The Limits of Leverage

TL;DR

This paper explores how leverage is limited by costs and volatility, showing that excessive leverage reduces returns and Sharpe ratios, with optimal leverage depending on asset volatility.

Contribution

It introduces a model analyzing leverage limits under proportional costs, revealing how costs and volatility constrain long-term returns and optimal leverage levels.

Findings

Leverage has an upper bound influenced by costs and volatility.

Higher asset volatility can lead to better returns due to lower relative costs.

Beyond a certain leverage point, returns and Sharpe ratios decline.

Abstract

When trading incurs proportional costs, leverage can scale an asset's return only up to a maximum multiple, which is sensitive to its volatility and liquidity. In a model with one safe and one risky asset, with constant investment opportunities and proportional costs, we find strategies that maximize long term returns given average volatility. As leverage increases, rising rebalancing costs imply declining Sharpe ratios. Beyond a critical level, even returns decline. Holding the Sharpe ratio constant, higher asset volatility leads to superior returns through lower costs.