Simple New Method to Predict Bear Markets (The Entropic Linkage between Equity and Bond Market Dynamics)

Abstract

An alternative derivation of the yield curve based on entropy or the loss of information as it is communicated through time is introduced. Given this focus on entropy growth in communication the Shannon entropy will be utilized. Additionally, Shannon entropy’s close relationship to the Kullback–Leibler divergence is used to provide a more precise understanding of this new yield curve. The derivation of the entropic yield curve is completed with the use of the Burnashev reliability function which serves as a weighting between the true and error distributions. The deep connections between the entropic yield curve and the popular Nelson–Siegel specification are also examined. Finally, this entropically derived yield curve is used to provide an estimate of the economy’s implied information processing ratio. This information theoretic ratio offers a new causal link between bond and equity markets, and is a valuable new tool for the modeling and prediction of stock market behavior.

Keywords: Shannon Entropy, Kullback-Leibler Divergence, Yield Curve; Volatility, Cauchy Distribution, Phase Transition; Equity Market; Flash Crash

JEL Classification: G1, G12, G14, G170, D84, E43