Nanyang Business School Forum on Risk Management and Insurance

The Time Variation in Risk Appetite and Uncertainty

by | Dec 22, 2018 | Asset Pricing, Risk Aversion, Statistics | 0 comments

Tags: Risk Appetite, Economic Uncertainty, Asset Pricing, Non-Gaussianity, Predictability, High Frequency Risk Aversion Index
More from: Geert Bekaert, Eric Engstrom, Nancy Xu

Editor’s Note: Presented at the 2018 China International Risk Forum. Posted by Nancy R. Xu, Assistant Professor of Finance, Carroll School of Management, Boston College; Geert Bekaert, Professor of Business, Finance Division, Columbia Business School; Eric C. Engstrom, Adviser, Research and Statistics Division, Federal Reserve Board.


It have become increasingly commonplace to assume that risk aversion or investor mood evolves over time. In recent years, the VIX, typically referred to as the “fear index”, reached around 45 during the peak of the European Debt Crisis with fears of government defaults, remained low during the year of 2017 perhaps indicating investor complacency, and experienced a sharp jump likely associated with fears for higher future interest rates during early February 2018. The literature has agreed that changes in risk aversion are important determinant of asset price dynamics. However, the literature hasn’t reached an agreement on a reliable measure of market-wide or aggregate risk aversion. The main contribution of our paper is to develop a measure of time-varying risk aversion that is extracted from a wide information set of asset prices and macro data while simultaneously satisfying the asset pricing theory. This risk aversion index disentangles from macroeconomic uncertainty and can be obtained at high frequency, which constitutes its two clear advantages.

Understanding market-wide risk aversion—one of the pure price-of-risk state variables—has been widely attempted across various literatures. For instance, the behavioral finance literature (see, e.g., Lemmon and Portnaiguina (2006) and Baker and Wurgler (2006) for a discussion) has developed “sentiment indices,” and there are now a wide variety of “risk aversion” or “sentiment” indicators available, created by financial institutions (see Coudert and Gex (2008) for a survey). The “structural” dynamic asset pricing literature has meanwhile proposed time-varying risk aversion as a potential explanation for salient asset price features (see Campbell and Cochrane (1999) and a large number of related articles), whereas reduced-form asset pricing models, aiming to simultaneously explaining stock return dynamics and option prices, have also concluded that time-varying prices of risk are important drivers of stock return and option price dynamics (see Bakshi and Wu, 2010; Bollerslev, Gibson, and Zhou, 2011; Broadie, Chernov, and Johannes, 2007). Risk aversion has also featured prominently in recent monetary economics papers that suggest a potential link between loose monetary policy and the risk appetite of market participants, spurring a literature on what structural economic factors would drive risk aversion changes (see, e.g., Rajan, 2006; Adrian and Shin, 2009; Bekaert, Hoerova, and Lo Duca, 2013). In international finance, Miranda-Agrippino and Rey (2015) and Rey (2015) suggest that global risk aversion is a key transmission mechanism for US monetary policy to be exported to countries worldwide and is a major source of asset return comovements across countries (see also Xu, 2017). Finally, several papers on sovereign bonds (e.g. Bernoth and Erdogan, 2012) have stressed the importance of global risk aversion in explaining their dynamics and contagion across countries.

In this paper, we aim to resolve several challenges by formulating this new measure of time-varying risk aversion that has the following four features:

First, because economic uncertainty also varies through time and should affect risk premiums in financial markets, we want to separately identify the aversion to risk and the amount of risk. To achieve that, we build on the dynamic no-arbitrage asset pricing theory. Risk aversion constitutes the second factor in the pricing kernel that is not perfectly driven by economic fundamentals. The estimation strategy is to first pre-determine economic uncertainties and then extract the latent risk aversion by matching risky asset moments including risk premiums, physical and risk-neutral variances.

Second, extant risk aversion measures do not incorporate large cross-asset class information while simultaneously satisfying the pricing theory. To better link to the aggregate asset pricing literature, our approach imposes pricing consistency across multiple risky asset classes (stock and corporate bond markets) regarding the joint dynamics among asset-specific cash flow dynamics, macroeconomic fundamentals and risk aversion.

Third, our model introduces non-linearity to the economy through both the amount of risk (i.e., uncertainties) and price of risk (i.e., risk aversion) channels. This modeling choice turns out to be important, as it is the downside uncertainty, not the upside uncertainty, that contributes to the time variation features of asset moments through the lens of this theoretical model. Moreover, the asymmetric risk aversion explains 88% of equity risk premium and more than 50% of variances. Our asymmetric risk aversion is in spirit consistent with the existing theories, e.g. the sensitivity function in the Campbell and Cochrane’s model. Despite featuring non-Gaussian dynamics, the model retains closed-form solutions for asset prices.

Fourth, our measure can be calculated from observable financial information at high frequencies, for example daily. This is potentially attractive for both academic researchers, practitioners and policy makers in order to identify the relative importance of high-frequency financial and risk variables to inform about the market-wide risk aversion.

In addition, our paper offers several important empirical byproducts. For instance, we find that risk aversion is much less persistent than the risk aversion process implied by standard habit models. Our paper also formally justifies the close relationship between equity variance risk premiums and aggregate risk aversion, whereas we find that credit spreads and corporate bond volatility are highly correlated with economic uncertainty. Moreover, model-implied risk premiums beat standard instrument sets predicting excess returns on equity and corporate bonds in an out-of-sample horse race. A financial proxy to our economic uncertainty predicts output growth negatively and significantly, even in the presence of the VIX. Finally, admittedly, the use of different asset classes in deriving a single measure of risk aversion imposes the important assumption that different markets are priced in an integrated setting. This may not (always) be the case. There may well be a link between risk aversion and the existence of arbitrage opportunities. That is, in uncertain, risk averse times, there is insufficient risky capital available, which causes different asset classes to be priced incorrectly (see, for example, Gilchrist, Yankov, and Zakrajsek, 2009). While consistent pricing across risky asset classes is a maintained assumption in our benchmark model, we can easily test whether this pricing kernel driven by fundamentals and risk aversion—empirically extracted from risky asset markets—prices safe assets. We find lack of evidence for market integration. Hence, different asset markets reflect differential information about risk appetite versus economic uncertainty.

In this paper, we formulate a no-arbitrage asset pricing model where the representative agent in the economy takes this time-varying uncertainty into account when pricing equity and corporate bonds, but also faces preference shocks imperfectly correlated with a wide set of macro fundamentals. By matching model implications with empirical observations, we estimate a series of time-varying aggregate risk aversion. This is one of the first papers to extract risk aversion from multiple risky asset classes while simultaneously satisfying the theory.

* This index is now available for download at:
https://www.nancyxu.net/risk-aversion-index.

The complete paper is available at:
https://papers.ssrn.com/abstract=3069078.

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