1. Introduction In this post I work through the main results in Ang, Hodrick, Xing, and Zhang (2006) which shows not only that i) stocks with more exposure to changes in aggregate volatility have higher average excess returns, but also that ii) … [Continue reading]

# Using the Cross-Section of Returns

1. Introduction The empirical content of the discount factor view of asset pricing can all be derived from the equation below: \begin{align} 0 = \mathrm{E}[m \cdot r_n] \quad \text{for all } … [Continue reading]

# Phase Change in High-Dimensional Inference

1. Introduction In my paper Feature Selection Risk (2014), I study a problem where assets have $Q \gg 1$ different attributes and traders try to identify which $K \ll Q$ of these attributes matter via price changes: \begin{align} \Delta p_n &= … [Continue reading]

# Intra-Industry Lead-Lag Effect

1. Introduction Hou (2007) documents a really interesting phenomenon in asset markets. Namely, if the largest securities in an industry as measured by market capitalization perform really well in the current week, then the smallest securities in … [Continue reading]

# Investigation Bandwidth

1. Motivation Time is dimensionless in modern asset pricing theory. e.g., the canonical Euler equation: \begin{align} P_t &= \widetilde{\mathrm{E}}_t[ \, P_{t+1} + D_{t+1} \, ] \label{eqn:euler} \end{align} says that the price of an asset at … [Continue reading]