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Risk-Constrained Kelly Portfolios Under Alpha-Stable Laws

Author

Listed:
  • Niels Wesselhöfft

    (Humboldt-Universität zu Berlin, IRTG 1792)

  • Wolfgang K. Härdle

    (Humboldt-Universität zu Berlin, IRTG 1792
    School of Business, Singapore Management University
    Charles University)

Abstract

This paper provides a detailed framework for modeling portfolios, achieving the highest growth rate under risk constraints such as value at risk (VaR) and expected shortfall (ES) in the presence of $$\alpha $$α-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 risk. 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 $$\alpha $$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 $$\alpha $$α-stable distributions, a semiparametric scaling approximation, based on hourly NASDAQ data, is proposed. Our paper also uncovers that including long put options into the portfolio optimization, improves portfolio growth for a given level of VaR or ES, leading to a new Kelly portfolio providing the highest geometric mean.

Suggested Citation

  • Niels Wesselhöfft & Wolfgang K. Härdle, 2020. "Risk-Constrained Kelly Portfolios Under Alpha-Stable Laws," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 801-826, March.
    • Handle: RePEc:kap:compec:v:55:y:2020:i:3:d:10.1007_s10614-019-09913-y
    DOI: 10.1007/s10614-019-09913-y
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    More about this item

    Keywords

    Growth-optimal; Kelly criterion; Protective put; Portfolio optimization; Stable distribution; Value at risk; Expected shortfall;
    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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