Oscillating Between Fear and Relief: A Volatility-Based Aggregate Market Return-State Model

Abstract

Is there a generalizable relationship between aggregate market returns and implied volatility variables that can extend the predictions made by existing volatility forecasting models? The purpose of this study is to explore any existing implied volatility in the market return relationship. I distinguish between two state variables: implied volatility level and implied volatility changes. VIX and S&P 500 daily data were obtained for the period 1990 to 2016. The relationships are examined with linear, non-linear, and quantile regressions, a cross-sectional analysis including difference of mean tests, and multiple cross-sectional event studies to investigate market behaviour around each cross-sectional observation. This study finds evidence for significant asymmetric and non-linear relationships between implied volatility variables and macro market returns. Volatility-based macro market return-states, as described by the cross-sections, are found to rigorously filter for sign and magnitude of returns, and have significantly different return expectations. Since volatility is more easily forecast than market prices, these findings hold significant value for investors and risk managers, both in managing tail risk and in making investment decisions.