The Empirical Risk-Return Relation: a factor analysis approach

Financial economists have long been interested in the empirical relation between the conditional mean and conditional volatility of excess stock market returns, often referred to as the risk-return relation. Unfortunately, the body of empirical evidence on the risk-return relation is mixed and inconclusive. A key criticism of the existing empirical literature relates to the relatively small amount of conditioning information used to model the conditional mean and conditional volatility of excess stock market returns. To the extent that financial market participants have information not reflected in the chosen conditioning variables, measures of conditional mean and conditional volatility--and ultimately the risk-return relation itself--will be misspecified and possibly highly misleading. We consider one remedy to these problems using the methodology of dynamic factor analysis for large datasets, whereby a large amount of economic information can be summarized by a few estimated factors. We find that several estimated factors contain important information about one-quarter ahead excess returns and volatility that is not contained in commonly used predictor variables. Moreover, the factor-augmented specifications we examine predict an unusual 16-20 percent of the one-quarter ahead variation in excess stock market returns, and exhibit remarkably stable and strongly statistically significant out-of-sample forecasting power. Finally, in contrast to several pre-existing studies that rely on a small number of conditioning variables, we find a positive conditional correlation between risk and return that is strongly statistically significant, whereas the unconditional correlation is weakly negative and statistically snginficantpredictability, conditioning information, large dimension factor models

Macro Factors in Bond Risk Premia

Empirical evidence suggests that excess bond returns are forecastable by financial indicators such as forward spreads and yield spreads, a violation of the expectations hypothesis based on constant risk premia. But existing evidence does not tie the forecastable variation in excess bond returns to underlying macroeconomic fundamentals, as would be expected if the forecastability were attributable to time variation in risk premia. We use the methodology of dynamic factor analysis for large datasets to investigate possible empirical linkages between forecastable variation in excess bond returns and macroeconomic fundamentals. We find that several common factors estimated from a large dataset on U.S. economic activity have important forecasting power for future excess returns on U.S. government bonds. Following Cochrane and Piazzesi (2005), we also construct single predictor state variables by forming linear combinations of either five or six estimated common factors. The single state variables forecast excess bond returns at maturities from two to five years, and do so virtually as well as an unrestricted regression model that includes each common factor as a separate predictor variable. The linear combinations we form are driven by both "real" and "inflation" macro factors, in addition to financial factors, and contain important information about one year ahead excess bond returns that is not captured by forward spreads, yield spreads, or the principal components of the yield covariance matrix.

A Factor Analysis of Bond Risk Premia

This paper uses the factor augmented regression framework to analyze the relation between bond excess returns and the macro economy. Using a panel of 131 monthly macroeconomic time series for the sample 1964:1-2007:12, we estimate 8 static factors by the method of asymptotic principal components. We also use Gibb sampling to estimate dynamic factors from the 131 series reorganized into 8 blocks. Regardless of how the factors are estimated, macroeconomic factors are found to have statistically significant predictive power for excess bond returns. We show how a bias correction to the parameter estimates of factor augmented regressions can be obtained. This bias is numerically trivial in our application. The predictive power of real activity for excess bond returns is robust even after accounting for finite sample inference problems. Forecasts of excess bond returns (or bond risk premia) are countercyclical. This implies that investors are compensated for risks associated with recessions.

Macro Factors in Bond Risk Premia

Are there important cyclical fluctuations in bond market premiums and, if so, with what macroeconomic aggregates do these premiums vary? We use the methodology of dynamic factor analysis for large datasets to investigate possible empirical linkages between forecastable variation in excess bond returns and macroeconomic fundamentals. We find that "real" and "inflation" factors have important forecasting power for future excess returns on U.S. government bonds, above and beyond the predictive power contained in forward rates and yield spreads. This behavior is ruled out by commonly employed affine term structure models where the forecastability of bond returns and bond yields is completely summarized by the cross-section of yields or forward rates. An important implication of these findings is that the cyclical behavior of estimated risk premia in both returns and long-term yields depends importantly on whether the information in macroeconomic factors is included in forecasts of excess bond returns. Without the macro factors, risk premia appear virtually acyclical, whereas with the estimated factors risk premia have a marked countercyclical component, consistent with theories that imply investors must be compensated for risks associated with macroeconomic activity. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: [email protected], Oxford University Press.