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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.

  • Why is the answer of +1 apparently incorrect? Is this an exam question? – Bob Baerker Dec 7 '19 at 1:28
  • @BobBaerker It is from a quiz. I tried reading up on this and 1 seemed the most logical answer. – newguywantingtoimprove Dec 7 '19 at 3:01
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It depends. If the market return were always positive, the correlation would be 1. If it were symmetrically distributed around 0, the correlation would be 0. If market return were always negative, the correlation would be -1.

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  • If the timing selection is in agreement with the market's direction and is always correct, why wouldn't the correlation be +1 regardless of whether going long or short? Or is the measure of correlation based on something else? – Bob Baerker Dec 7 '19 at 1:27
  • If the market is always down, you would always be short. If you are always short, your return is (roughly) the opposite of the market. – Charles Fox Dec 7 '19 at 1:29
  • In the symmetric at 0 case, if you plotted perfect market timing returns against the market returns, it would look like a "V" centered at 0. It would have a high correlation with market volatility, 0 correlation with the market. No correlation is very different from independent. – Charles Fox Dec 7 '19 at 1:31
  • Pardon my ignorance, there are parts of stats that I'm still not great at. I go to excel, and create 2 columns of returns. I use the correlation function, and the closer the 2 columns are, the higher the correlation. If the columns are identical, the correlation is 1. In fact, just playing with the numbers, if my return is exactly x% of market return (even, say, half) the correlation still shows as 100%. Can you help me understand your answer, compared to this? – JTP - Apologise to Monica Dec 7 '19 at 10:33
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    If the second column is a perfect market timing strategy, the formula would be =if(a1>0,a1,-a1) for cell b1. Just drag that formula down. Making all of column A negative with this formula in column B will cause the correlation go to -1. Setting the formula in column A to =Rand()-0.5 will make the correlation close to 0. – Charles Fox Dec 7 '19 at 22:32

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