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nbbo2
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If you use logreturns it becomes simpler:

logreturn on stock A: log(price_At+1/price_At)

logreturn on stock B: log(price_Bt+1/price_Bt)

then

total logreturn on pairs trade: logreturn on stock A + logreturn on stock B =

=log((price_At+1*price_Bt)/(price_At*price_Bt+1))=

=spreadt+1 - spreadt

Now it is all consistent, thanks to the property that $\log(x y)=\log(x)+\log(y)$

(Of course no one stops you from calculating simple returns as well, your program can print both. simplereturn = -1.0 + exp(logreturn) )

(Also, I assumed hedge ratio of 1, like you did)

If you use logreturns it becomes simpler:

logreturn on stock A: log(price_At+1/price_At)

logreturn on stock B: log(price_Bt+1/price_Bt)

then

total logreturn on pairs trade: logreturn on stock A + logreturn on stock B =

=log((price_At+1*price_Bt)/(price_At*price_Bt+1))=

=spreadt+1 - spreadt

Now it is all consistent, thanks to the property that $\log(x y)=\log(x)+\log(y)$

If you use logreturns it becomes simpler:

logreturn on stock A: log(price_At+1/price_At)

logreturn on stock B: log(price_Bt+1/price_Bt)

then

total logreturn on pairs trade: logreturn on stock A + logreturn on stock B =

=log((price_At+1*price_Bt)/(price_At*price_Bt+1))=

=spreadt+1 - spreadt

Now it is all consistent, thanks to the property that $\log(x y)=\log(x)+\log(y)$

(Of course no one stops you from calculating simple returns as well, your program can print both. simplereturn = -1.0 + exp(logreturn) )

(Also, I assumed hedge ratio of 1, like you did)

Source Link
nbbo2
  • 11.8k
  • 3
  • 22
  • 36

If you use logreturns it becomes simpler:

logreturn on stock A: log(price_At+1/price_At)

logreturn on stock B: log(price_Bt+1/price_Bt)

then

total logreturn on pairs trade: logreturn on stock A + logreturn on stock B =

=log((price_At+1*price_Bt)/(price_At*price_Bt+1))=

=spreadt+1 - spreadt

Now it is all consistent, thanks to the property that $\log(x y)=\log(x)+\log(y)$