We provide a long-run risks based explanation for the predictability puzzles in bond and currency markets. In our model, time-varying macroeconomic (i.e., consumption) volatility carries a separate risk compensation and ensures that the risk premium in asset markets is time-varying. In particular, periods of high macroeconomic volatility are associated with (i) an increase in nominal bond risk premium and a steeper slope of the nominal yield curve, and (ii) expected depreciation of the currency and a low domestic minus foreign interest rate differential, thus providing the economic channels for explaining the violations of expectations hypothesis. We show that the model qualitatively matches the violations of the expectations hypothesis seen in the data, while at the same time accounting for the level and volatilities of nominal yields and equity returns. In all, we argue that the long-run risks model provides a coherent explanation of the key puzzles in bond and currency markets.
In the data, asset prices exhibit large negative moves at frequencies of about 18 months. These large moves are puzzling as they do not coincide, nor are they followed by any significant moves in the real side of the economy. On the other hand, we find that measures of investor’s uncertainty about their estimate of future growth have significant information about large moves in returns. We set-up a recursive-utility based model in which investors learn about the latent expected growth using the cross-section of signals. To model the learning of the agents about the unobserved expected growth, we specify a belief-updating model (Kalman Filter is a special case) which incorporates the recency bias of investors in forecast formation. The uncertainty (confidence measure) about investor’s growth expectations, as in the data, is time-varying and subject to large moves. In the confidence risks model, recency bias in conjunction with confidence risk fluctuations lead to large moves in asset prices. In calibrations we show that the model can account for the large return move evidence in the data, distribution of asset prices, predictability of excess returns and other key asset market facts.
The insurance for large downward moves in the asset prices provided by the out-of-the money put options is expensive relative to standard models. This suggests that investors are concerned with large negative moves in prices, which occur approximately once a year in the data; however, in the data there is no evidence for corresponding large moves in consumption at such frequencies. I present a long-run risks type model where economic inputs (consumption) are Gaussian, and the agent learns about the unobserved expected growth from the cross-section of signals using recency-biased belief-updating model. The uncertainty about expected growth (confidence measure), as in the data, is time-varying and subject to jumps. In the long-run risks setup, recency-biased learning and confidence risk fluctuations lead to large jump premia, which can explain option-price puzzles and large moves in returns in the absence of jumps in consumption. The estimation results suggest that the model provides a good fit to the data at plausible preference and model parameter values.