Implied vs. realized volatility

Implied volatility is extracted from current option prices. It is not a pure point forecast. It belongs to a risk-neutral valuation that also reflects hedging demand, skew, liquidity, and risk premia.

Realized volatility is calculated afterward from actual underlying returns. A valid comparison uses matching horizons: today's 30-day VIX should be compared with annualized S&P 500 volatility over the following 30 days, not with volatility over the previous month.

• IV / VIX Forward-looking risk valuation derived from option prices.
• Realized volatility Ex-post movement measured from underlying returns.
• Volatility spread A simplified measure: VIX minus subsequent realized volatility.
• Variance risk premium Academic work usually measures variance, meaning volatility squared.

The CFA analysis uses the full VIX history from 1990 and compares each observation with the S&P 500's next 30 days of realized volatility. Across the reported 35-year period, the average VIX was 19.59%, while subsequent realized volatility averaged 15.50%. The average gap was therefore 4.09 volatility points.

The medians tell the same story: 17.77% for VIX versus 13.12% for realized volatility. During the quieter 1990-1996 segment, VIX often exceeded subsequent volatility by roughly five to seven points.

But not always: At the start of the 2008 financial crisis and the COVID shock, realized volatility initially rose faster than VIX. VIX then overshot after the shock and stayed elevated while actual movement declined. VIX is therefore neither a perfect forecast nor permanently too high.

Peter Carr and Liuren Wu go beyond a simple VIX comparison. They synthesize a variance swap rate from a broad strip of calls and puts. That rate represents risk-neutral expected variance. At the end of the 30-day horizon, they compare it with actual realized variance.

The sample covers five equity indexes and 35 individual stocks over roughly seven years from 1996 to early 2003. For SPX, average annualized realized variance was 4.07 versus a synthetic swap rate of 6.81; the realized minus swap difference was −2.74. The paper finds strongly negative premia for the S&P 500, S&P 100, and Dow Jones, while all five index averages were negative.

Individual stocks were less uniform. Only seven of 35 had a significantly negative premium at the 95% level under the raw-difference measure; 23 of 35 were significant using log premia. The index effect was therefore clearer and more stable than the result for every single stock.

• Robustness The index conclusion survived bid-, mid-, and ask-based option inputs.
• Market regimes S&P and Dow premia stayed negative in both bullish and bearish subsamples.
• Systematic factor Stocks with higher variance beta to SPX tended to have more negative premia.
• Not fully explained CAPM, size, value, and momentum factors explained only a small part.

Investors do not buy options only because they forecast a move. They buy insurance against crashes, volatility jumps, and unstable portfolio values. Equity-index volatility often rises sharply when prices fall, so long options or long variance can become especially valuable in bad states of the world.

The option seller takes the other side: premium is received today, but short-gamma, short-vega, and tail risk remain. Because investors are willing to pay for this protection, implied volatility can often exceed the ordinary movement that is later realized.

This is the structural edge: option sellers sell insurance, not merely a volatility forecast. Carr and Wu interpret the negative long-variance return as compensation to short variance for carrying adverse volatility shocks.

A higher average VIX does not mean every option is overpriced or every short trade is profitable. A 4.09-point average volatility gap is not the direct return of an iron condor, short put, or covered call. Strike, skew, expiration, path, delta hedging, fees, and management determine actual P/L.

• Gap and crash risk Realized volatility can suddenly exceed implied volatility by a wide margin.
• Negative convexity Short-gamma losses accelerate during a large underlying move.
• Vol-of-vol Rising IV can reprice a short option before theta has time to help.
• Left-skewed returns Many small gains can be offset by a small number of severe losses.
• Implementation costs Spreads, slippage, margin, and taxes reduce the theoretical premium.

Those unpleasant loss states are precisely why the premium can persist. If it were risk-free, competition would be expected to remove it quickly.

1. Match horizons: Compare 30-day IV with subsequent 30-day RV, not an arbitrary historical window.
2. Classify the regime: Read VIX, VVIX, and term structure together.
3. Respect skew and event risk: Index puts often contain more insurance premium than symmetric calls.
4. Prefer defined risk: Consider structures such as bull put spreads instead of unlimited naked short options.
5. Control size: Margin should withstand a volatility jump and several losing trades at once.

The historical spread is a useful starting point for an option-selling framework. It does not replace trade selection or risk management and does not guarantee a positive return in any individual month.

Primary sources: CFA Institute, How Well Does the Market Predict Volatility? and Carr & Wu, Variance Risk Premiums.