Theta: Watching Time Value Bleed Out
Press play and watch the time value drain out day by day. The curve's shape is the whole lesson.
Worth reading first: Every Premium Is Two Numbers Stacked Together
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Every option loses value as it ages. The extrinsic value in a contract has to reach zero on a known date, and it spends every day between now and then heading there. Theta measures how quickly.
For a buyer that is a cost they have accepted. For a seller it is the whole business. Press play and watch it happen.
Sixty days of decay, animated
Two puts on the same stock. One at the money, one well out of it. Press play and watch their time value drain. Notice the two curves have different shapes, not just different sizes.
- $100 strike (at the money)
- $90 strike (out of the money)
What the number means
Theta = dollars of option value lost per calendar dayTheta is negative for anyone holding the option and positive for anyone short it.
A put with a theta of −$0.04 loses about four cents a share a day, or $4 a contract, if nothing else moves. Sell that contract and you gain $4 a day.
Note that this is per calendar day, not per trading day. Time value decays over weekends and holidays too, because the contract does not pause. That is why a position can look fine on Friday and open Monday visibly cheaper for no obvious reason. Nothing happened. Three days passed.
Decay is not a straight line
This is what the animation is for. If time value decayed evenly, a 60-day option would lose a sixtieth of it each day and the curve would be a ramp. It is not. The slope gets steeper as expiration approaches.
Roughly, extrinsic value decays in proportion to the square root of the time left. Halving the days does not halve the value. It removes about 29% of it. The practical effects are large.
| Days remaining | Time value left | Lost so far | Lost in this window |
|---|---|---|---|
| 60 days | 100 | 0% | — |
| 45 days | 87 | 13% | 13% |
| 30 days | 71 | 29% | 16% |
| 21 days | 59 | 41% | 12% |
| 14 days | 48 | 52% | 11% |
| 7 days | 34 | 66% | 14% |
| 2 days | 18 | 82% | 16% |
| 0 days | 0 | 100% | 18% |
An at-the-money option’s time value as expiration approaches, indexed to 100 at 60 days out.
Look at the right-hand column. The last week gives up as much time value as the first fifteen days did, and the final two days give up more than either. A seller collects decay slowly at first and then quickly.
Theta is largest at the money
Compare the two curves in the widget. The at-the-money option starts with much more time value and loses much more of it per day. The out-of-the-money put has less to give up and gives it up gently.
This comes straight from the extrinsic value hump. Theta is the rate at which that hump collapses, so it is biggest where the hump is tallest. Which gives premium selling its central tension: the strikes paying the most decay per day are the strikes most likely to be assigned.
Theta pays for risk. It is not a yield
It is easy to read a position's theta as income. “I am short four contracts collecting $22 a day” sounds like rent. It is not, and the animation shows why: the stock was held perfectly still.
Stocks move. Delta and gamma can wipe out weeks of theta in an afternoon. Theta is what you are paid for carrying that risk, and collecting it only works out if the risk does not show up. That is a statement about probability, not a payment schedule.
Put plainly: theta tells you what the position earns if nothing happens. It says nothing about how often nothing happens.
What can go wrong
Holding a short option into the last days for the final scraps. Decay is fastest there and so is everything else. The premium left is often not worth the gamma risk of collecting it.
Expecting decay on a deep in-the-money contract. There is hardly any extrinsic value left. Theta is near zero and the position behaves like stock.
Treating theta as a daily wage. It is payment for holding directional and volatility risk, and it can be erased faster than it builds up.
Forgetting weekends. Buying a Friday option and expecting Monday's price to be unchanged is a disappointment you can avoid.
Key takeaways
- Theta is the dollars of extrinsic value an option loses per calendar day, weekends included.
- Decay is not linear. It speeds up sharply in the final weeks, roughly with the square root of the time left.
- Theta is largest at the money, which is also where assignment risk is highest. You cannot separate the two.
- Entering at 30-45 days and closing near 21 are attempts to catch the steep part of the curve without holding through the riskiest stretch.
- Theta pays for risk rather than yielding it. It measures what you earn if nothing happens, not the odds that nothing happens.
Check your understanding
1. You are short a contract with theta of $6 per day. It is Friday afternoon. All else equal, how much decay accrues by Monday’s open?
2. An option has 60 days left. Roughly how much of its time value remains at 30 days?
3. Which short option collects the most theta per day, all else equal?
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