We present evidence that several popular low-frequency measures of effective spread suffer from a volatility-induced bias and that volatility is the primary driver of the variation of these liquidity proxies. Using data for U.S. equities and major foreign exchange rates, we show that the bias arises when the effective spread is small relative to volatility. We document that the bias has become more acute over time and show that volatility-biased measures fail to replicate some well-known results in empirical finance. We conclude by providing guidance on the choice of low-frequency measures in empirical applications.

We examine a production-based asset-pricing model with an unobservable mean growth rate following a two-state Markov chain and with an ambiguity-averse representative agent. Our model requires a low coefficient of relative risk aversion to produce: (i) a high equity premium and volatile equity returns, (ii) a low and smooth risk-free rate, (iii) smooth consumption growth and volatile investment growth, (iv) countercyclical equity premium and market price of risk, (v) conditional heteroscedasticity in returns, and (vi) long-horizon predictability of excess returns.

We propose a new methodology for modeling and estimating time-varying downside risk and upside uncertainty in equity returns and for assessment of risk–return trade-off in financial markets. Using the salient features of the binormal distribution, we explicitly relate downside risk and upside uncertainty to conditional heteroskedasticity and asymmetry through binormal GARCH (BiN-GARCH) model. Based on S&P 500 and international index returns, we find strong empirical support for existence of significant relative downside risk, and robust positive relationship between relative downside risk and conditional mode.

We use the Bayesian method introduced by Gallant and McCulloch (2009) to estimate consumption-based asset pricing models featuring smooth ambiguity preferences. We rely on semi-nonparametric estimation of a flexible auxiliary model in our structural estimation. Based on the market and aggregate consumption data, our estimation provides statistical support for asset pricing models with smooth ambiguity. Statistical model comparison shows that models with ambiguity, learning, and time-varying volatility are preferred to the long-run risk model. We also analyze asset pricing implications of the estimated models. Received April 12, 2016; editorial decision September 11, 2018 by Editor Stijn Van Nieuwerburgh.

This paper provides a comprehensive survey of existing measures of uncertainty, risk, and volatility, noting their conceptual distinctions. It summarizes how they are constructed, their relative advantages in usage, and their effects on financial market and economic outcomes. The measures are divided into four categories based on the construction methodology: news-based, survey-based, econometric-based, and market-based measures. While heightened uncertainty is typically associated with negative real and financial outcomes, the magnitude of these effects and the interpretation of transmission channels crucially depend on identification considerations.