Risk-Constrained Kelly Portfolios Under Alpha-Stable Laws

Niels Wesselhöfft () and Wolfgang Härdle
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Niels Wesselhöfft: Humboldt-Universität zu Berlin, IRTG 1792

Computational Economics, 2020, vol. 55, issue 3, No 3, 826 pages

Abstract: 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.

Keywords: Growth-optimal; Kelly criterion; Protective put; Portfolio optimization; Stable distribution; Value at risk; Expected shortfall (search for similar items in EconPapers)
JEL-codes: C13 C46 C61 C73 G11 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10614-019-09913-y

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