How to calculate an earnings expected move from the straddle

The expected move for an earnings report is read off the options market: take the at-the-money straddle for the first expiration after the report, add the call and the put, and treat the total as a plus-or-minus dollar range around today's price. A stock at $250 with a $13.57 straddle is expected to move about $13.57 either way.

What that range means is where most explanations go wrong. The common rule of multiplying the straddle by 0.85 is usually described as a one standard deviation, 68% range. Under the model the option price is built on, it is closer to a coin flip.

Three ways to calculate the expected move

The straddle price

Add the mid prices of the at-the-money call and put for the first expiration after the earnings date. The result is a dollar amount. Divide by the stock price for a percentage. This is the version most brokers and screeners show, because it needs no model at all: it is just what the market charges to own the move.

Implied volatility

Take the implied volatility of that same expiration and scale it to the time remaining: stock price times implied volatility times the square root of days to expiration over 365. This gives the one standard deviation move directly, under the lognormal model that implied volatility comes from. Our implied volatility term structure post covers where that number comes from and how it differs across expirations.

The 0.85 rule

Multiply the straddle by 0.85. Many sources present this as an adjustment that turns the straddle into a one standard deviation move. The arithmetic below says it does something else.

What share of outcomes the band covers

For an at-the-money straddle with little time left, the Black-Scholes price is very close to the stock price times implied volatility times the square root of time, times the square root of 2 divided by pi. That last factor is about 0.798. In plain terms, the straddle is worth about 80% of a one standard deviation move, because what it pays is the average size of the move, and the average size of a normally distributed move is 0.8 of its standard deviation.

That gives the coverage of each band directly, under the distribution the option price assumes:

• Plus or minus one straddle: about 57.5% of outcomes.
• Plus or minus 0.85 times the straddle: about 50%.
• Plus or minus one standard deviation, about 1.25 times the straddle: about 68%.

These figures hold up when you check them directly. Pricing one-week at-the-money straddles with Black-Scholes at implied volatilities of 40%, 80% and 150%, and measuring each band against the lognormal distribution, the ratio of straddle to one standard deviation stays between 0.796 and 0.798 in all three, and the 0.85 band covers between 50.2% and 50.4% every time.

None of this makes the 0.85 rule useless. It is a convention, and a consistent convention is fine. The mistake is labeling it on a chart as a 68% range, because readers will then treat a move outside it as a two-in-three surprise when, by the market's own pricing, it is closer to an even bet.

A worked example

The numbers are illustrative arithmetic, not a quote for any real stock. A $250 stock reports in four days, with the first post-earnings expiration four days out and implied volatility of 65%, with rates set to zero to keep the example clean.

• Straddle: $13.57, or 5.43% of the price. Band: $236.43 to $263.57, covering 57.5% of outcomes under the model.
• 0.85 rule: $11.53. Band: $238.47 to $261.53, covering 50.3%.
• One standard deviation from implied volatility: $17.01, or 6.80%. Band: $232.99 to $267.01, covering 68.3%.

Three different ranges, all legitimately called "the expected move" somewhere. Whichever one you chart, write which it is in the legend.

Why real earnings moves do not follow the model

Two caveats belong in the chart's notes. Both are reasons to be careful about reading the band as a probability.

The first is that the straddle is not pure earnings. An expiration four days out still carries ordinary day-to-day volatility on top of the event. The further out the expiration, the more of the straddle is normal time value rather than the report itself, which is why you use the first expiration after the date and not a monthly option two weeks later.

The second is shape. An earnings move is a jump, and the distribution of jumps is often closer to two humps (it beat, it missed) than to one bell. The coverage figures above hold under the lognormal assumption the price is built on. Real outcomes can land outside the band more often or less often than that, and the only honest way to know for a given stock is to count its own history. Our return distribution post covers how to look at that history before you trust a normal curve drawn over it.

How to chart the expected move

The standard view is bands on price: the stock's daily closes, with the expected move drawn as a shaded range starting on the report date and ending at the expiration used to price it.

• Anchor the band to the close before the report, since that is the price the straddle was measured against.
• Draw the band as a box that ends at the expiration date. A band that extends past the expiration is claiming something the option never priced.
• Plot past reports on the same chart: each earlier expected move as a band, with the actual move marked as a dot. After eight or twelve quarters you can see whether this stock usually stays inside its band or regularly breaks it, which is the one piece of evidence that tells you how to read the next band.
• Label the method in the legend: straddle, 0.85 rule, or one standard deviation from implied volatility.

If you are sourcing the option prices yourself, where to get free options chain data covers the free routes and where they are delayed. The IV rank and IV percentile post is a useful companion view: it shows whether the implied volatility behind this quarter's straddle is rich or cheap against the past year.

[QUADESTO-EMBED: Daily closes for one stock with the pre-earnings straddle band shaded from the report date to the first post-earnings expiration, the previous eight reports shown as bands with the realized move as a dot, and a toggle between straddle, 0.85 rule and one standard deviation bands]

Where Quadesto fits

Quadesto turns your own price and options data into branded finance charts like this one, shared as a link, embedded as an iframe, or exported as an image. Whatever you build it with, write the method into the legend so a reader knows which expected move they are looking at.