Asset Pricing and Volatility
Friday, Jan. 4, 2019 8:00 AM - 10:00 AM
- Chair: Jeroen Dalderop, University of Notre Dame
Cross-Sectional Dependence in Idiosyncratic Volatility
AbstractThe variability in stock prices that is unrelated to the common risk factors is called the idiosyncratic risk. It is measured by the idiosyncratic volatility: the volatility of asset returns once the impact of the common risk factors has been removed. The idiosyncratic volatility is important for portfolio management, arbitrage, and option pricing. The empirical evidence suggests the idiosyncratic volatilities are cross-sectionally correlated. This paper introduces an econometric framework for analysis of cross-sectional dependence in the idiosyncratic volatilities of assets using high frequency data. We first consider the estimation of standard measures of dependence in the idiosyncratic volatilities such as covariances and correlations. Next, we study an idiosyncratic volatility factor model, in which we decompose the variation in idiosyncratic volatilities into two parts: the variation related to the systematic factors such as the market volatility, and the residual variation. When using high frequency data, naive estimators of all the above measures are biased due to the use of the error-laden estimates of idiosyncratic volatilities. We provide bias-corrected estimators. We also provide the asymptotic theory that allows us to test whether the residual (non-systematic) components of the idiosyncratic volatilities exhibit cross-sectional dependence. We apply our methodology to the 30 Dow Jones Industrial Average components, and document strong cross-sectional dependence in their idiosyncratic volatilities. We consider two different sets of idiosyncratic volatility factors, and find that neither can fully account for the cross-sectional dependence in idiosyncratic volatilities. We map out the network of dependencies in residual (non-systematic) idiosyncratic volatilities across the stocks.
Pseudo-True SDFs in Conditional Asset Pricing Models
AbstractThis paper is motivated by the need to bridge some gap between modern asset pricing theory and recent developments in econometric methodology. While asset pricing theory enhances the use of conditional pricing models, econometric inference of conditional models can be challenging due to misspecification or weak identification. To tackle the case of misspecification, we utilize the conditional Hansen and Jagannathan (1997) (HJ) distance as studied by Gagliardini and Ronchetti (2016), but we set the focus on interpretation and estimation of the pseudo-true value defined as the argument of the minimum of this distance. While efficient GMM has no meaning for estimation of a pseudo-true value, the HJ-distance not only delivers a meaningful loss function, but also features an additional advantage for the interpretation and estimation of managed portfolios whose exact pricing characterizes the pseudo-true pricing kernel (SDF). For conditionally affine pricing kernels, we display some managed portfolios which are well-defined independently of the pseudo-true value of the parameters, although their exact pricing is achieved by the pseudo-true SDF. For nonlinear SDFs, we propose a smooth minimum distance (SMD) estimator (Lavergne and Patilea (2013)) that avoids a focus on specific directions as in the case of managed portfolios. Albeit based on kernel smoothing, the SMD approach avoids instabilities and the resulting need of trimming strategies displayed by classical local GMM estimators when the density function of the conditioning variables may take arbitrarily small values. In addition, the fact that SMD may allow fixed bandwidth asymptotics is helpful regarding the curse of dimensionality. By contrast with the true unknown value for a well-specified model, the estimated pseudo-true value, albeit defined in a time-invariant (unconditional) way, may actually depend on the choice of the state variables that define fundamental factors and their scaling weights. Therefore, we may not want to be overly parsimonious about the set of explanatory variables. Finally, following Antoine and Lavergne (2014), we show how SMD can be further robustified to deal with weaker identification contexts. Since SMD can be seen as a local extension of the method of jackknife GMM (Newey and Windmeijer (2009)), we characterize the Gaussian asymptotic distribution of the estimator of the pseudo-true value using classical U-statistic theorems.
Estimating Policy Functions Implicit in Asset Prices
AbstractI propose a semiparametric asset pricing model to measure how consumption and dividend policy depends on unobserved state variables, such as economic uncertainty and risk aversion. Under a flexible specification of the stochastic discount factor, the state variables are recovered from cross-sections of asset prices and volatility proxies, and the shape of the policy functions is identified from the pricing functions. The model leads to closed-form price-dividend ratios under polynomial approximations of the unknown functions and affine state variable dynamics. In the empirical application uncertainty and risk aversion are separately identified from the heterogeneous impact of uncertainty on dividend policy across small and large firms. I find an asymmetric and convex response in consumption (-) and dividend growth (+) towards uncertainty shocks, which together with moderate uncertainty aversion, can generate large leverage effects and divergence between macroeconomic and stock market volatility.
- C2 - Single Equation Models; Single Variables
- C5 - Econometric Modeling