How Proportional Trading Costs Limit the Benefits of Leverage

Summary

This document examines how proportional transaction costs constrain leveraged investing in a market with one safe asset and one risky asset. It considers strategies designed to maximize long-term returns while maintaining an average volatility level, and explains how increasing leverage raises the costs of rebalancing.

The central result is that these rising costs reduce the Sharpe ratio, and beyond a critical leverage level they can reduce returns as well. The analysis also says that, at a fixed Sharpe ratio, higher asset volatility can correspond to higher returns because the costs are lower. The excerpt provides no model equations, data, or empirical tests, so it does not show how the conclusions vary across market conditions or how to estimate the critical leverage level in practice. Its claims are limited to the stated model assumptions.

Key ideas

• Proportional transaction costs can limit how much leverage improves investment returns.
• Rising leverage increases rebalancing costs and can lower the Sharpe ratio.
• Beyond a critical leverage level, additional leverage can reduce returns.
• Under the model, higher asset volatility can support higher returns at a fixed Sharpe ratio through lower costs.

Tags

# The Limits of Leverage


# The Limits of Leverage









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.