Hellinger’s distance to normal distribution as market invariant

Authors

  • Vardan Bardakհchyan Yerevan State University
  • Mesrop Mesropyan Yerevan State University

DOI:

https://doi.org/10.46991/BYSU:G/2023.14.1.064

Keywords:

Market invariant, Sensitivity analysis, Hellinger’s distance, distance to normal distribution, financial portfolio theory, simulated market, Student’s distribution

Abstract

Main purpose of distance based portfolio constructions is for portfolio imitation. Here we used distance from normal distribution for other purpose. We attempted to find static market invariant within possible linear combinations of given random variables. We conjectured that “closeness” to normal distribution of possible portfolios in market may reliably represent market microstructure with possible correlations between assets. Taking the squared Hellinger’s distance, we sought for each level of desired mean return the portfolio whose return distribution is closest to Gaussian, with variance taken from efficient frontier found by initially solving mean-variance problem. We found that minimal distance differs significantly from market to market. The sensitivity check showed small average sensitivity for 5% change of a 5% portion of data, small sensitivity for adding new variables in simulated market, and extreme sensitivity to bin numbers. Though distance to normality differed among markets, its sensitivity being small enough in average sometimes showed extreme changes.

Author Biographies

Vardan Bardakհchyan, Yerevan State University

Candidate of Physico-mathematical Sciences, Lecturer at YSU Chair of Actuarial and Financial Mathematics

Mesrop Mesropyan, Yerevan State University

Bachelor student at YSU Faculty of Mathematics and Mechanics

References

Attilio, Meucci. 2005. Risk and Asset Allocation. Springer.

Best , J. M., and R. R. Grauer. 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results." Review of Financial Studies 4 (2): 315—342.

Borghesi, Christian, Matteo Marsili, and Salvatore Miccichè. 2007. "Emergence of time-horizon invariant correlation structure in financial returns by subtraction of the market mode." Physical Review E 76 (2).

Bucci, Fr., L. Fabrizio, Jean-Philippe Bouchaud, and Michael Benzaquen. 2020. "Are trading invariants really invariant? Trading costs matter." Quantitative Finance 1-10.

Gourieroux, C., J. P. Laurent, and O. Scaillet. 2000. "Sensitivity analysis of Values at Risk." Journal of Empirical Finance 7 (3-4).

Hyvärinen, Aap., J. Karhunen, and Er. Oja. 2001. Independent Component Analysis. 1st ed: Wiley.

Kyle, Albert S., and Anna A. Obizhaeva. 2016. "Market microstructure invariance: Empirical hypotheses." Econometrica 84 (4): 1345–1404.

Kyle, Albert S., Anna A. Obizhaeva, and Tugkan Tuzun. 2020. "Microstructure invariance in U.S. stock market trades." Journal of Financial Markets 49.

Pincak, R. 2013. "The string prediction models as invariants of time series in the forex market." Physica A: Statistical Mechanics and its Applications 392 (24): 6414—6426.

Reddy, Y. V., and A. Sebastin. 2008. "Non-Linear Time Series Invariants to Study Price Manipulation in stock market." Metamorphosis: A Journal of Management Research vol. 7 (1): 7-23.

Stoyanov, Stoyan V., Svetlozar T. Rachev, and Frank J. Fabozzi. 2013. "Sensitivity of portfolio VaR and CVaR to portfolio return characteristics." Annals of Operations Research 205 (1): 169-187.

Svetlozar, T., S. T. Rachev, S.V. Stoyanov, and F. J. Fabozzi. 2011. A Probability Metrics Approach to Financial Risk Measures. Wiley-Blackwell.

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Published

2023-04-17

How to Cite

Bardakհchyan V., & Mesropyan, M. (2023). Hellinger’s distance to normal distribution as market invariant. Bulletin of Yerevan University G: Economics, 14(1 (40), 64–71. https://doi.org/10.46991/BYSU:G/2023.14.1.064

Issue

Section

Economic and mathematical modeling