Market instability and the size-variance relationship

Sergey V Buldyrev,Andrea Flori,Fabio Pammolli

doi:10.1038/s41598-021-84680-1

Sergey V Buldyrev, Andrea Flori + Show 1 more

Open Access

https://doi.org/10.1038/s41598-021-84680-1

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Abstract

We show that some key features of the behavior of mutual funds is accounted for by a stochastic model of proportional growth. We find that the negative dependence of the variance of funds’ growth rates on size is well described by an approximate power law. We discover that during periods of crisis the volatility of the largest funds’ growth rates increases with respect to mid-sized funds. Our result reveals that a lower and flatter slope provides relevant information on the structure of the system. We find that growth rates volatility poorly depends on the size of the funds, thus questioning the benefits of diversification achieved by larger funds. Our findings show that the slope of the size-variance relationship can be used as a synthetic indicator to monitor the intensity of instabilities and systemic risk in financial markets.

Highlights

When market prices would have eventually rebounded. This behavior seems more feasible for larger funds, whose intervention in the allocations might have a relevant impact on stock prices. To verify if this behavior can have a real effect, we exclude from the analysis of growth rates those funds whose equity exposure at the beginning or the end of the quarter constitutes less than 98% of the total value of the fund or more than 102% after removing such observations, the increase of the variance for large funds during the crisis period disappears and the size-variance relationship can be better fitted by the power law σr = S−β
The assumption about the absence of correlations between the growth rate of units is clearly violated in the mutual fund industry
We observe that the impact of the changes of the number of shares of stocks held in the portfolios is much greater than the fluctuations in stock prices, dominating the variations of portfolios’ market values

Summary

Introduction

Variations in the slope of the size-variance relationship can relate, for instance, to a change in the stock price correlations and/or to a change in the investment behavior of both fund managers and retail investors which modify portfolio exposures.

Results

Conclusion