Market instability and the size-variance relationship

Area of Science:

• Quantitative Finance
• Financial Market Analysis
• Systemic Risk Modeling

Background:

• Mutual fund behavior exhibits complex dynamics not fully captured by traditional models.
• Understanding the relationship between fund size and growth rate volatility is crucial for financial stability.
• Periods of market crisis highlight the need for robust risk assessment tools.

Purpose of the Study:

• To investigate mutual fund behavior using a stochastic proportional growth model.
• To analyze the size-variance relationship of fund growth rates and its implications during crises.
• To identify indicators for monitoring financial market instabilities and systemic risk.

Main Methods:

• Application of a stochastic model of proportional growth to mutual fund data.
• Statistical analysis of the variance of funds' growth rates in relation to fund size.
• Examination of volatility changes during crisis periods.

Main Results:

• The negative dependence of growth rate variance on fund size follows an approximate power law.
• During crises, the largest funds exhibit increased growth rate volatility compared to mid-sized funds.
• Growth rate volatility shows a weak dependence on fund size, challenging diversification benefits for large funds.

Conclusions:

• A lower and flatter slope in the size-variance relationship indicates systemic structure.
• The slope of the size-variance relationship serves as a synthetic indicator for market instability.
• Findings question the assumed benefits of diversification for larger mutual funds in volatile markets.