Final_1.pdf

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