Implied vs. realized volatility

Implied volatility is extracted from option prices and reflects expected movement, protection demand, skew, liquidity, and risk premia.

Realized volatility is measured afterward. A valid comparison matches horizons: today's 30-day VIX versus the S&P 500's following 30 days.

• Volatility spread VIX minus subsequent realized vol.
• Variance risk premium Academic work measures volatility squared.

The CFA study reports 19.59% average VIX versus 15.50% subsequent realized volatility, an average gap of 4.09 points. Medians were 17.77% and 13.12%.

VIX was often, but not always, higher. Realized volatility temporarily overtook VIX at the start of 2008 and COVID; VIX later overshot. Those shock periods are the risk carried by option sellers.

Carr and Wu synthesize a variance swap rate from a broad option portfolio and compare it with realized variance after 30 days.

Long-side definition: realized variance minus swap rate. A negative number means variance buyers paid more than was later realized.

• Data Five indexes and 35 stocks, roughly 1996 to early 2003.
• SPX Realized variance 4.07, swap rate 6.81, difference −2.74.
• Robust Strongly negative S&P and Dow premia in bullish and bearish subsamples.
• Single stocks Much less uniform than indexes.

Investors buy options as insurance against crashes and volatility jumps. That protection is valuable because index volatility often rises when prices fall.

Option sellers receive premium but carry short-gamma, short-vega, and tail risk. They are paid for bearing adverse risks, not for knowing the future better.

VIX minus realized volatility is not the direct P/L of a short put or iron condor. Strike, skew, expiration, path, fees, and management determine results.

• Crashes Realized volatility can sharply exceed IV.
• Negative convexity Short-gamma losses accelerate.
• Return shape Many small gains may face a few severe losses.

1. Match IV and RV horizons.
2. Read VIX, VVIX, and term structure together.
3. Account for skew and event risk.
4. Prefer defined-risk structures such as a bull put spread.
5. Size for multiple simultaneous losses.

The historical gap is a starting point, not a profit guarantee.

Sources: CFA Institute and Carr & Wu.