Markowitz-style Quartic Optimization for the Improvement of Leveraged ETF Trading

This paper seeks to unconventionally maximize the volatility of a portfolio through a quartic optimization based on Markowitz’s modern portfolio theory, which generally seeks to do exactly the opposite. It shows that through this method, a daily leveraged exchange traded fund (ETF) strategy investigated by Posterro can be significantly improved upon in terms of its Sharpe ratio. The original strategy seeks to use a combination of momentum trading and tracking error in leveraged ETFs to trade during the last half an hour of the trading day, but it suffers in a low volatility market. By maximizing the volatility to take better advantage of tracking error and momentum, this problem is addressed by both increasing the mean daily return and significantly decreasing the variance of the strategy’s daily returns. GARCH forecasting is also implemented to assist in the maximization of the daily portfolios’ variances, though this does not prove to make a statistically significant difference in the strategy’s performance