Competition Between Volatility and Overall Market Gain and the Performance of Leveraged Index Funds

Abstract

A simple yet powerful mathematical model is developed for comparison of the performance of leveraged funds versus that of their underlying index. The model strictly separates the pure market volatility from the actual long term gain of the market. This allows to study the interplay between volatility of various amplitude and gain. The fund performance is analyzed for different factors of leverage and clear limits for still acceptable market volatility are identified. For low volatility values the performance of leveraged index funds significantly exceeds the performance of what the leverage factor would suggest, reaching gains as large as 7x the gain of the index for a 3x leveraged fund. This favorable regime quickly deteriorates for intermediate values of market volatility and produces increasingly negative returns once the daily fluctuations exceed 1.5 to 2%. The model provides a practical understanding of the risks and opportunities of leveraged funds.