The Move the Market Priced

From an annual number to a band in dollars

Implied volatility is quoted on an annual basis, and an option expires in weeks, so the first step is to scale the number to the life of the contract. Volatility scales with the square root of time rather than with time itself: divide the days to expiry by 365 to get the time fraction about 5.75% for three weeks in the example above, and take the square root, approximately 0.24. Multiply the annualised figure by that and the answer is 12.47%. Applied to an $85 stock that is $10.60, so the one-sigma band runs from about $74.40 to $95.60. The square root is the part that changes how short expiries are read. Quadrupling the time only doubles the expected move, which means the last week of a contract carries a disproportionate share of the daily drama and that a very short-dated option can look trivially cheap while pricing a wider percentage move than a three-month one in the same name. It also means the number is a distribution rather than a promise: one standard deviation covers roughly two thirds of outcomes, so about a third of the time the stock finishes outside the band. A band is not a forecast of the range a stock will trade in, and it is certainly not a ceiling — it is the magnitude of movement the premium is being charged for. That framing is what makes the number useful, because it converts an opinion into a comparison. If your work suggests this catalyst moves the stock around 5% and the market has priced 12.5%, you have found a specific disagreement about the size of the move, and you can act on it — selling the premium, or buying a narrower structure — knowing exactly what you are disagreeing with. If the last three of these events moved 20% and the market has priced 12.5%, the same arithmetic points the other way. Either conclusion can be wrong, but it can be checked afterwards, which is the property an intuition about “expensive options” does not have. One expiry, worked — 21 days as a fraction of a year: 21 ÷ 365 = 5.75% · Square root of the time fraction: √0.0575 ≈ 0.2399 · Expected move: 52% × 0.2399 ≈ 12.47% ← · In dollars on an $85 stock: $10.60 · One-sigma band: $74.40 to $95.60 ← The same calculation works backwards and is worth doing once: a band that looks absurdly wide for a stable utility is the market saying something, and a band that looks narrow for a biotech into trial data is usually a sign the expiry sits before the event rather than after it.

What the band does not tell you

A priced move is symmetric, and real events are not. The market charges one number for the size of the move, and the skew — the fact that out-of-the-money puts usually cost more than equally out-of-the-money calls — is the part of the curve that expresses which direction the market fears. A learner who reads only the expected move has the magnitude and not the tilt, which is why the same 12.5% band can precede a stock that the options market expects to fall harder than it rises. The second limit is that implied volatility is a mixture rather than a pure forecast of the event. When an expiry spans an earnings date and several quiet weeks, the annualised figure is a blend of a small number of violent days and a majority of ordinary ones, and unblending it requires the term structure — comparing the expiry that contains the event with the one after it. That is a refinement rather than a first step, but the failure it prevents is common: a learner computes a band, compares it with a normal week’s movement, concludes the premium is expensive, and sells a straddle into a catalyst that the premium was correctly charging for. The third limit is the one with the largest consequences: a view about direction is not a view about size, and option positions need the second one. Being right that a stock rises is compatible with losing money on a long call if the rise is smaller than the move that was priced, and being right that a stock falls is compatible with losing money on a long put for the same reason. The expected move is the number that lets a learner separate those two questions before the position exists, which is why it sits between the Greeks and the income strategies. • The band is symmetric, so read the skew separately for the direction the market fears. • An expiry that spans an event blends violent and quiet days into one annualised figure. • Compare the expiry containing the event with the one after it to unblend the term structure. • A direction view and a size view are different forecasts; options pay on the second. The most expensive version of this mistake is selling short-dated premium into a scheduled catalyst because the annualised volatility looked high. The number is high because the event is in the expiry — which is the one case where the premium is doing its job rather than overcharging.

The band is a price, not a probability

The expected move is derived from an option price, which means it inherits every assumption embedded in that price. The cleanest way to see it is through the position that isolates it: an at-the-money straddle — buying the call and the put at the same strike — pays off in proportion to how far the stock moves, in either direction. There is a widely used approximation that the straddle price is about **eighty percent** of the one-standard-deviation move, which is why practitioners often quote the straddle and think of it as the market’s move. The two numbers describe the same thing, and the eighty-percent relationship is what makes the arithmetic in this lesson consistent with the price you actually pay. The first thing the band is not is a probability statement about a range. Converting an implied volatility into a dollar interval and calling it the one-sigma band implies a specific distribution — returns that are symmetric and normal, so that roughly two thirds of outcomes fall inside and about one in twenty lies beyond two standard deviations. Equity returns are not normal. They have **fatter tails** and they are slightly skewed: extreme moves happen more often than the normal distribution predicts, and the market knows this, which is why it charges more implied volatility for out-of-the-money options than the at-the-money price would suggest. So an expected move computed at the money **understates** the frequency of large outcomes, and the band should be read as a centre of gravity rather than as a fence. The second thing it does not tell you is direction, and the skew is where the market expresses its asymmetry. Downside puts usually carry higher implied volatility than equivalent upside calls, which means the band built from the at-the-money price is the average of two different distributions and neither of them is the one the market is charging for. When you compare your own view of an event to the market’s, the comparison that matters is not “the band is three percent and I think it moves five percent” but which options are priced richly — a view that the market is overpaying for downside protection is a different trade from a view that the move will be large, and the expected move does not distinguish them. One number, three different statements — At-the-money straddle price: The market’s price for movement in either direction — a cost, not a forecast · The one-sigma band from implied volatility: Depends on assuming normal returns; fat tails make it too narrow · The skew across strikes: Where the market puts its asymmetry — and what the at-the-money band averages away ← A useful habit before an event: write down your own expected move first, then read the implied move, then decide which strikes are cheap. Comparing a view to a band is a start; comparing it to a skew is the actual analysis.

Unblending the event: variance adds, so subtract it

A band computed from one expiry answers a mixed question when that expiry contains a catalyst. The read before this one said the annualised figure is a blend and that unblending needs the term structure; here is the arithmetic that does it. The trick is that **variance** — the square of volatility — is additive across non-overlapping stretches of time, while volatility itself is not. Take an expiry that sits before the event, and one that sits after it, and the second expiry’s total variance is the first expiry’s variance plus whatever the market has priced for the stretch between them, which contains the event. Subtract and you have the event’s own contribution in variance units; take the square root and it is a move in percent. Before doing it, convert every expiry to a fraction of a year and every volatility to its square. Worked through with two expiries on the same $50 stock. An expiry three days out, before the report, quotes 30% implied; an expiry twelve days out, after it, quotes 45%. The three-day variance is 0.30 squared times 3/365, which is 0.00074; the twelve-day variance is 0.45 squared times 12/365, which is 0.00666. The difference, 0.00592, belongs to the nine days between the expiries and is dominated by the event, and its square root is 7.7%. So the market is charging a 2.7% one-sigma move for the three days before the report and an incremental 7.7% for the window containing it — which is a number that can be compared with what the stock did on its last eight reports, and with your own view. The mixed reading was 8.2% for the whole twelve days; the unblended reading is 7.7% for the event plus 2.7% of ordinary movement, and the separation is what lets you say whether the event is cheap or expensive rather than whether the option is. Three caveats keep the calculation honest. First, the subtraction must produce a positive number; if the later expiry implies less total variance than the earlier one, something else is in the data — a dividend, a half-day, a stale or wide quote, or an event in the intermediate window that the term structure has already priced — and the fix is to check the quotes before trusting the arithmetic. Second, the estimate is highly sensitive to both inputs, since it is a difference of squares: a material error in either implied volatility moves the answer a long way, so use mid quotes and comparable strikes rather than a bid that flatters the direction you want. Third, the result is still a price rather than a forecast, and the skew means the number extracted from at-the-money options is an average across two directions the market does not price identically. What the method gives you is not certainty about the event; it is the ability to separate what the market is charging for the report from what it charges for an ordinary week — which is the difference between “options are expensive” and “this particular event is priced at twice its recent average”. Unblending one report on a $50 stock — Front expiry, 3 days, 30% IV: Variance = 0.30² × 3/365 = 0.00074 → a 2.7% one-sigma move · Back expiry, 12 days, 45% IV: Variance = 0.45² × 12/365 = 0.00666 → 8.2% over the whole period · Difference, the event window: 0.00592 → a 7.7% incremental one-sigma move ← · Compare with the last eight reports: Turns “options are expensive” into “this event is priced above its own history” ← The same subtraction runs in reverse: if you think the event is overpriced, the trade is to sell the expiry that contains it and own the one that does not — a calendar spread, and the arithmetic that sizes it is the variance difference you just computed.

Sources

• Volatility, expected move and the square-root-of-time ruleHull, “Options, Futures, and Other Derivatives”
• Interpreting implied volatility as a priced distributionNatenberg, “Option Volatility and Pricing”
• Event risk and the term structure of implied volatilityCBOE Education — Volatility Around Events