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Implied vs. Realized Volatility: A Valid Comparison

For educational purposes only; not investment advice.

Direct answer

Section titled “Direct answer”

Implied volatility (IV) is an annualized volatility input inferred from an option price at a particular time. Realized volatility (RV) is an annualized statistic calculated from returns that actually occur during a defined interval. IV is known at the start but depends on prices and a model; the matching future RV is unknown until the interval ends.

A valid comparison fixes the same underlying, dates, horizon, sampling frequency, annualization rule, and preferably a relevant strike or model-free variance measure. A current 30-day IV cannot be tested against last year’s RV as if both described the same period.

What the comparison does—and does not—measure

Section titled “What the comparison does—and does not—measure”

At time t, an option model solves for IV from the option quote. After the horizon, one simple close-to-close RV estimate is:

RV = standard deviation of daily returns × √252

This is only one RV convention. Researchers and platforms may use realized variance, intraday returns, range data, different demeaning rules, or different trading-day counts. The intended measure must be recorded before comparing results.

Because option value is nonlinear in volatility, analysis often compares variance, the square of volatility:

implied variance = IV²

realized variance = RV²

IV contains more than a neutral point forecast. Option supply and demand, compensation for bearing jump and volatility risk, skew, rates, dividends, and model assumptions can all affect it. Academic literature documents variance risk premiums, but their sign and size are not guaranteed for every asset, strike, or period.

The trading exposure also matters. An unhedged call or straddle combines direction, convexity, time decay, and volatility. A dynamically Delta-hedged option more directly isolates realized price variation, but its result depends on hedge timing, gaps, transaction costs, financing, discrete rebalancing, and changing Greeks. “Long volatility” is therefore not a single payoff.

Matched-horizon example

Section titled “Matched-horizon example”

On April 1, suppose a 30-calendar-day at-the-money option measure shows IV of 36%. The comparison interval is fixed in advance: April 1 through May 1, using 21 adjusted close-to-close log returns and annualizing with 252 trading days.

After May 1, those returns produce a daily standard deviation of 1.512%:

RV = 1.512% × √252 = 24.00%

The volatility difference is 36% - 24% = 12 points. The corresponding annualized variance figures are:

0.36² = 0.1296

0.24² = 0.0576

implied variance - realized variance = 0.0720

This ex-post observation says the selected implied input exceeded the subsequently measured close-to-close variability. It does not, by itself, calculate a trade’s profit.

Suppose an unhedged at-the-money straddle was sold for $8.20 with a 100-share multiplier. If the stock finishes $3.00 from the strike, its expiration payoff is $3.00, and gross profit is ($8.20 - $3.00) × 100 = $520. If it finishes $10.00 from the strike, gross result is ($8.20 - $10.00) × 100 = -$180. Fees, exercise, assignment, and any early exit are excluded. RV alone does not specify the terminal distance or the path, so it cannot replace the payoff calculation.

Risks and comparison checklist

Section titled “Risks and comparison checklist”
  • Horizon mismatch: compare the IV observation with RV over the same subsequent dates, not merely a similarly named historical window.
  • Surface mismatch: one strike’s IV includes skew; an ATM quote, volatility index, and variance-swap rate are not interchangeable.
  • Estimator mismatch: close-to-close RV can omit intraday movement and can differ from realized variance or range estimators.
  • Path and jump risk: one gap can dominate option P&L and a discretely hedged position even when a summary RV looks moderate.
  • Execution drag: bid-ask spreads, commissions, hedge slippage, borrow, and financing can consume a statistical spread.
  • Nonlinear exposure: Delta, Gamma, Theta, and Vega change through time; entry IV minus final RV is not a P&L formula.
  • Tail and assignment risk: short options can create losses, margin demands, early assignment, and stock positions beyond the premium received.

Record the IV timestamp and price side, strike and expiry, event calendar, RV formula and dates, hedge rule, cash flows, costs, and final payoff before attributing a result to volatility.

Common misconceptions

Section titled “Common misconceptions”
  • “IV is the market’s exact volatility forecast.” It is a model-implied price input that may include risk premiums and technical effects.
  • “RV is known when the option is purchased.” Past RV is known; the future RV matching the option horizon is not.
  • “IV above RV proves options were overpriced.” The comparison omits payoff shape, hedging, jumps, skew, and costs.
  • “A volatility seller profits whenever IV exceeds RV.” The actual contract and path determine profit and loss.
  • “Volatility points and variance are the same.” 36% - 24% and 0.36² - 0.24² are different quantities.
  • “Low past RV makes a future jump unlikely enough to ignore.” Historical calm cannot remove event or tail risk.
Section titled “Related topics”

Authoritative sources

Section titled “Authoritative sources”