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The Limits of Leverage

Banff International Research Station for Mathematical Innovation and Discovery

When trading incurs proportional costs, leverage can scale an asset\'s\r\nreturn only up to a maximum multiple, which is sensitive to the asset\'s\r\nvolatility and liquidity. In a continuous-time model with one safe and\r\none risky asset with constant investment opportunities and proportional\r\ntransaction costs, we find the efficient portfolios that maximize long\r\nterm expected returns for given average volatility. As leverage and\r\nvolatility increase, rising rebalancing costs imply a declining Sharpe\r\nratio. Beyond a critical level, even the expected return declines. For\r\nfunds that seek to replicate multiples of index returns, such as\r\nleveraged ETFs, our efficient portfolios optimally trade off alpha\r\nagainst tracking error.\r\n(Joint work with Eberhard Mayerhofer)

Mathematics; Game theory, economics, social and behavioral sciences; Probability theory and stochastic processes; Mathematical finance

video/mp4

Author affiliation: Boston University and Dublin City University

2014-10-29

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/50929

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/