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Asymmetric Volatility and Risk in Equity Markets

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What they found

Stock volatility rises more after price drops than after equal-sized rises. Two explanations compete: the leverage effect (a falling stock price raises the firm's debt-to-equity ratio, making equity riskier) and volatility feedback (if expected volatility rises, required returns rise and prices must fall now). Using Japanese market and portfolio data, the authors found that the leverage effect alone cannot explain the magnitude of the asymmetry and that volatility feedback plays a major role, with the asymmetry being mostly a market-wide rather than firm-level phenomenon.

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

Margin and leverageA small deposit controlling a much larger position, and the point at which losses trigger a margin call.Position you controlnotional value $100,000your margin deposit: $5,000$100,000 / $5,000 = 20:1 leverageYour deposit absorbs every dollar of loss$5,000$2,500$0Equity leftMARGIN CALLequity has fallen to $2,5000%1%2%2.5%3%4%5%How far the price moves against you
Margin and leverage. A $5,000 deposit can control a $100,000 position, which is 20:1 leverage. Because the loss is measured on the full $100,000, a 2.5% move against you halves the deposit and brings a margin call, and a 5% move uses all of it.

What you can use

  • Volatility spikes on the way down and fades on the way up; risk models and position sizes should treat declines as more dangerous than rallies of equal size.
  • The asymmetry is largely market-wide, which is why index option skew is steeper than single-stock skew.
  • Rising expected volatility itself pushes prices down, so a volatility spike is not just a symptom of a sell-off but part of its cause.

Caveats

Japanese data from 1985 to 1994; technical econometric modeling. Both explanations have empirical support and the debate continues.

Tags: volatility, leverage-effect, asymmetry, volatility-feedback

Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.