The Limits of Leverage

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)Non UBCUnreviewedAuthor affiliation: Boston University and Dublin City UniversityFacult