Time decay

Hold a share for a month and nothing happens to it just because a month passed. Hold an option for a month and something does: it has a month less to work with.

Time decay is that loss. If every other pricing factor stays exactly where it is, an option will be worth less tomorrow than it is today, and less again the day after, until on expiry day its time-value is zero and only its intrinsic value remains.

The workbook draws the blunt inference: because one of the two components of an option price is inherently biased towards falling, option sellers are at a fundamental advantage compared to option buyers. The buyer needs the underlying to move, and to move soon. The seller needs only for the calendar to keep turning.

Time decay is measured by theta, the change in option price for a one-day decrease in time to expiry. Theta is negative for a long option — call or put, it makes no difference — and positive for the writer.

Three properties matter for the exam:

• It attacks time value only. Intrinsic value is immune. A deep in-the-money option decays slowly because most of its premium is intrinsic; an at-the-money option decays fastest because all of its premium is at risk.
• It accelerates. The last week loses far more time value than an equivalent week three months out. The decay curve steepens into expiry.
• It runs on calendar days, not trading days. A long weekend costs the buyer three days of theta and delivers no chance to trade.

This is why a directional view that is right but early still loses money on options, and why strategies such as the covered-call, the short-straddle and the credit spread are, at bottom, ways of selling time.

Theta = Change in option premium ÷ Change in time to expiry

Expected decay over n days ≈ Theta × n        (theta held constant)

Rupee decay per contract = Theta × Lot size × Days

At expiry: Premium = Intrinsic value, and Time value = 0, for every option on the board.

A call option has 5 days to expiry and a theta of 1.2. The contract size is 50.

Daily decay   = Rs 1.20 per unit
Per contract  = 1.20 × 50 = Rs 60 a day
Over 5 days   = Rs 300 per contract

Now set that against a real position. The option is quoted at Rs 95 with the index at 17,562 and a strike of 17,500. One lot costs 95 × 50 = Rs 4,750.

The index has not moved a single point, and Rs 240 of the Rs 4,750 is gone.

And the table understates it, because theta is not constant — it accelerates. On the final day the remaining Rs 90 of time value has to reach zero, so the last day alone destroys more than the previous four put together.

Turn the position around. The writer of that same lot collected Rs 4,750 and has watched Rs 240 of it become unconditionally his, having done nothing and taken no view. That is the arithmetic behind the workbook's claim that the seller starts with the advantage — and behind the fact that the seller also posts margin for it, because his loss is the unlimited one.

Chapter 16.7 introduces time decay under the "Time to expiration" pricing factor and names options wasting assets; the same section defines theta as its measure. Expect a conceptual question on why an option loses value with the passage of time, a "who benefits from time decay" question — the seller — and a theta computation of the kind above.

• Time decay hurts long calls and long puts equally. It is not a bearish or bullish force; it is a long-option force.
• It eats time value, never intrinsic value. An option deep in the money barely decays.
• Decay is fastest at the money and fastest near expiry. A flat, linear estimate understates the last week badly.
• The seller's advantage is not a free lunch. He carries unlimited downside and pays margin for it; the buyer pays premium and owes nothing more.
• Being right too early is the same as being wrong for an option buyer — decay does not wait for the thesis.
• Theta is quoted per day, so multiply by the lot size before comparing it with anything in rupees.