Examination of implied volatility as a proxy for financial risk

Volatility is an important risk metric that is widely used as an input for models to estimate financial risk or to price derivatives. The VIX is an index derived from S&P 500 options prices and it is designed to provide the market's expected 30-day volatility. We examine the VIX as a proxy for implied volatility and risk. Our studies show that the VIX routinely over-estimates actual volatility in normal times but it underestimates volatility in times of crises. We demonstrate that the level of the VIX does not provide any meaningful answers to the important question of how risk affects future stock returns. We propose a more appropriate use of the VIX and show that a positive trend in the VIX, rather than its level, dramatically improves the forecasts of future stock returns. We also investigate no-arbitrage conditions by inverting the Black-Scholes-Merton model and derive an implied risk-free rate as well as an alternative volatility measure. Our model produces implied rates that are about 130 basis points higher than average risk-free rates. Our alternative measure for the VIX provides better estimates of future realized volatility during times of crises.