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A Market Volatility Factor Model

Posted in Volatility Effects

How much of the variation in stock returns flows from actual (realized or backward-looking) and implied (forward-looking) market volatilities? In the January 2010 version of his paper entitled “Option Implied Volatility Factors and the Cross-Section of Market Risk Premia”, Junye Li investigates the effectiveness of a three-factor model of stock returns based on market return (beta), diffusion volatility (moderate and persistent component) and jump volatility (large and mean-reverting component). The author also examines how the value premium and size effect relate to the two volatility factors and how relying only on realized market volatility affects results. Using weekly (Wednesday) data for the S&P 500 Index, S&P 500 Index options (filtering out options with extremely long/short durations, extreme moneyness and low activity) and the S&P 500 Volatility Index (VIX) spanning January 1997 through September 2008 (608 weeks), he concludes that:

  • In general, higher (lower) market volatility factors based on both realized and implied volatilities relate to lower (higher) returns for individual stocks. In other words, assets with high sensitivity to these market volatility factors tend to command high risk premiums. The regression-derived impact of diffusion volatility (-0.73%) is larger and statistically more significant than that of the jump volatility factor (-0.22%), indicating that investors fear persistent volatility more than volatility shocks.
  • Using market volatility factors derived from both realized and implied volatilities, the value premium relates mainly to the diffusion factor, while the size effect relates to both market volatility factors. On average:
    • The diffusion volatility risk premium is 0.54% (0.12%) per month on value (growth) stocks.
    • The diffusion volatility risk premium is 0.40% (0.09%) per month on small (big) stocks
    • The jump volatility risk premium is 0.12% (-0.01%) per month on small (big) stocks.
  • Results based only on realized (backward-looking) volatility differ from those based on both realized and implied volatilities, sometimes conflicting and often statistically insignificant.

The following figure, taken from the paper, compares the diffusion and jump market volatility factors, extracted from S&P 500 Index options and VIX, over the entire sample period. Results suggest that the two components of market volatility should affect investors differently. The jump volatility factor spikes during the Asian financial crisis, the Russian financial crisis and the failure of Long-Term Capital Management.

In summary, evidence suggests that investors may be able to exploit market volatility derived from forward-looking (implied volatility) measures, especially the persistent diffusion volatility component.

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