A Leverage-Based Measure of Financial Instability

We employ a model of leverage-induced explosive behavior in financial markets to develop a measure of financial market instability. Specifically, we derive a quantitative condition for how large levered investors can become relative to the whole market before the demand curve for securities suddenly becomes upward-sloping and small price declines cascade as levered investors are forced to liquidate. The size and leverage of all levered investors and the elasticity of demand of unlevered investors define the minimum market size for stability (or MinMaSS), the smallest market size that can support a given group of levered investors. The ratio of actual market size to MinMaSS, termed the instability ratio, can give regulators and policymakers advance warning of financial crises. We apply the instability ratio in an investigation of the 1998 demise of the hedge fund Long-Term Capital Management. We find that a forced liquidation of the fund threatened to destabilize some financial markets, particularly the markets for bank funding and equity volatility