Risk-Constrained Kelly Portfolios Under Alpha-Stable Laws

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 α -stable laws. Although the maximization of the expected logarithm of wealth induces outperforming an...

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Bibliographic Details
Published in:Computational economics 2020-03, Vol.55 (3), p.801-826
Main Authors: Wesselhöfft, Niels, Härdle, Wolfgang K.
Format: Article
Language:English
Subjects:
Behavioral/Experimental Economics
Computer Appl. in Social and Behavioral Sciences
Computer simulation
Constraints
Data points
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Financial market
Frequencies
Growth rate
Mapping
Math Applications in Computer Science
Operations Research/Decision Theory
Optimization
Portfolios
Put & call options
Risk acceptance
Risk analysis
Sampling
Scaling
Wealth
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Summary: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 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 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 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.
ISSN:0927-7099
1572-9974
DOI:10.1007/s10614-019-09913-y