Friday, October 31, 2025

Expected Move Calculation

 🧩 What “Expected Move” Means

The expected move tells you how much the stock is expected to move (up or down) over a given period — based purely on option prices (i.e., implied volatility), not on direction.

It’s derived from the standard deviation implied by option prices — essentially, a 1σ (one standard deviation) move in probability terms.

That means:

  • There’s about a 68% probability the stock stays within ±1σ range over that time.


🔢 The Formula

For 1 month expected move, you can use:

Expected Move=Stock Price×IV×T365\text{Expected Move} = \text{Stock Price} \times \text{IV} \times \sqrt{\frac{T}{365}}

Where:

  • Stock Price = Current underlying price

  • IV = Implied Volatility (in decimal form, e.g. 28% → 0.28)

  • T = Number of days until expiration (typically 30 for one month)


🧮 Example Calculation

Let’s assume:

  • Stock Price (S) = ₹1,000

  • IV = 28% = 0.28

  • T = 30 days

Now plug in:

Expected Move=1000×0.28×30365\text{Expected Move} = 1000 \times 0.28 \times \sqrt{\frac{30}{365}}

First compute the time component:

30365=0.0822=0.2868\sqrt{\frac{30}{365}} = \sqrt{0.0822} = 0.2868

Then multiply:

1000×0.28×0.2868=80.31000 \times 0.28 \times 0.2868 = 80.3

Expected Move ≈ ₹80 (±8%) in one month

That means:

  • There’s about a 68% chance the stock trades between ₹920 and ₹1,080 in one month.


🧠 Intuitive Understanding

  • IV represents annualized standard deviation (the market’s estimate of yearly volatility).

  • To find a shorter-period volatility, you scale it down by the square root of time.

  • The √(T/365) term adjusts IV to the time frame of interest.


📈 Quick Reference

PeriodFormula MultiplierMeaning (for IV=28%)
1 Day√(1/365) = 0.052~1.46% daily move
1 Week√(7/365) = 0.138~3.9% weekly move
1 Month√(30/365) = 0.287~8% monthly move
3 Months√(90/365) = 0.496~14% 3-month move
1 Year√(365/365) = 1.028% annual move

⚠️ Notes

  • This is a statistical (not directional) forecast — it doesn’t say which way it’ll move.

  • For multi-month periods, use the appropriate T.

  • IVs differ across maturities — ideally, use the IV of the option with 30 days to expiry.

Two Key Volatilities

TypeSymbolMeaning
Implied Volatility (IV)σᵢForward-looking — derived from option prices. Reflects what traders expect future volatility will be.
Realized (Historical) Volatility (HV)σʳBackward-looking — measures how much the stock actually moved in the past.

So:

  • IV = Market’s forecast

  • HV = Actual weather that followed

If IV ≫ HV → options are expensive (market expecting big move)
If IV ≪ HV → options are cheap (market complacent)


⚙️ Step 2. Formula for Realized Volatility

You can compute annualized realized volatility using daily returns:

σr=252×Stdev(daily returns)\sigma_r = \sqrt{252} \times \text{Stdev}(\text{daily returns})

Where:

  • daily returns = (Priceₜ / Priceₜ₋₁) - 1

  • 252 = trading days in a year

This gives volatility in annualized %, directly comparable to IV.


🧮 Step 3. Compare Example

Let’s continue with your earlier IV = 28% example for a ₹1,000 stock.

Now suppose over the last 30 trading days, the stock’s daily percentage changes (returns) had a standard deviation of 1.1% per day.

Then:

σr=1.1%×252=1.1%×15.87=17.46%\sigma_r = 1.1\% \times \sqrt{252} = 1.1\% \times 15.87 = 17.46\%

So:

  • IV = 28%

  • HV = 17.5%


📊 Step 4. Interpretation

MetricValueInterpretation
IV (from options)28%Market expects more volatility ahead
Realized Volatility17.5%Stock has been calmer recently
IV – HV = 10.5%Options are expensive; traders expect more turbulence

That means the expected 1-month move (₹80) may be larger than what typically happens if realized vol stays at 17.5%.


🧠 Step 5. Practical Use

  1. For Options Traders:

    • If IV ≫ HV → Consider selling options (collecting high premium)

    • If IV ≪ HV → Consider buying options (expecting bigger move than priced in)

  2. For Stock Investors:

    • Compare implied move with your own expectations.
      If the market is pricing in too much fear, that might create buy opportunities (e.g., during panic).

  3. For Hedging or Event Analysis:

    • Around results, elections, RBI meetings — IV spikes, often higher than realized post-event.


🔢 Example Recap Table

MetricFormulaExample Result (S=₹1000, IV=28%, HV=17.5%)
1M Expected MoveS × IV × √(30/365)₹80
1M Historical MoveS × HV × √(30/365)₹50
Difference₹30 premium priced in

So the market is expecting ₹80 move while the past behavior supports ₹50.

If you think realized volatility will remain near 17–18%, the options are overpriced.

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