Why Perfect Market Timing Does Not Imply Perfect Return Correlation

Summary

The document asks whether a strategy with perfect foresight—taking a long position before market gains and a short position before losses—would have a return series perfectly correlated with the market. The question assumes a symmetric market-return distribution and raises the intuition that flawless direction calls might imply correlation of one.

The reply explains that the strategy’s returns are positive in either market direction, while the market’s own returns can be positive or negative. Because the two series therefore do not move proportionally in every observation, their simple correlation is less than one. This is a qualitative explanation only: the document gives no market-return magnitudes, trading convention, or numerical correlation. It illustrates that perfect directional timing and perfect linear correlation are different properties, without specifying the correlation value.

Key ideas

• Perfect foresight can produce positive strategy returns during both market rises and falls.
• Market returns themselves retain both positive and negative observations.
• Correlation measures linear co-movement, so perfect directional timing does not guarantee correlation of one.
• The document provides no numerical correlation or assumptions about return magnitudes.

Tags

# Correlation between the perfect market-timing strategy and the market itself?


# Correlation between the perfect market-timing strategy and the market itself?












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.

## Answer by wjamdanf1234 (score 1)

https://quant.stackexchange.com/a/50291

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.