# Hellinger distance to normal distribution as market invariant

@inproceedings{Mesropyan2022HellingerDT, title={Hellinger distance to normal distribution as market invariant}, author={Mesrop T. Mesropyan and V. G. Bardakhchyan}, year={2022} }

Main purpose of distance based portfolio constructions is in portfolio imitation. Here we construct portfolio based on Hellinger’s distance from normal distribution. We empirically found that minimum of this distance drastically varies from market to market. Thus we suppose that it may be regarded as a form of market invariant, in a sense of helpful tool for market segmentation. We analyze its sensitivity. Though mean sensitivity was small it showed extreme sensitivity in some cases.

## References

SHOWING 1-10 OF 12 REFERENCES

### Sensitivity of portfolio VaR and CVaR to portfolio return characteristics

- EconomicsAnn. Oper. Res.
- 2013

This work considers the problem of improving marginally portfolio VaR and CVaR through a marginal change in the portfolio return characteristics and studies the relative significance of standard deviation, mean, tail thickness, and skewness in a parametric setting assuming a Student’s t or a stable distribution for portfolio returns.

### On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results

- Economics
- 1991

This paper investigates the sensitivity of mean-variance(MV)-efficient portfolios to changes in the means of individual assets. When only a budget constraint is imposed on the investment problem, the…

### Are trading invariants really invariant? Trading costs matter

- EconomicsQuantitative Finance
- 2020

We revisit the trading invariance hypothesis recently proposed by Kyle, A.S. and Obizhaeva, A.A. [‘Market microstructure invariance: Empirical hypotheses.’ Econometrica, 2016, 84(4), 1345–1404] by…

### Emergence of time-horizon invariant correlation structure in financial returns by subtraction of the market mode.

- EconomicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

This work investigates the emergence of a structure in the correlation matrix of assets' returns as the time horizon over which returns are computed increases from the minutes to the daily scale, and finds that the structure of correlations in the overnight returns is markedly different from that of intraday activity.

### Market Microstructure Invariance: Empirical Hypotheses

- Economics
- 2016

Using the intuition that financial markets transfer risks in business time, “market microstructure invariance” is defined as the hypotheses that the distributions of risk transfers (“bets”) and…

### A Probability Metrics Approach to Financial Risk Measures

- Computer Science
- 2016

The aim of A Probability Metrics Approach to Financial Risk Measures is to provide an accessible, technically rigorous yet intuitive, introduction to the theory of probability metrics for the nonspecialist.

### Non-Linear Time Series Invariants to Study Price Manipulation in stock market

- Economics
- 2008

Several studies have found the successive prices at which trades of shares are executed in a stock exchange to form times series with non-linear characteristics. Invariants of a non- linear time…

### The string prediction models as invariants of time series in the forex market

- Computer Science
- 2013

### Risk and asset allocation

- Economics
- 2005

The statistics of asset allocation.- Univariate statistics.- Multivariate statistics.- Modeling the market.- Classical asset allocation.- Estimating the distribution of the market invariants.-…