Price Dividend Ratio Factors : Proxies for Long Run Risk

We evaluate the empirical support for a broad class of long run risk models using information in factors extracted through principal component analysis of the covariance matrix of log price dividend ratios of twenty five equity portfolios formed on Size and Book-to-Market. We identify two price-dividend ratio factor proxies for economy wide long run risk, one tracking the volatility of the growth rate in economy wide aggregate consumption, and the other predicting the growth rates in the stock index portfolio dividends and aggregate consumption, consistent with the implications of these models. We show that that the long run risk factor driving expected consumption growth is not recoverable from the cross section of excess returns alone. The price dividend ratio factors perform better than the stock index price dividend ratio and the corporate yield spread, and has information in addition to what is in the slope of the term structure of interest rates, in forecasting the growth rate in real time consumption and stock index dividends. The covariance of excess returns with factor innovations explain the cross section of excess returns on size, book/market, earnings/price ratio, long term reversal, and short term reversal sorted portfolios in a manner robust to look-ahead and useless factor biases. Our findings suggest that the widely used Fama and French (1993) three factor model and the long run risk models studied in the literature are not necessarily inconsistent with each other. They may be representing the same underlying phenomenon, but emphasizing different aspects of reality.