Constrained Kelly portfolios under alpha-stable laws

Niels Wesselhöfft and Wolfgang Härdle

No 2019-004, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

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.

Keywords: growth-optimal; Kelly criterion; protective put; portfolio optimization; stable distribution; Value at Risk (search for similar items in EconPapers)
JEL-codes: C13 C46 C61 C73 G11 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/230780/1/irtg1792dp2019-004.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zbw:irtgdp:2019004

Access Statistics for this paper

More papers in IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series" Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().