expAB= [1 1] – 1.1032 ×[0.75 1] = [.1726 –.1032]
expAC= [1 1] – 1.1613 ×[1 .75] = [–.1613 .129]
Step 5. Calculate the common factor portfolio variance/variance of residual
exposure.
Step 6. Calculate the specific variance of the portfolio.
To simplify our illustration, let us assume the specific variance for all of the
stocks to be 0.0016.
= .0016 + 1.1032^2 ×.0016 = .0035
= .0016 + 1.1613^2 ×.0016 = .0037
Step 7. Calculate the SNR ratio with white noise assumptions for residual
stock return.
SNRAC AC
AC
===cf
σ
σ
spec.
.
.
061
049
1 245
SNRAB AB
AB
===cf
σ
σ
spec.
.
.
059
046
1 282
σABspec==..0037 061
var()rrACspec =var()Aspec +γAC^2 var()rCspec
σABspec==..00035 059
var()rrABspec =var()Aspec +γAB^2 var()rBspec
σACcf ==..0024 049
var..
..
..
.
.
()rACcf =−[].
−
(^1613129) =
0625 0225
0225 1024
1613
129
0024
σABcf ==..0021 046
var..
..
..
.
.
()rABcf =−[].
−
(^17261032) =
0625 0225
0225 1024
1726
1032
0221
Pairs Selection in Equity Markets 101