Julian Thimme

Ambiguity in the Cross-Section of Expected Returns: An Empirical Assessment

This article estimates and tests the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji based on stock market data. We introduce a novel methodology to estimate the conditional expectation, which characterizes the impact of a decision maker’s ambiguity attitude on asset prices. Our point estimates of the ambiguity parameter are between 25 and 60, whereas our risk aversion estimates are considerably lower. The substantial difference indicates that market participants are ambiguity averse. Furthermore, we evaluate if ambiguity aversion helps explaining the cross-section of expected returns. Compared with Epstein and Zin preferences, we find that incorporating ambiguity into the decision model improves the fit to the data while keeping relative risk aversion at more reasonable levels. Supplementary materials for this article are available online.

Volatility-of-Volatility Risk

We show that time-varying volatility of volatility is a significant risk factor which affects the cross-section and the time-series of index and VIX option returns, beyond volatility risk itself. Volatility and volatility-of-volatility measures, identified model-free from options data as the VIX and VVIX indices, respectively, are only weakly related to each other. Delta-hedged index and VIX option returns are negative on average, and more negative for strategies more exposed to volatility and volatility-of-volatility risks. Volatility and volatility of volatility significantly and negatively predict future delta-hedged option payoffs. The evidence is consistent with a no-arbitrage model featuring time-varying volatility and volatility-of-volatility factors, which are negatively priced by investors.

INTERTEMPORAL SUBSTITUTION IN CONSUMPTION: A LITERATURE REVIEW

This paper reviews the status quo of the empirical literature about the elasticity of intertemporal substitution (EIS) in consumption. Aiming to answer the question what the true magnitude of the parameter really is, it discusses several recent advances of the theory and highlights challenges for the estimation. Although the general discussion still seems to be prevailed by Halls early EIS estimates close to zero, we show that several deviations from the time-additive constant relative risk aversion model speak in favor of considerably higher values. Our treatment is supposed to provide researchers a hint at which parameter is a reasonable and incontrovertible choice for the calibration of models in macroeconomics and finance.

INTERTEMPORAL SUBSTITUTION IN CONSUMPTION: A LITERATURE REVIEW: INTERTEMPORAL SUBSTITUTION IN CONSUMPTION

This paper reviews the status quo of the empirical literature about the elasticity of intertemporal substitution (EIS) in consumption. Aiming to answer the question what the true magnitude of the parameter really is, it discusses several recent advances of the theory and highlights challenges for the estimation. Although the general discussion still seems to be prevailed by Halls early EIS estimates close to zero, we show that several deviations from the time‐additive constant relative risk aversion model speak in favor of considerably higher values. Our treatment is supposed to provide researchers a hint at which parameter is a reasonable and incontrovertible choice for the calibration of models in macroeconomics and finance.

Elephants and the Cross-Section of Expected Returns

Cross-sectional asset pricing tests with GMM can generate spuriously high explanatory power for factor models when the moment conditions are specified such that they allow the estimated factor means to substantially deviate from the observed sample averages. In fact, by shifting the weights on the moment conditions, any level of cross-sectional fit can be attained. This property is a feature of the GMM estimation design and applies to strong as well as weak factors, and to all sample sizes and test assets. We reveal the origins of this bias theoretically, gauge its size using simulations, and document its relevance empirically.

Implied Volatility Duration and the Early Resolution Premium

We introduce Implied Volatility Duration (IVD) as a new measure for the timing of uncertainty resolution, with a high IVD corresponding to late resolution. Portfolio sorts on a large cross-section of stocks indicate that investors demand on average about seven percent return per year as a compensation for a late resolution of uncertainty. This premium is higher in times of low market returns and cannot be explained by standard factor models. In a general equilibrium model, we show that the expected excess return differential between ‘late’ and ‘early’ stocks can only be positive, if the investor’s relative risk aversion exceeds the inverse of her elasticity of intertemporal substitution, i.e., if she exhibits a preference for early resolution of uncertainty in the spirit of Epstein and Zin (1989). Our empirical analysis thus provides a purely market-based assessment of the relation between two preference parameters, which are notoriously hard to estimate.

Predictability and the Cross-Section of Expected Returns in Models with Long-Run Risks

In long-run risks models excess returns on arbitrary assets are predictable via the price-dividend ratio and the variance risk premium of the aggregate stock market. We propose a simple empirical test for the ability of such a model to explain the cross-section of expected returns by sorting stocks based on the sensitivity of expected returns to these quantities. We show that models with only one uncertainty-related state variable, like the classic long-run risks model, are not able to pass this test. However, even extensions with more state variables mostly fail. We derive criteria for the market prices of risks a model has to meet to be in line with the data.

High order smooth ambiguity preferences and asset prices

This paper extends the recursive smooth ambiguity decision model developed in Klibanoff, Marinacci, and Mukerji (2005, 2009) by relaxing the uniformity imposed on higher order acts. This generalization permits a separation of intertemporal substitution, risk attitude, and attitudes towards different sources of uncertainty. Our decision model is suited in situations where subjects may treat several kinds of uncertainty in different manners. We apply our preference specification to a consumption-based asset pricing model with long run risks and assess the impact of ambiguity on asset prices and predictability patterns. We find that modeling attitudes towards uncertainty through high order smooth ambiguity preferences has important implications for asset prices. Our model generates a highly volatile price-dividend ratio and predictability patterns in line with the data.