Uncertainty, sentiments and time-varying risk premia

Why are stock prices much more volatile than the underlying dividends? The excess volatility of prices can in principle be attributed to two different causes: time-varying discount rates for expected future dividends, arising from variation in risk premia; or the irrational exuberance of investors, bidding prices up and down even in the absence of changes in the underlying value of the asset. No consensus has so far emerged among economists as to the prevalence of one or the other source of price variation. I propose in this paper a novel way to approach this problem, by identifying changes in the uncertainty faced by investors regarding the fundamental value of an asset and exploiting the different response in prices that such changes in uncertainty would generate through sentiments or risk premia. I then apply this framework to the S&P 500 index from 1872 till 2019: the positive correlation found between uncertainty and prices (or, equivalently, the negative correlation between uncertainty and implied risk premia) is not compatible with rational investors' behavior and suggests instead the presence of a significant sentiments component in stock prices.