Leveraged ETFs: How Biased Statistics Affect Your Portfolio

The price action of leveraged ETFs differs fundamentally from that of standard ETFs, and the generic explanation 'compounding' means nothing. Leveraged ETFs is the only publication in which LETF dynamics are developed completely—from the definition of return through the mathematical constraints defining leverage in a geometric Brownian motion framework to application of Ito’s lemma and the final solution.

Employing a comprehensive approach, solutions are derived under both the arithmetic and logarithmic models of return, motivating intuitive understanding of LETFs. As the first publication to mathematically define the value decay of LETFs, this text expands upon the academic research literature, which previously could only describe decay by example and evaluate it by process of elimination.

Leveraged ETFs explains why these funds trade the way they do, helping investors and finance professionals avoid trading mistakes. Clear examples related to markets and formulas easily implemented in spreadsheet software will help independent investors and finance professionals assess risk/reward objectively (and not just for leveraged holdings).

Included is an accessible review of the necessary math. Take for example the oft-repeated adage about volatility being a drag on the returns of all assets: readers will not only know it is false but will be wise to the flaw in the thinking (and math) of those who believe it. Readers will also know why short/inverse funds exhibit more value decay than long LETFs (and by how much). Only those understanding the fundamentals are not surprised at how their portfolios respond.

Alpay Kaya’s experience in the research & development of systematic trading strategies spans asset classes and financial instruments. Formerly the head of FX research at Koch Capital, his strategies (long/short equity, FX options, and rate futures) have performed consistently well in live trading at notionals in excess of $100MM. With an educational background in Control Systems, his research on robust optimal control with applications to aviation has been published in professional journals and conference proceedings. The author holds engineering degrees from the University of California at Berkeley and the University of Akron.