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Let's say you have a dependent variable and many independent variables. What are the preferred metrics for sorting and selecting variables based on explanatory power? Let's say you are not concerned with correlation among your inputs.

My thoughts are below. Let me know if I'm missing anything obvious, or if there is a metric that you feel dominates the others.

  1. Spearman correlation controlling for sector
  2. Granger causality
  3. Johansen test for cointegration
  4. Grinold's Information Ratio
  5. Economic performance of the factor during a factor backtest (i.e. drawdown, sharpe, etc.)
  6. Volatility of the factor premium
  7. Persistency of the factor premium
  8. Monotonic relation test
  9. Significance test on spread return (Q5-Q1) vs. Mean Return
  10. R^2 of factor after building some kind of model

My preference would be correlation coefficient.

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You should be concerned with correlation among your inputs or at least used technics such as ridge regression when estimating your model. –  Zarbouzou Jun 30 '11 at 9:03
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2 Answers

up vote 3 down vote accepted

I'd add:

  1. Variance reduction
  2. Fraction same sign / Hit rate

Additionally, you might look at the relationship between the Q5-Q1 spread itself and the dependent (i.e. are larger/smaller spreads associated with some feature of the dependent).

Turnover may also be an issue as slippage and friction come into consideration. Measures such as percent turnover in the Q5-Q1 portfolio, and correlation coefficient decay over lagged periods can prove insightful in selecting factors with higher stability and persistence.

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Hi I-CJW, can you elaborate a bit more on variance reduction? –  Quant Guy Jul 20 '11 at 19:09
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