What Ties Return Volatilities to Price Valuations and Fundamentals?∗

The relation between the volatility of stocks and bonds and their price valuations is strongly time-varying, both in magnitude and direction, defying traditional asset pricing models and conventional wisdom. We construct and estimate a model in which investors’ learning about regular and unusual fundamental states leads to a non-monotonic V −shaped relation between volatilities and prices. Structural forecasts from our model predict future return volatility and covariances with R2 ranging between 40% and 60% at the 1-year horizon. The model’s success stems largely from backing out the endogenous and time-varying pro (counter) cyclical weights that investors assign to earnings (inflation) news. JEL Classification Code: G10, G11, G12, G14 Introduction While it is intuitive that the volatilities and comovements of stocks and bonds are strongly related to the state of economic fundamentals, it is surprising that the financial literature has been unable to empirically demonstrate such a strong link between them, as evidenced in the following quote from a recent paper by Nobel prize laureate Robert Engle. “After more than 25 years of research on volatility, the central unsolved problem is the relation between the state of the economy and aggregate financial volatility. The number of models that have been developed to predict volatility based on time series information is astronomical, but the models that incorporate economic variables are hard to find. Using various methodologies, links are found but they are generally much weaker than seems reasonable. For example, it is widely recognized that volatility is higher during recessions and following announcements but these effects turn out to be a small part of measured volatility.” [Engle and Rangel (2008)] For example, in a seminal paper, Schwert (1989) notes that stock market volatility is higher during recessions, which is now a widely accepted and influential stylized fact for volatility. While it is true that volatility is countercyclical, the regression of stock market volatility on the NBER recession indicator over 1960 – 2008, has a fairly low R2 of only about 13%. For bond volatilities the regression R2s are only around 15% for alternative maturity bonds. In fact, the R2 of virtually all the macroeconomic variables that have been tested in the literature, which we will discuss in more detail in this paper, jointly explain a very small proportion of stock market volatility. In this paper we argue that the relation between volatility and the macroeconomy is in fact very complex and goes beyond the simple boom-bust business cycle variation. This fact can be seen by looking at the top panel of Figure 1, which shows the massive variation, both in magnitude and in direction, of the correlation between stock return volatility and the price/earning (P/E) ratio. While conventional wisdom and most asset pricing models would predict a negative correlation between aggregate volatility and P/E ratio,1 in line with the empirical finding that volatility tends to rise during recessions while the P/E ratio tends to drop, the top panel of Figure 1 shows that this is not really the case in the data. In fact, the correlation between volatility and P/E ratio is often strongly 1 For instance, both the habit formation model of Campbell and Cochrane (1999) [see Figures 3 and 5] and the long-run risk model of Bansal and Yaron (2004) [see Section II.C.3] imply a negative relation between valuation ratios and volatility.