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When arbitraging ETF holdings against the ETF, how does one manage the portfolio over time? Assume the strategy creates a long signal in pair A (stock X/ ETF) and a short signal in pair B ( stock Y / ETF). The hedge ratios are 0.5 for pair A and 2 for pair B so the following trades would get executed:

(+) 5 Shares Stock X (-) 10 Shares ETF

(-) 10 Shares Stock Y (+) 5 Shares ETF

The overall position would be + 5X, -5ETF, -10Y

Does that make sense so far?

Now lets assume the long signal for pair A weakens and the position is closed. In this case the 5 shares X would be sold and 10 shares ETF would be bought so that the new position now equals pair B.

I guess my question is : Is my train of thought right in that one can simply add these ETF positions or is there something I am overlooking ?

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  • $\begingroup$ Yes, what you say seems right. $\endgroup$ – noob2 Sep 8 '20 at 5:59
  • $\begingroup$ It's Johansen eigen-decomposition: ETF in the first column, components in the others. Cross-validate the whole machinery with 1 lag. As soon as eigenvectors change, rebalance the number of units of each asset on which you're long/short. $\endgroup$ – Lisa Ann Sep 8 '20 at 6:06

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