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There are uncountably many factor models to estimate stock returns, such as CAPM, Fama-French, Carhart-Momentum, APT etc.

Which models can estimate the market (index) return?

I found only three models: Cay, Dividends and Average Correlation.

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Yes, those are probably the variables that predict the better the stock market return. However, the OOS evidence is usually weak.

Goyal & Welch provide a good summary on predictors: http://rfs.oxfordjournals.org/content/21/4/1455.abstract

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