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What would be the correlation between a perfect market-timing strategy [that it always goes long (short) one unit of the market the day before the market goes up (down)] and the market itself, given the market has a symmetric distribution?

I was thinking 1 but apparently it is incorrect.

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if You can time with perfect foresight your returns are always positive and the market returns can be positive or negative. So if you did a simple correlation of these two vectors then it would be less than one.

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  • $\begingroup$ And if the market returns distribution is symmetric (positive x return has same probability as -x return) then the correlation is going to be zero. $\endgroup$
    – Alex C
    Commented Dec 14, 2019 at 2:16
  • $\begingroup$ Yes. I misread the part about symmetry of the market. Thanks for adding this! $\endgroup$
    – wjamdanf1234
    Commented Dec 14, 2019 at 2:18

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