Leverage efficiency

TL;DR

This paper explores the concept of leverage efficiency, proposing that optimal leverage tends to stabilize around 1, and discusses its implications for market stability, asset pricing, and detecting fraud, supported by empirical data analysis.

Contribution

It introduces the hypothesis of leverage efficiency, linking it to market stability, asset pricing anomalies, and fraud detection, with empirical validation across diverse asset data.

Findings

Analysis supports the leverage efficiency hypothesis

Market deviations from leverage efficiency can lead to bubbles

Proposes methods for fraud detection based on stochastic properties

Abstract

Peters (2011a) defined an optimal leverage which maximizes the time-average growth rate of an investment held at constant leverage. It was hypothesized that this optimal leverage is attracted to 1, such that, e.g., leveraging an investment in the market portfolio cannot yield long-term outperformance. This places a strong constraint on the stochastic properties of prices of traded assets, which we call "leverage efficiency." Market conditions that deviate from leverage efficiency are unstable and may create leverage-driven bubbles. Here we expand on the hypothesis and its implications. These include a theory of noise that explains how systemic stability rules out smooth price changes at any pricing frequency; a resolution of the so-called equity premium puzzle; a protocol for central bank interest rate setting to avoid leverage-driven price instabilities; and a method for detecting fraudulent investment schemes by exploiting differences between the stochastic properties of their prices and those of legitimately-traded assets. To submit the hypothesis to a rigorous test we choose price data from different assets: the S&P500 index, Bitcoin, Berkshire Hathaway Inc., and Bernard L. Madoff Investment Securities LLC. Analysis of these data supports the hypothesis.