Expected move (implied move)

Formula and straddle shortcut

Implied volatility is an annualised standard deviation of returns. Scaling it by the square root of the horizon gives the standard deviation over that horizon, and multiplying by the price turns it into points: EM = S × σ × √(T). In Black-Scholes, an at-the-money straddle is worth about √(2/π) ≈ 0.798 times that amount, which is why the straddle price, or the straddle divided by 0.8, is widely used as an implied move. The straddle has the advantage of using market prices directly, including any smile effect at the money.

Worked example

With the index at 5,000 and implied volatility at 16%, the one-standard-deviation move is 5,000 × 0.16 × √(1/365) = 41.9 points for one day, 110.8 points for a week and 229.4 points for 30 days. On a 100 underlying with 20% volatility, the 30-day at-the-money straddle costs 4.57 against a one-standard-deviation move of 5.73: the ratio is 0.798.

Reading it correctly

• It is a width, not a direction: the band is centred on the forward price.
• Under a normal approximation about 68% of outcomes fall inside ±1 standard deviation; index returns have fatter tails, so larger moves are more frequent than the normal suggests.
• Use the implied volatility of the expiry matching the horizon, not an annual average; before an event, the first expiry after it carries the event's variance.
• Calendar-day and trading-day scaling give different numbers; state the convention.
• The implied move includes a risk premium; realized moves have historically been smaller on average for equity indices, with large exceptions.

In Senzoukria

Senzoukria does not print an expected move. Its GEX module shows the ATM IV of the front expiry and an IV term structure with one at-the-money implied volatility per expiry, which are the inputs of the formula above. Because the curated chains are ETFs such as SPY and QQQ, a move computed on them must be scaled to the futures price before it is drawn on an ES or NQ chart.