% −%d” ) # yyyy− −ddmm
s t a r t<−f o r m a t ( Sys . Date ( ) − 3 6 5 , ”%Y m−% −%d” )
l = length ( tckr )
dat = a r r a y ( dim = c ( 2 5 2 , 6 , l ) )
for ( i in 1: l ){
dat0 = ( getSymbols ( t c k r [ i ] , s r c=” yahoo ” , from=s t a r t , t o=end ,
auto . a s s i g n = FALSE) ) # C anc e l auto . a s s i g n i f you want t o
manipulate the o b j e c t
dat [ 1 : l e n g t h ( dat0 [ , 2 ] ) , , i ] = dat0 [ , 2 : 6 ]
}
dat = dat [ 1 : l e n g t h ( na . omit ( dat [ , 1 , 1 ] ) ) , , ]
Eran Raviv Trading Strategies using R April 02, 2012
6. introduction
Connection and data
The quest
Final Comments
For Intra-day use IB
IB has extensive API. Connect to their trading
platform (TWS) using Java and C among others.
Eran Raviv Trading Strategies using R April 02, 2012
7. introduction
Connection and data
The quest
Final Comments
For Intra-day use IB
IB has extensive API. Connect to their trading
platform (TWS) using Java and C among others.
Eran Raviv Trading Strategies using R April 02, 2012
8. introduction
Connection and data
The quest
Final Comments
For Intra-day use IB
IB has extensive API. Connect to their trading
platform (TWS) using Java and C among others.
Account is not that easy to set up, many forms to fill
out and hefty sum to transfer, especially if you would
like to day trade.
Eran Raviv Trading Strategies using R April 02, 2012
9. introduction
Connection and data
The quest
Final Comments
For Intra-day use IB
IB has extensive API. Connect to their trading
platform (TWS) using Java and C among others.
Account is not that easy to set up, many forms to fill
out and hefty sum to transfer, especially if you would
like to day trade.
Eran Raviv Trading Strategies using R April 02, 2012
10. introduction
Connection and data
The quest
Final Comments
For Intra-day use IB
IB has extensive API. Connect to their trading
platform (TWS) using Java and C among others.
Account is not that easy to set up, many forms to fill
out and hefty sum to transfer, especially if you would
like to day trade.
Jeffrey A. Ryan did outstanding work, we can now
trade via R.
Eran Raviv Trading Strategies using R April 02, 2012
11. introduction
Connection and data
The quest
Final Comments
For Intra-day use IB
Easy:
l i b r a r y ( IBrokers )
I B r o k e r s v e r s i o n 0 . 9 − 1 : Implementing API V e r s i o n 9 . 6 4
This s o f t w a r e comes with NO WARRANTY. Not i n t e n d e d f o r
p r o d u c t i o n u s e ! See ? I B r o k e r s f o r d e t a i l s }
con = twsConnect ( c l i e n t I d = 1 , h o s t = ' l o c a l h o s t ' , p o r t
= 7 4 9 6 , v e r b o s e = TRUE, t i m e o u t = 5 , f i l e n a m e =
NULL)
Eran Raviv Trading Strategies using R April 02, 2012
12. introduction
Connection and data
The quest
Final Comments
For Intra-day use IB
Easy:
l i b r a r y ( IBrokers )
I B r o k e r s v e r s i o n 0 . 9 − 1 : Implementing API V e r s i o n 9 . 6 4
This s o f t w a r e comes with NO WARRANTY. Not i n t e n d e d f o r
p r o d u c t i o n u s e ! See ? I B r o k e r s f o r d e t a i l s }
con = twsConnect ( c l i e n t I d = 1 , h o s t = ' l o c a l h o s t ' , p o r t
= 7 4 9 6 , v e r b o s e = TRUE, t i m e o u t = 5 , f i l e n a m e =
NULL)
High frequency data if you have the patience to
program it.
Eran Raviv Trading Strategies using R April 02, 2012
13. introduction
Connection and data
The quest
Final Comments
For Intra-day use IB
Easy:
l i b r a r y ( IBrokers )
I B r o k e r s v e r s i o n 0 . 9 − 1 : Implementing API V e r s i o n 9 . 6 4
This s o f t w a r e comes with NO WARRANTY. Not i n t e n d e d f o r
p r o d u c t i o n u s e ! See ? I B r o k e r s f o r d e t a i l s }
con = twsConnect ( c l i e n t I d = 1 , h o s t = ' l o c a l h o s t ' , p o r t
= 7 4 9 6 , v e r b o s e = TRUE, t i m e o u t = 5 , f i l e n a m e =
NULL)
High frequency data if you have the patience to
program it.
Limitation on the number of requests.
Eran Raviv Trading Strategies using R April 02, 2012
14. introduction
Connection and data
The quest
Final Comments
For Intra-day use IB
Easy:
l i b r a r y ( IBrokers )
I B r o k e r s v e r s i o n 0 . 9 − 1 : Implementing API V e r s i o n 9 . 6 4
This s o f t w a r e comes with NO WARRANTY. Not i n t e n d e d f o r
p r o d u c t i o n u s e ! See ? I B r o k e r s f o r d e t a i l s }
con = twsConnect ( c l i e n t I d = 1 , h o s t = ' l o c a l h o s t ' , p o r t
= 7 4 9 6 , v e r b o s e = TRUE, t i m e o u t = 5 , f i l e n a m e =
NULL)
High frequency data if you have the patience to
program it.
Limitation on the number of requests.
In any case not more than one year, but you can store
it.
Eran Raviv Trading Strategies using R April 02, 2012
15. introduction
Connection and data
The quest
Final Comments
For Intra-day use IB
Easy:
l i b r a r y ( IBrokers )
I B r o k e r s v e r s i o n 0 . 9 − 1 : Implementing API V e r s i o n 9 . 6 4
This s o f t w a r e comes with NO WARRANTY. Not i n t e n d e d f o r
p r o d u c t i o n u s e ! See ? I B r o k e r s f o r d e t a i l s }
con = twsConnect ( c l i e n t I d = 1 , h o s t = ' l o c a l h o s t ' , p o r t
= 7 4 9 6 , v e r b o s e = TRUE, t i m e o u t = 5 , f i l e n a m e =
NULL)
High frequency data if you have the patience to
program it.
Limitation on the number of requests.
In any case not more than one year, but you can store
it.
Professional yahoo group at:
http://finance.groups.yahoo.com/group/TWSAPI/
Eran Raviv Trading Strategies using R April 02, 2012
16. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Outline for section 3
1 introduction
2 Connection and data
3 The quest
Sign Prediction
Filtering
Time Series Analysis
Pairs Trading
4 Final Comments
Eran Raviv Trading Strategies using R April 02, 2012
17. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Selected Ideas
Over the years I have backtested many ideas, among others:
Sign Prediction
Eran Raviv Trading Strategies using R April 02, 2012
18. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Selected Ideas
Over the years I have backtested many ideas, among others:
Sign Prediction
Filtering
Eran Raviv Trading Strategies using R April 02, 2012
19. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Selected Ideas
Over the years I have backtested many ideas, among others:
Sign Prediction
Filtering
Multivariate time series modelling
Eran Raviv Trading Strategies using R April 02, 2012
20. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Selected Ideas
Over the years I have backtested many ideas, among others:
Sign Prediction
Filtering
Multivariate time series modelling
Pairs trading
Eran Raviv Trading Strategies using R April 02, 2012
21. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Selected Ideas
Over the years I have backtested many ideas, among others:
Sign Prediction
Filtering
Multivariate time series modelling
Pairs trading
Eran Raviv Trading Strategies using R April 02, 2012
22. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Selected Ideas
Over the years I have backtested many ideas, among others:
Sign Prediction
Filtering
Multivariate time series modelling
Pairs trading
Born to trade, forced to work.
Eran Raviv Trading Strategies using R April 02, 2012
23. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Table of Contents
1 introduction
2 Connection and data
3 The quest
Sign Prediction
Filtering
Time Series Analysis
Pairs Trading
4 Final Comments
Eran Raviv Trading Strategies using R April 02, 2012
24. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Sign Prediction
Sign prediction using:
Logistic Regression (glm)
Support Vector Machine (svm)
♣ library(e1071)
K-Nearest Neighbour (knn)
♣ library(class)
Neural Networks (nnet)
♣ library(nnet)
Eran Raviv Trading Strategies using R April 02, 2012
25. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Sign Prediction - continued
Working with daily returns, so target is to predict
tomorrow’s move. (Avoid overnight)
Explanatory variables considered:
I five lags (one week)
II Spread between the volume and the rolling average of
most recent 5 days.
III Volatility - average of the last five days.
Eran Raviv Trading Strategies using R April 02, 2012
26. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Sign Prediction - continued
Volatility is measured as the average of three different
intra-day volatility measures which are more efficient
(converge faster) than the standard ”sd” estimate:
Parkinson (1980):
1 N hi 2
σ= 4N ln2 i=1 (ln li )
Eran Raviv Trading Strategies using R April 02, 2012
27. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Sign Prediction - continued
Volatility is measured as the average of three different
intra-day volatility measures which are more efficient
(converge faster) than the standard ”sd” estimate:
Parkinson (1980):
1 N hi 2
σ= 4N ln2 i=1 (ln li )
German Klass (1980):
1 N 1 hi 2 1 N ci
σ= N i=1 2 (ln li ) − N i=1 (2ln2 − 1)(ln ci−1 )2
Eran Raviv Trading Strategies using R April 02, 2012
28. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Sign Prediction - continued
Volatility is measured as the average of three different
intra-day volatility measures which are more efficient
(converge faster) than the standard ”sd” estimate:
Parkinson (1980):
1 N hi 2
σ= 4N ln2 i=1 (ln li )
German Klass (1980):
1 N 1 hi 2 1 N ci
σ= N i=1 2 (ln li ) − N i=1 (2ln2 − 1)(ln ci−1 )2
Rogers and satchell (1991):
1 N hi hi l l
σ= N i=1 (ln li )(ln oi ) + (ln cii )(ln oii )
Eran Raviv Trading Strategies using R April 02, 2012
29. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Sign Prediction - continued
dat0 = ( getSymbols ( t c k r [ 1 ] , s r c=” yahoo ” , from=s t a r t , t o=end ,
auto . a s s i g n = FALSE) )
l = l e n g t h ( dat0 [ , 1 ] )
d a t e s 0 = ( i n d e x ( dat0 ) ) # t r i c k t o g e t t r a d i n g d a t e s
t t = NULL # we now p a r s e i t i n t o IB mode
#
for ( i in 1: l ){
tt [ i ] = paste ( substr ( dates0 [ i ] , 1 , 4 ) , substr ( dates0 [ i ] , 6 , 7 ) ,
s u b st r ( dates0 [ i ] , 9 , 1 0 ) , sep = ”” )
t t [ i ] = p a s t e ( t t [ i ] , ” 2 3 : 0 0 : 0 0 GMT” )
}
c o n t=t ws Eq ui ty ( ' p l u g your f a v o u r i t e symbol ' , 'SMART ' , ' NYSE ' )
mat1 = a r r a y ( dim = c ( l , 4 0 0 , 8 ) )#T y p i c a l day s h o u l d have 390
mins
for ( i in 1: l ){
m1 = a s . m a t r i x ( r e q H i s t o r i c a l D a t a ( con , cont , t t [ i ] , b a r S i z e =
” 1 min” ,
d u r a t i o n = ” 1 d” , useRTH = ” 1 ” , whatToShow = ”TRADES” , time .
f o r m a t = ” 1 ” , v e r b o s e = TRUE) )
mat1 [ i , 1 : l e n g t h (m1 [ , 1 ] ) , ] = m1
Sys . s l e e p ( 1 4 ) # IB r e s t r i c t i o n , WAIT.
#
}
Eran Raviv Trading Strategies using R April 02, 2012
30. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Sign Prediction - continued
Sample code:
l o g i t 1 = glm ( y˜ l a g y+v o l a t+volume , data=dat [ 1 : t1 , ] , f a m i l y=
b i n o m i a l ( l i n k = ” l o g i t ” ) , na . a c t i o n=na . p a s s )
summary ( l o g i t 1 ) #t 1 i s end o f t r a i n i n g , TT i s f u l l l e n g t h .
l i b r a r y ( nnet )
nnet1 = nnet ( a s . f a c t o r ( y ) ˜ l a g y+v o l a t+volume , data=dat [ 1 : t1 , ] ,
s i z e =1 , t r a c e=T)
summary ( nnet1 )
library ( class )
knn1 = knn ( dat [ 1 : t1 , ] , dat [ ( t 1 +1) : TT, ] , c l = dat $ y [ 1 : t 1 ] , k=25 ,
prob=F)
sum ( knn1==dat $ y [ ( t 1 +1) ] ) / (TT 1 +1)#H i t r a t i o
−t
l i b r a r y ( e1071 )
svm1 = svm ( dat [ 1 : t1 , 2 : 4 ] , y=dat [ 1 : t1 , 1 ] , t y p e = ”C” )
# I n sample :
sum ( svm1 $ f i t==dat $ y [ ( 1 ) : t 1 ] ) / t 1
# out o f sample :
svmpred=p r e d i c t ( svm1 , newdata = dat [ ( t 1 +1) : TT, 2 : 4 ] )
sum ( svmpred==dat $ y [ ( t 1 +1) :TT ] ) / (TT 1 +1)#H i t r a t i o
−t
Eran Raviv Trading Strategies using R April 02, 2012
31. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Table of Contents
1 introduction
2 Connection and data
3 The quest
Sign Prediction
Filtering
Time Series Analysis
Pairs Trading
4 Final Comments
Eran Raviv Trading Strategies using R April 02, 2012
32. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Deviation from the mean
Motivation =⇒ Disposition effect, the Voodoo of
financial markets.
Standardise the deviation from the (rolling) mean.
Eran Raviv Trading Strategies using R April 02, 2012
34. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Table of Contents
1 introduction
2 Connection and data
3 The quest
Sign Prediction
Filtering
Time Series Analysis
Pairs Trading
4 Final Comments
Eran Raviv Trading Strategies using R April 02, 2012
35. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Motivation
Momentum in Microstructure - Dermot Murphy and
Ramabhadran S. Thirumalai (Job Market Paper -
2011)
Are You Trading Predictably? -Steven L. Heston
,Robert A. Korajczyk ,Ronnie Sadka, Lewis D.
Thorson. (2010)
Eran Raviv Trading Strategies using R April 02, 2012
36. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Motivation
Momentum in Microstructure - Dermot Murphy and
Ramabhadran S. Thirumalai (Job Market Paper -
2011)
Are You Trading Predictably? -Steven L. Heston
,Robert A. Korajczyk ,Ronnie Sadka, Lewis D.
Thorson. (2010)
We find predictable patterns in stock returns. Stocks
whose relative returns are high in a given half-hour
interval today exhibit similar outperformance in the
same half-hour period on subsequent days. The effect
is stronger at the beginning and end of the trading
day. These results suggest...
Eran Raviv Trading Strategies using R April 02, 2012
37. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
VAR models
For each day t = {1, ..., T }, the return of half an hour
k = {1, ..., 13} , and the lag number p = {1, ..., P }:
1
a1,1 a1 1,2 · · · a1
y1,t c1 1,k y1,t−1
y2,t c2 a1 1 1
2,1 a2,2 · · · a2,k y2,t−1
. = . + . . .. . . + ··· +
. . .
. . . .
. . . .
. .
yk,t ck a1 1 1
k,1 ak,2 · · · ak,k yk,t−1
p p p
a1,1 a1,2 · · · a1,k
y1,t−p e1,t
ap p
ap y2,t−p e2,t
2,1 a2,2 · · · 2,k
. . + .
. . ..
.
. .
. . . . .
. . .
p p
ak,1 ak,2 · · · ap
k,k
yk,t−p ek,t
Eran Raviv Trading Strategies using R April 02, 2012
38. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
VAR models
For each day t = {1, ..., T }, the return of half an hour
k = {1, ..., 13} , and the lag number p = {1, ..., P }:
1
a1,1 a1 1,2 · · · a1
y1,t c1 1,k y1,t−1
y2,t c2 a1 1 1
2,1 a2,2 · · · a2,k y2,t−1
. = . + . . .. . . + ··· +
. . .
. . . .
. . . .
. .
yk,t ck a1 1 1
k,1 ak,2 · · · ak,k yk,t−1
p p p
a1,1 a1,2 · · · a1,k
y1,t−p e1,t
ap p
ap y2,t−p e2,t
2,1 a2,2 · · · 2,k
. . + .
. . ..
.
. .
. . . . .
. . .
p p
ak,1 ak,2 · · · ap
k,k
yk,t−p ek,t
Problem: for P = 1, how many parameters?
Eran Raviv Trading Strategies using R April 02, 2012
39. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
VAR models (cont’d)
Possible solution =⇒ Dimension Reduction.
Eran Raviv Trading Strategies using R April 02, 2012
40. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
VAR models (cont’d)
Possible solution =⇒ Dimension Reduction.
Stepwise Regression, Lasso, Variable selection
(according to some Information Criteria), Principal
Component Regression, Ridge Regression, Bayesian
VAR and many more.
Very nice vars package to start you off, though as most
built-ins, not flexible enough. (e.g. rolling windows
and/or shrinking)
Eran Raviv Trading Strategies using R April 02, 2012
41. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Table of Contents
1 introduction
2 Connection and data
3 The quest
Sign Prediction
Filtering
Time Series Analysis
Pairs Trading
4 Final Comments
Eran Raviv Trading Strategies using R April 02, 2012
42. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs Trading
Well known and widely used. (e.g. Statistical Arbitrage
in the U.S. Equities Market, Marco Avellaneda and
Jeong-Hyun Lee (2008))
Eran Raviv Trading Strategies using R April 02, 2012
43. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs Trading
Well known and widely used. (e.g. Statistical Arbitrage
in the U.S. Equities Market, Marco Avellaneda and
Jeong-Hyun Lee (2008))
Suitable for the conservative mind. (we see why in a
minute..)
Eran Raviv Trading Strategies using R April 02, 2012
44. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs Trading
Well known and widely used. (e.g. Statistical Arbitrage
in the U.S. Equities Market, Marco Avellaneda and
Jeong-Hyun Lee (2008))
Suitable for the conservative mind. (we see why in a
minute..)
Eran Raviv Trading Strategies using R April 02, 2012
45. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs Trading (cont’d)
The Idea:
ra = βa rm + ea
rb = βb rm + eb
rab = wa (βa rm + ea ) + wb (βb rm + ea )
= rm (wa βa + wb βb ) + noise
and so with weights wa = − βaβb b and wb = 1 − wa we can
−β
net out the market. (and other factors if you will)
Eran Raviv Trading Strategies using R April 02, 2012
46. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs Trading (cont’d)
Choose symbols with similar properties.
Net out the market and create the spread:
# sp1 = s t o c k p r i c e 1 , g=s i z e o f moving window ,
#
# n = l e n g t h ( sp1 )
#
for ( i in g : n){
b e t 0 [ i ]=lm ( sp1 [ ( i −g+1) : ( i −1) ] ˜ sp2 [ ( i −g+1) : ( i −1) ] ) $ c o e f [ 1 ] #
# n o t e −> i −1
b e t 1 [ i ]=lm ( sp1 [ ( i −g+1) : ( i −1) ] ˜ sp2 [ ( i −g+1) : ( i −1) ] ) $ c o e f [ 2 ]
s p r e a d [ , i ]= sp1 [ ( i −g+1) : i ]− r e p ( b e t 0 [ i ] , g )−b e t 1 [ i ] *
sp2 [ ( i −g+1) : i ]
}
Text book example (actually from: Quantitative
Trading: How to Build Your Own Algorithmic Trading
Business )
Eran Raviv Trading Strategies using R April 02, 2012
47. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs Trading (cont’d)
Choose symbols with similar properties.
Net out the market and create the spread:
# sp1 = s t o c k p r i c e 1 , g=s i z e o f moving window ,
#
# n = l e n g t h ( sp1 )
#
for ( i in g : n){
b e t 0 [ i ]=lm ( sp1 [ ( i −g+1) : ( i −1) ] ˜ sp2 [ ( i −g+1) : ( i −1) ] ) $ c o e f [ 1 ] #
# n o t e −> i −1
b e t 1 [ i ]=lm ( sp1 [ ( i −g+1) : ( i −1) ] ˜ sp2 [ ( i −g+1) : ( i −1) ] ) $ c o e f [ 2 ]
s p r e a d [ , i ]= sp1 [ ( i −g+1) : i ]− r e p ( b e t 0 [ i ] , g )−b e t 1 [ i ] *
sp2 [ ( i −g+1) : i ]
}
Text book example (actually from: Quantitative
Trading: How to Build Your Own Algorithmic Trading
Business )
The GLD and GDX spread
Eran Raviv Trading Strategies using R April 02, 2012
48. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs Trading (cont’d)
The GLD and GDX spread:
Eran Raviv Trading Strategies using R April 02, 2012
49. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs Trading Issues
Estimation of the market neutral portfolio is tricky:
Price levels or price changes?
Eran Raviv Trading Strategies using R April 02, 2012
50. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs Trading Issues
Estimation of the market neutral portfolio is tricky:
Price levels or price changes?
Stability over time
Eran Raviv Trading Strategies using R April 02, 2012
51. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs Trading Issues
Estimation of the market neutral portfolio is tricky:
Price levels or price changes?
Stability over time
Errors on both sides. (both y and x are measured with
errors)
Eran Raviv Trading Strategies using R April 02, 2012
52. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs trading issues
Stability over time:
Eran Raviv Trading Strategies using R April 02, 2012
53. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs trading issues
Errors on both sides:
sta = αstb + ea
stb = βsta + eb
1
α =
β
⇓
Portfolio is different and will depend on which instrument
goes on the LHS and which on the RHS.
Eran Raviv Trading Strategies using R April 02, 2012
54. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs trading - possible solutions
Price levels or price changes?
Eran Raviv Trading Strategies using R April 02, 2012
55. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs trading - possible solutions
Price levels or price changes?
flip a coin (solid option)
average the estimates
Eran Raviv Trading Strategies using R April 02, 2012
56. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs trading - possible solutions
Price levels or price changes?
flip a coin (solid option)
average the estimates
Eran Raviv Trading Strategies using R April 02, 2012
57. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs trading - possible solutions (cont’d)
Stability over time
Eran Raviv Trading Strategies using R April 02, 2012
58. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs trading - possible solutions (cont’d)
Stability over time
Choose window length that fits your style, the shorter
the more you trade.
Recent paper (though in different context) suggests to
average estimates across different windows to partially
hedge out uncertainty. (M. Hashem Pesaran, Andreas Pick.
Journal of Business and Economic Statistics. April 1, 2011)
Kalman filter the coefficients.
Eran Raviv Trading Strategies using R April 02, 2012
59. introduction Sign Prediction
Connection and data Filtering
The quest Time Series Analysis
Final Comments Pairs Trading
Pairs trading - possible solutions (cont’d)
Errors on both sides, two highly correlated possible
solutions:
Demming regression (1943). (Total least squares - just
minimize numerically both sides simultaneously)
Geometric Mean Regression - force coherence through:
sta = αstb + ea
stb = βsta + eb
1
γ = α×
β
Eran Raviv Trading Strategies using R April 02, 2012
60. introduction
Connection and data
The quest
Final Comments
Outline for section 4
1 introduction
2 Connection and data
3 The quest
Sign Prediction
Filtering
Time Series Analysis
Pairs Trading
4 Final Comments
Eran Raviv Trading Strategies using R April 02, 2012
61. introduction
Connection and data
The quest
Final Comments
Miscellaneous remarks
Trading costs!, consider it when backtesting.
Eran Raviv Trading Strategies using R April 02, 2012
62. introduction
Connection and data
The quest
Final Comments
Miscellaneous remarks
Trading costs!, consider it when backtesting.
You cannot be too careful, stay pessimistic.
Eran Raviv Trading Strategies using R April 02, 2012
63. introduction
Connection and data
The quest
Final Comments
Miscellaneous remarks
Trading costs!, consider it when backtesting.
You cannot be too careful, stay pessimistic.
Adopt rigorous robustness checks, different
instruments, different time frames and even different
markets.
Eran Raviv Trading Strategies using R April 02, 2012
64. introduction
Connection and data
The quest
Final Comments
Miscellaneous remarks
Trading costs!, consider it when backtesting.
You cannot be too careful, stay pessimistic.
Adopt rigorous robustness checks, different
instruments, different time frames and even different
markets.
Use paper money for at least a full quarter, it will help
you handle operational problems. (e.g. outages and
time zones issues)
Eran Raviv Trading Strategies using R April 02, 2012
65. introduction
Connection and data
The quest
Final Comments
Miscellaneous remarks
Trading costs!, consider it when backtesting.
You cannot be too careful, stay pessimistic.
Adopt rigorous robustness checks, different
instruments, different time frames and even different
markets.
Use paper money for at least a full quarter, it will help
you handle operational problems. (e.g. outages and
time zones issues)
It is (very) stressing work, know it before you start.
Eran Raviv Trading Strategies using R April 02, 2012
66. introduction
Connection and data
The quest
Final Comments
Miscellaneous remarks
Trading costs!, consider it when backtesting.
You cannot be too careful, stay pessimistic.
Adopt rigorous robustness checks, different
instruments, different time frames and even different
markets.
Use paper money for at least a full quarter, it will help
you handle operational problems. (e.g. outages and
time zones issues)
It is (very) stressing work, know it before you start.
Know what you are doing, what is your edge? why it is
(not) there?
Eran Raviv Trading Strategies using R April 02, 2012
67. introduction
Connection and data
The quest
Final Comments
THANKS
and good luck at the tables..
Eran Raviv Trading Strategies using R April 02, 2012
