Alpay Kaya, CFA

La vérité existe. On n'invente que le mensonge. —Braque (Truth exists. One only invents falsehood.)


A Finance professional living in Florida, Alpay Kaya’s experience in algorithmic trading R&D spans asset classes and financial instruments. The former Head of FX/Rates Research at the proprietary trading unit of Koch Industries, his strategies (long/short Equities, FX options, & Rates futures) have performed consistently well in live trading at asset values in excess of $100 million. His research currently focuses on discrepancies between abstraction and prevailing analytical techniques, which may employ unrealistic assumptions so as to achieve superficially ‘elegant’ solutions. With an educational background in Control Systems/Applied Math, his research on robust optimal control with applications to aviation has been published in professional journals and conference proceedings. Alpay Kaya, Chartered Financial Analyst, holds Engineering degrees from the University of Akron and the University of California at Berkeley. He was drawn to the investing sector because it connects math and human behavior.

His recent book VALUE IN VOLATILITY fills a heretofore ignored need in the finance publication space, that of a practitioner’s guide based on sound mathematics. For three decades since the early 1980s, two macroeconomic shifts have supported the buy & hold returns of equity investors. Interest rates have decreased, the 10-year rate from a record high of 15% to a record low of 1.5%. The fraction of US GDP transferring to corporate profits has increased from a record low of 3% to a record high of 12%. Going forward, investors will need to earn returns from strategic investing; literally, buy low and sell high. The math of leveraged ETFs represent just the right generalization of single-name stock price evolution such that understanding them engenders a fundamental understanding of market assets.

The earlier LEVERAGED ETFs is a comprehensive exposition on the mathematics of this misunderstood class of financial instruments. The price action of leveraged ETFs differs greatly from that of standard ETFs, and the generic explanation ‘compounding’ means nothing. 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.


4 comments on “About

  1. Clay Diggs
    October 21, 2014

    I am beginning to think that slippage in leveraged ETF’s is an issue only to fund management but not investors. My thinking is that leveraged ETF’s are fungible just as non leveraged ETF’s and common stock. While leverage will certainly cause more volatility than non leveraged assets if you buy and hold a leveraged ETF for longer than one upward spike in the asset price, aside from opportunity cost you may still benefit from the next price spike assuming the next price hike does in fact occur. While the long term buy & hold of leveraged ETF’s is not advisable as they are fundamentally different than non leveraged equities it will not lead to slippage from the investor perspective. Do you think my opinions are correct? Thank you – Clay

    • Alpay Kaya
      October 22, 2014

      I avoid the term slippage because it has been used in reference to return differences between historical simulation and live trading (e.g., transaction fees, price moves). In relation to LETFs, it could also include leverage deviation from the stated return objective. I use the term value decay (or negative drift) in reference to the difference in value evolution of LETFs and a theoretically ideal leveraged system. All related derivations are in my print book, with the Kindle book showing results only.

      Investments effecting leverage not equal to +1 are fundamentally different from those that do; and for this reason, they exhibit value decay.

  2. Frederic Khoury
    August 18, 2013

    Hello Alpay,

    I read your book on leveraged ETFs and wanted to thank you for writing such a great explanation about those instruments.
    I am interested in learning more about intraday value calculation for ETFs. Would you have any reading recommendations?

    • Alpay Kaya
      August 20, 2013

      I’m glad you enjoyed the book. The text of U.S. Patent 6,088,685 describes such a process. Although the patent was later declared invalid in court on the basis of ‘prior art’, its content remains valid. Beyond that, the fungibility of money and the assets backing (leveraged) ETFs, combined with the actions of profit-seeking arbitrageurs, supports the intraday tracking of these funds vis-à-vis their indices.

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