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Hi guys Could you help me here?

I would like to calculate the return of a Pairs Trading strategy. For example:

18/11 - Open the Trade: I will go long on A and Short on B:

Stock A : $ 32.24 Stock B : $ 29.82

Ratio: $\frac{(Price of StockA)}{(Price of StockB)} = 1,0812$

I will buy: $\frac{($30.000)}{32.24} = 900$ (approximately)) units of Stock A. The cost is: $900*32.24 = \$29,016.00$

And Sell: $\frac{($30.000)}{29.82} = 1000$ (approximately)) units of Stock B : $ = 1000*29.82 = \$29,820.00$

The Cost of Open the Trade:$ \$29,820.00 - \$29,016.00 = \$804 $


At 20/11 I will Close the Trade:

Price of Stock A At 20/11: $ \$32.63$ Price of Stock B At 20/11: $ \$30.08$

Ratio: $\frac{(Price of StockA)}{Price of StockB} = 1,0848$

I will sell $900$ units of Stocks A: $900*32.63 = \$29,367$ and I will buy $1000$ units of Stock B: $1000*30.08 = \$30,080$

The cost of Close the Trade: $ \$29,367 - \$30,080 = -\$713$


To calculate Profit/Loss of this strategy I just sum the The cost of Open the Trade and The cost of Close the Trade which is $\$91$ on this case.

My question is: How can I calculate the $\%$ return of this strategy?

But I've been reading and it got a little confusing for me.

Many thanks!

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    $\begingroup$ Short answer is that the return equals P&L divided by your equity. Long answer = longwinded proof of concept gladly given, if required :-) Had you doubled the size of your pairs trade, would that change the % return? Done millions rather than thousands? If not, you’re getting into concepts of return that have no intuitive meaning to mainstream investors. Happy to explain, if useful. $\endgroup$ – demully Nov 19 '19 at 21:31
  • $\begingroup$ @demully you mean by shor answer this: $ \frac{(\$91)}{\$29,016.00}$ ? I didnt understand the long answer part. $\endgroup$ – Laura Nov 19 '19 at 21:33
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    $\begingroup$ The problem you face is that the long and the short are self-financing. You borrow X to sell X worth of the short to give you X cash to finance X's worth of your long. Which gives you a profit or loss of Y. This is only meaningful in % terms compared to the Z capital you have to risk this P&L. The same Y P&L for investors with more or less Z to support this position leads to different "% returns". $\endgroup$ – demully Nov 19 '19 at 22:43
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    $\begingroup$ Ah OK... his "returns" are expressed in unit terms, not % terms ;-) His nice chart is just my Y, ie P&L, given his position sizing. The % return you seek is a function of this AND how much capital you have to bear said risk. That is the ungiven, for all of us. $\endgroup$ – demully Nov 19 '19 at 23:29
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    $\begingroup$ Now that's the basis for a question in it's own right, to which I promise I will attempt a proper answer, beyond comments to clarify comments :-) $\endgroup$ – demully Nov 20 '19 at 1:21

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