Kyle WisniewskiEquity Research Lab · Instrument 05 of 07
Expected move
The one-standard-deviation move a volatility implies over a horizon, from listed options where a licensed source exists and from realized history otherwise, always labelled.
Traders quote "the expected move" as a single number: how far the stock is likely to travel, up or down, over the next month. The number is only a volatility scaled to a horizon, and its meaning depends entirely on where the volatility came from. This instrument computes it and insists on saying which.
What it measures
Annualized volatility times the square root of the horizon in years gives the one-standard-deviation move as a fraction of the price; multiplied out, it is a band around the current price. When a licensed source of listed implied volatility exists, the band reflects what option buyers are paying for; when it does not, the band is built from realized volatility over several trailing windows, and the artifact labels it as such. The Black–Scholes relationship between option prices and volatility runs underneath: it is how an implied volatility is recovered from a price, and how a straddle cross-check is made.
Assumptions
Returns are lognormal within the horizon, so the band is symmetric in log terms. Volatility is constant over the horizon. Neither is true in the buildout, where volatility clusters and earnings days dominate the month; the band is a scale, not a forecast. The realized-volatility basis uses close-to-close returns over twenty-one, sixty-three, and two hundred and fifty-two days plus an exponentially weighted estimate, all published for comparison.
When it misleads
A realized-volatility band can be quiet just before an event the options market has already priced, which is why the basis is labelled and why the memo says when an earnings date falls inside the horizon. A one-sigma band contains the outcome about two thirds of the time by construction; the tails are where the thesis is tested, and this instrument does not describe them.
How the lab uses it
The expected move gives the reader a sense of scale: whether a thesis that needs a fifty percent revaluation is asking the stock to do something it does several times a year or something it has never done. It also sizes the disconfirming evidence, since a move inside the band is noise and a move outside it is news. The demo below draws a seeded fan of price paths at a chosen volatility so the band can be seen against the paths it summarizes.
Scale a volatility to a horizon
Illustrative inputs — not a company's figuresChange the volatility or the horizon and watch the band and the fan respond. The straddle line is the desk's rule of thumb; the Black–Scholes round trip shows the price-to-volatility inversion the lab uses when it has option prices.
- One-sigma move11.5%σ·√(days/365)
- Straddle approximation9.1%0.7979·σ·√T, the expected absolute move
- At-the-money call / put$4.73 / $4.40Black–Scholes at the stated rate
- Volatility recovered from the call40.00%37 bisection steps
Read the figure as a table
| Point | +1σ band | −1σ band | path 1 | path 2 | path 3 | path 4 | path 5 | path 6 | path 7 | path 8 | path 9 | path 10 | path 11 | path 12 | path 13 | path 14 | path 15 | path 16 | path 17 | path 18 | path 19 | path 20 | path 21 | path 22 | path 23 | path 24 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| day 0 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 | $100.00 |
| day 6 | $105.26 | $95.00 | $99.23 | $103.59 | $96.15 | $110.18 | $89.71 | $108.95 | $97.21 | $101.50 | $105.15 | $99.58 | $96.17 | $107.09 | $102.44 | $101.56 | $98.11 | $96.60 | $97.33 | $94.97 | $94.36 | $113.97 | $105.97 | $101.97 | $94.23 | $101.09 |
| day 12 | $107.52 | $93.00 | $105.61 | $106.82 | $91.46 | $111.62 | $90.09 | $112.30 | $90.74 | $108.22 | $106.39 | $100.25 | $96.62 | $102.45 | $103.25 | $100.43 | $88.28 | $96.24 | $94.01 | $96.60 | $97.88 | $103.57 | $105.64 | $111.73 | $102.88 | $99.62 |
| day 18 | $109.29 | $91.50 | $107.07 | $107.75 | $95.94 | $103.31 | $88.19 | $108.43 | $97.70 | $116.67 | $107.17 | $104.77 | $91.56 | $98.97 | $105.21 | $100.80 | $85.91 | $103.80 | $89.50 | $96.28 | $92.00 | $98.00 | $106.35 | $113.21 | $105.23 | $95.85 |
| day 24 | $110.80 | $90.25 | $102.75 | $109.14 | $90.63 | $102.71 | $80.21 | $117.65 | $105.16 | $121.89 | $101.29 | $107.66 | $92.53 | $110.83 | $98.67 | $100.84 | $87.11 | $96.61 | $85.25 | $97.28 | $93.82 | $97.63 | $103.66 | $120.13 | $114.52 | $94.59 |
| day 30 | $112.15 | $89.17 | $98.70 | $106.18 | $95.57 | $97.63 | $82.60 | $122.26 | $99.66 | $124.71 | $98.58 | $107.49 | $94.72 | $114.27 | $96.42 | $109.31 | $82.99 | $101.58 | $89.16 | $87.04 | $96.34 | $87.71 | $101.50 | $114.30 | $120.71 | $104.05 |
At 40% annualized volatility the one-standard-deviation move over 30 days is 11.5%, a band from $88.53 to $111.47; 14 of 24 seeded paths finish inside it.