Expected Move: Straddle Formula, Implied Volatility and Limits

The expected move is the size of price move that options are pricing in by a given expiry. The standard measure is the cost of an at-the-money straddle (one call plus one put at the current price) as a share of the stock price. Vyreon reports it for the next expiry and for the expiry nearest 30 days.

Expected Move Formula

expected move = (call price + put price at the current price) ÷ stock price

A straddle pays off when the price moves far enough in either direction, so its cost is the market's price for movement through expiry, with no view on direction.

Illustrative example: a stock trades at $100. The at-the-money call costs $2.40 and the put costs $2.20. The straddle costs $4.60, so the expected move is 4.6%, or about ±$4.60 by expiry.

Expected Move And Implied Volatility

The straddle and implied volatility describe the same pricing. For an at-the-money straddle, a standard approximation is:

straddle ÷ price ≈ 0.8 × σ × √t

where σ is the annualized implied volatility and t is the time to expiry in years. The 0.8 comes from √(2/π) ≈ 0.798, the average size of a normally distributed move measured in standard deviations.

Illustrative example: IV of 20% over 30 days gives σ√t = 20% × √(30/365) ≈ 5.7%, and 0.8 × 5.7% ≈ 4.6%. So a one-standard-deviation move (5.7%) is larger than the straddle-based expected move (4.6%). Both numbers are quoted as an "expected move", so check which one a source is quoting.

How Vyreon Measures It

• Prices: closing midpoints, (bid + ask) ÷ 2, of the call and the put.
• At the current price: the straddle cost is linearly interpolated between the listed strikes on either side of the day's closing price. If that is not possible, the nearest strike within 2% of the price is used.
• Two horizons: the first listed expiry after today, and the expiry nearest 30 calendar days that is at least 7 days out. Each is shown with its expiry date and days remaining.
• Units: the straddle cost in dollars per share, and as a share of the price.
• The selection rule and the straddle method stay the same every day, so the series can be charted over time. The selected expiry and its days remaining change from day to day, and both are shown.

Shorter expiries naturally show smaller expected moves. Compare an expected move with the same horizon on other days, not a 3-day figure with a 30-day one.

What The Expected Move Does Not Tell You

• It is not a probability bound or a guaranteed range. Under the simple model behind it, the price ends outside the straddle-based move a little over 40% of the time, and outside ±1 standard deviation about a third of the time. Real markets have fatter tails than the model.
• It is not a forecast of direction. It prices movement in either direction.
• It includes everything before expiry, such as ordinary daily movement, scheduled events and risk premiums. Before earnings, a large part can be the announcement itself. See earnings expected move and IV crush.
• Wide bid-ask spreads make the midpoint less certain for thinly traded options. See option bid-ask spread.

Related: implied volatility · options-implied probability · earnings expected move and IV crush · IV term structure

Sources

• Menachem Brenner and Marti G. Subrahmanyam, "A Simple Formula to Compute the Implied Standard Deviation", Financial Analysts Journal (1988): the at-the-money approximation, call ≈ 0.4 × S × σ × √t, so a straddle ≈ 0.8 × S × σ × √t.
• Fischer Black and Myron Scholes, "The Pricing of Options and Corporate Liabilities", Journal of Political Economy (1973): the model behind implied volatility and the probabilities above.
• Benoit Mandelbrot, "The Variation of Certain Speculative Prices", Journal of Business (1963), and Eugene F. Fama, "The Behavior of Stock-Market Prices", Journal of Business (1965): returns with fatter tails than a normal distribution.
• John C. Hull, Options, Futures, and Other Derivatives (Pearson, many editions): straddles and implied volatility.