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Constrained Kelly portfolios under alpha-stable laws

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  • Wesselhöfft, Niels
  • Härdle, Wolfgang Karl

Abstract

This paper provides a detailed framework for modeling portfolios, achieving the highest growth rate under subjective risk constraints such as Value at Risk (VaR) in the presence of stable laws. Although the maximization of the expected logarithm of wealth induces outperforming any other significantly different strategy, the Kelly Criterion implies larger bets than a risk-averse investor would accept. Restricting the Kelly optimization by spectral risk measures, the authors provide a generalized mapping for different measures of growth and security. Analyzing over 30 years of S&P 500 returns for different sampling frequencies, the authors find evidence for leptokurtic behavior for all respective sampling frequencies. Given that lower sampling frequencies imply a smaller number of data points, this paper argues in favor of α-stable laws and its scaling behavior to model financial market returns for a given horizon in an i.i.d. world. Instead of simulating from the class of elliptically stable distributions, a nonparametric scaling approximation, based on the data-set itself, is proposed. Our paper also uncovers that including long put options into the portfolio optimization, improves the growth criterion for a given security level, leading to a new Kelly portfolio providing the highest geometric mean.

Suggested Citation

  • Wesselhöfft, Niels & Härdle, Wolfgang Karl, 2019. "Constrained Kelly portfolios under alpha-stable laws," IRTG 1792 Discussion Papers 2019-004, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    • Handle: RePEc:zbw:irtgdp:2019004
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    More about this item

    Keywords

    growth-optimal; Kelly criterion; protective put; portfolio optimization; stable distribution; Value at Risk;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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