Theta: Why the Second Half Costs More
Theta is how much an option loses to the passing of one day, holding everything else constant. Decay is not linear: value drains slowly at first and sharply near expiry, which changes what holding a position for the last stretch actually costs.
The decay curve on this page is a shape-accurate illustration in which extrinsic value falls with the square root of time remaining. It is correct about behaviour and is not a quote for any real contract.
How it works
An option’s price has two parts. Intrinsic value — what it would be worth if exercised now — and extrinsic value, which is everything else: the possibility that things change before expiry.
Theta is the daily cost of that second part. Every day that passes removes some of the possibility remaining, and the price falls accordingly even if nothing else moves.
And it is not evenly spread. That is the whole reason this page exists.
The measurement
Take a 45-day option with 4 of extrinsic value. Run the clock to the halfway point:
| Days elapsed | Extrinsic value remaining | Share of original |
|---|---|---|
| 0 | 4.00 | 100% |
| 22 of 45 (49%) | 2.80 | 70% |
| 45 (expiry) | 0.00 | 0% |
Half the calendar has gone and 70% of the value is still there. Which means the first half cost 30% of the premium and the second half costs 70% — more than twice as much for the same number of days.
That asymmetry is the practical content of theta. Holding a long option into the final stretch is paying the steepest part of the curve, and selling one is collecting it.
It is genuinely zero-sum. Every day the buyer loses to decay is a day the seller gains, which makes theta the cleanest transfer in the whole subject.
In practice: where it is largest
Decay concentrates near the money. Deep in-the-money options are mostly intrinsic value, which does not decay. Far out-of-the-money options have little value left to lose. The uncertainty — and therefore the extrinsic value — sits around the strike.
Theta and gamma are two sides of one trade. Gamma is the favourable curvature a buyer owns; theta is the rent paid for it. A seller collects the rent and is short the curvature. No position gets both.
In a quiet market theta is the only thing moving. Nothing about the underlying changes, and the option loses value every day regardless. That is why flat stretches are the worst environment for buyers and the best for sellers.
Buying more time is buying a shallower part of the curve. A long-dated option loses very little per day at the start, which is the argument for paying more for time than the thesis strictly requires.
What theta is not
It is not a straight line, and the mistake matters. Dividing the premium by the days remaining understates the cost of the final stretch by a wide margin.
It is not a reason to sell options. Collecting decay means being short the curvature, and one large move can remove many collected premiums. The credit spread page covers that trade honestly.
It is not the only thing eroding the position. A fall in expected volatility removes value at the same time, and vega is the number describing it.
And it is not constant across the position’s life. Today’s theta is not next week’s, which is why a position that felt cheap to hold becomes expensive without anything visible changing.
When it fails
Decay collected does not offset a large adverse move. A seller collecting a few points a week against a position that gaps ten points has lost the arithmetic badly, and that is the standard shape of a short-option loss.
Trading around decay costs spread. Rolling positions to keep collecting it pays two option spreads each time, on top of the 2% of a bar this site measures on the underlying.
Buying too little time is the buyer’s version of the failure. A short-dated option is cheap because it sits on the steepest part of the curve, and the discount is exactly the extra decay being accepted.
Holding to expiry by default is the fourth. Most of what a working long option is worth can be realised by closing it before the steep section, and holding on trades the largest decay for the smallest remaining upside.
And ignoring weekends is the fifth. Decay continues across days the market is closed, so a Friday-to-Monday hold pays three days of theta for one session of opportunity.
A sixth is reading a large theta figure as a large income. The number quoted is a daily amount at today’s price and today’s volatility, and it is only collectable by a position that survives to collect it. A short option showing an attractive daily figure is showing what it earns while nothing happens, not what it earns overall.
The practical use of all this is in two decisions. How much time to buy, and when to stop holding. Buying past the steep section and closing before re-entering it puts the shallow part of the curve on your side in both directions, and it costs nothing except the willingness to take a result before it is final.
The original data
7 of the 24,971 videos measured for this site cover theta, at a median of 18,398 views — a small supply, and most of it states that decay accelerates without ever putting a figure on how much.
The 70%-at-halfway figure was computed for this page from the square-root-of-time model stated at the top. Real contracts vary with volatility, dividends and rates; the shape — shallow, then steep — is common to all of them, and it is the shape that changes decisions.
Related
Gamma is what the decay is paying for. Options expiry is the deadline this curve runs into. And vega is the other thing quietly removing value at the same time.
I lost money on a position that was right about direction, and when I worked out why afterwards it was almost entirely this. I had held it through the steep part of the curve waiting for confirmation I did not need.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.