Volatility Analytics

Start here, because everything else on this page hangs off one comparison. VIX is what the market expects SPX volatility to be over the next 30 days, quoted as an annualized number. Realized Volatility (RV), also called HV30, is what the market actually delivered. It is computed from the last 30 daily SPX log returns. One is a forecast, the other is a measurement. The gap between them tells you whether fear is priced too high, too low, or about right. Most days that is the first thing I check.

VIX vs. Realized Volatility (SPX 1M)

A common mix-up: VIX is not Black-Scholes IV. It is a model-free weighted variance calculation. The CBOE takes the prices of all listed SPX options (calls and puts, across all strikes), weights each by 1/K² and the interval between strikes, sums them up, and takes the square root. No BSM inversion involved. So VIX captures the full risk-neutral variance surface rather than the ATM vol of a single option.

Rule of 16. To convert VIX to an expected daily SPX move, divide by 16 (the approximate square root of 252 trading days). VIX at 16 implies about a 1% daily move, 20 implies ~1.25%, 32 implies ~2%. It is the fastest mental shortcut I know for sizing positions or setting stop levels.

VIX vs RV: Interactive Time Series

Flip through the three buttons below. Each one is a regime you will actually meet: the quiet grind, the run-up into a known event, and the aftermath of a crash. Watch which line sits on top and how the shaded band flips color.

VIX vs. Realized Volatility: What Each Number Actually Measures

VIX: A Model-Free Measure of Expected 30-Day SPX Variance

VIX is published by the CBOE and represents the market's expectation of SPX volatility over the next 30 calendar days, expressed as an annualized percentage. It is not derived by inverting Black-Scholes on a single option, whatever you may have read elsewhere. It uses a model-free replication formula that aggregates the prices of all listed SPX options across every available strike, puts and calls alike, weighting each by the interval between strikes divided by the square of the strike price (ΔK / K²).

The result is proportional to the risk-neutral expected variance of SPX returns over the next 30 days, a quantity that can be replicated by holding a portfolio of variance swap payoffs across the full strike range. Taking the square root converts it to the familiar annualized vol percentage. Because it spans the entire strike surface rather than a single ATM option, VIX implicitly includes the fear premium embedded in OTM puts. Heavy demand for crash protection drives up put prices, which raises VIX even if ATM vol has not moved at all.

VIX is annualized. The Rule of 16 rescales it:

• Rule of 16 (daily move): VIX ÷ 16 ≈ expected daily 1σ SPX move in %. VIX=16 gives 1%/day, VIX=20 gives 1.25%/day, VIX=32 gives 2%/day
• Exact formula: VIX ÷ √252 = daily 1σ move. √252 ≈ 15.87, rounded to 16 for mental arithmetic
• 30-day expected move: VIX × √(30 ÷ 252). At VIX=20: 20% × 0.345 = 6.9% over 30 days
• Dollar move on SPX at 5,500: 6.9% × 5,500 = ±$380 one-sigma range
• 68% probability the price stays within 1σ, 95% within 2σ, under the log-normal assumption embedded in the formula

Why VIX overstates subsequent RV (structurally, not by accident). VIX was never a neutral forecast. Because it aggregates across the full strike range and OTM puts carry a crash-insurance premium, VIX systematically embeds extra fear on top of the expected realized vol. Portfolio managers need downside protection and will pay above fair value for it; option sellers demand compensation for the risk of a sudden spike. That gap is the Volatility Risk Premium (VRP), the persistent spread between VIX and the 30-day RV that follows. Historically, VIX has exceeded subsequent 30-day SPX realized vol in roughly 70-80% of months, with an average premium of ~3-5 vol points.

Realized Volatility: The Second Moment of the Return Distribution

Realized (historical) volatility is a backward-looking statistical measure calculated from the actual price series. The standard approach uses daily log returns:

Step-by-step: Computing HV30 (30-day Realized Volatility)

1. Log return each day: r_t = ln(P_t / P_t−1). Log returns are approximately normally distributed, and unlike raw % returns they are additive over time
2. First moment (mean): r̄ = (1/n) × Σ r_t, the average daily return. For volatility estimation the mean is often set to zero, because daily drift is negligible relative to daily swings
3. Second moment (variance): σ² = (1/n) × Σ (r_t − r̄)², the average squared deviation from the mean. This is what "second moment" means: the first moment measures where returns are centered, the second measures how spread out they are around that center
4. Standard deviation: σ_daily = √σ². Taking the square root brings the unit back to the same scale as returns (%), so you can read it as a typical daily swing
5. Annualize: HV30 = σ_daily × √252. Multiplying by √252 (trading days per year) scales the daily standard deviation to an annual figure, matching the convention used for IV

The Volatility Risk Premium (VRP): Why VIX > RV Most of the Time

I do not treat the persistent VIX-over-RV gap as a market inefficiency. It is rational compensation driven by two forces. Portfolio managers need crash insurance and pay above fair value for OTM puts, which inflates VIX. Option sellers demand a risk premium for the possibility that realized vol spikes beyond what they priced in. Both forces push in the same direction, structurally lifting VIX above expected future RV.

How big is the effect? Over the long run, VIX has exceeded subsequent 30-day RV in roughly 70-80% of months. The average premium runs about 3-5 vol points (VIX at 18 against realized vol of 14, say). And when it breaks, it breaks hard. March 2020 is the deepest inversion on record: RV exploded past 80% while VIX peaked around 85%, meaning the market barely had time to price in the speed of the move. The VIX−RV spread went deeply negative within days.

Two practical takeaways. First, systematically selling vol (straddles, iron condors, short VIX futures) harvests the VRP, and the premium is structurally real. But drawdowns during VRP destruction events (2018 Volmageddon, March 2020, April 2025) are extreme and demand strict position sizing. Second, watch the spread itself. When VIX−RV compresses toward zero for several consecutive weeks, the vol regime is shifting: either actual volatility is catching up (RV rising) or the fear premium is deflating (VIX falling). Both are worth acting on.

VIX vs. RV Side by Side

Volatility Term Structure

Term structure is ATM implied volatility plotted across expiration dates. It tells you where the market puts its fear on the calendar: near-term or further out.

There are really only three shapes worth memorizing. Contango slopes upward: near-term IV sits below long-term IV. That is the normal, calm state, since more time simply means more uncertainty. Backwardation inverts that. Near-term IV trades above long-term, which only happens when immediate fear is elevated: macro events, FOMC weeks, active sell-offs. The third shape is the event kink, where one specific expiration spikes above its neighbors because a known catalyst (earnings, a Fed meeting, OpEx) is priced into that date and no other.

Term Structure: Interactive Chart

Volatility Skew

If term structure spreads fear across time, skew spreads it across price. Skew shows how IV changes across strike prices for a single expiration. Strikes carry different implied volatilities because the market prices risk asymmetrically, and the shape of that curve tells you which direction it is worried about.

Volatility Smile. Both OTM puts AND calls elevated relative to ATM. This is binary event risk: the market fears a big move but can not decide the direction.

IV Skew: Interactive Chart

Put/Call Ratios

The Put/Call ratio divides total put activity by total call activity, measured either by volume (what traded today) or open interest (what's held overnight). Simple arithmetic, but it is the most direct sentiment read the options market offers.

The levels I anchor to:

• P/C > 1.0: more put activity than calls, meaning bearish sentiment or heavy hedging demand
• P/C < 0.7: call-heavy flow, bullish or speculative
• Above 1.5 gets interesting as a contrarian buy signal. Everyone is already hedged, so the downside is often priced in
• Below 0.4 is the mirror image: excessive call buying, complacency risk

Put/Call Ratio: Interactive Chart