Long call: what time costs you even when the direction is right

Structure and P&L at expiration: one leg, three numbers

A long call has one leg: you buy one call with a strike of 100 that expires in 30 days. Every number on this page assumes a current price of $100, implied volatility (IV) of 30%, a 4% risk-free rate, no dividends, 30 days to expiration, and one contract (100 shares).

Three numbers describe the position at expiration:

• Net debit: $359.11 ($3.59 a share). This is also the max loss. The premium is paid once, up front, and no margin is involved.
• Breakeven: $103.59, the strike plus the premium per share. The price has to finish above it for the trade to show a profit.
• Max profit: unlimited. Each $1 above the breakeven adds $100 at expiration.

At entry the position has a Delta of +53.24 (it moves like about 53 shares), an instantaneous Theta of −$6.24 a day, and a Vega of +$11.40 per point of IV. Those three numbers cover price, time, and IV; this page is about the second one.

Time profile: prices from $90 to $110 over 30 days

The time profile table above holds each price fixed and lets the days pass. Read across the $100 row: $0, −$50 on day 7.5, −$108 on day 15, −$183 on day 22.5, −$249 on day 27, and −$359 at expiration. At the strike, the whole premium is time value, and all of it is gone by expiration.

The first 15 days cost $108 and the last 15 cost $251. The final 3 days alone cost $110, 31% of the total.

Away from the strike, time matters less, because there is less time value left to lose. At $110 the call shows $89 less after 30 days (+$730 to +$641); at $90 it loses only $47 more (−$312 to −$359). At $105, the position falls from +$321 to +$141: what remains at expiration is the intrinsic value.

Why decay speeds up in the last week (Theta from −$6.24 to −$31.87 a day)

At $100, instantaneous Theta is −$6.24 a day on day 0, −$8.62 on day 15, −$11.97 on day 22.5, −$18.63 on day 27, and −$31.87 with 1 day left. The time value of an at-the-money option shrinks roughly with the square root of the time left, so each day removes a larger share of what is still there.

If decay were spread evenly, the last quarter of the days (day 22.5 to day 30) would carry 25% of it. At $100 it carries 49%, and the last tenth of the days carries 31%.

The Lab’s time-effect map shows the same thing as color: the band of negative values around the strike gets darker toward expiration. A long call has no time-neutral line at all; at every price and every day, the next day costs money.

IV and time, which hurts more: a 5-point IV drop equals about 9 days of decay

If IV falls by 5 percentage points (pp) right after you buy, the position shows −$57 on day 0 with the price unchanged. At the day-0 rate of $6.24 a day, that is about 9 days of time decay arriving at once. A 5-point rise does the opposite: +$57.

Later in the trade, the same IV shift still matters. On day 15, a −5 pp shift takes the $100 row from −$108 to −$149.