Step 1: Calculate the common factor variance and covariance.
(sqrt(.2099) is the volatility, 45.8%(volatility of 41.3%)(volatility of 39.2%)Step 2: Calculate the correlation (absolute value of correlation is the distance
measure).
If we have to choose one pair for purposes of trading, based on the distance
measure, our choice would therefore be the pair (A,B).
Step 3: Calculate the cointegration coefficient. A detailed discussion on the
reasoning for the formula is provided in the next chapter.
Step 4: Calculate the residual common factor exposure in the paired port-
folio. This is the exposure that causes mean drift.
λACAC
C
===
cov( )
var( ).
.
.
1787
1539
1 1613
λABAB
B
===
cov( )
var( ).
.
.
1887
171
1 1032
corrACAC
AC
,
cov ,var var.
..
()=.
()
() ()
=
×
=
0 1787
2099 171539
0 9431
corrABAB
AB
,
cov ,var var.
..
()=.
()
() ()
=
×
=
0 1887
2099 171
0 9957
cov( , )..
...
AC=[].
(^11) =
0625 0225
0225 1024
1
75
1787
cov( , )..
..
.
AB=[].
(^11) =
0625 0225
0225 1024
75
1
1887
var( )...
...
C =[].
(^175) =
0625 0225
0225 1024
1
75
1539
var( )...
..
.
B=[].
(^751) =
0625 0225
0225 1024
075
1
171
var( )..
..
A =[].
(^11) =
0625 0225
0225 1024
1
1
2099
100 STATISTICAL ARBITRAGE PAIRS