Part XI · Swing trading · Chapter 11M

Choosing an expiry

Days to expiry for swing trades

Where we are

Chapter 11L chose between the index and a stock. When the trade uses options, one more choice sets its Greek profile: the expiry. The wrong expiry for a thesis is a structural mismatch that no execution skill can recover, so this chapter gives the matching rule and the arithmetic behind it.

What you need first

Days to expiry (Chapter 5B), and the at-the-money price shortcut $C \approx 0.4\,S\sigma\sqrt{T}$ (Chapter 5E).
Gamma and theta, which grow as $1/\sqrt{T}$ , and vega, which grows as $\sqrt{T}$ (Chapter 5C).
Charm and 0DTE options (Chapters 5D and 9B), and LEAPS (Chapter 5G).
The four setups with their holds and time stops (Chapter 11H), pre-earnings momentum (Chapter 11I) and the vanna unwind (Chapter 11K).

1 · How time to expiry sets the Greeks

The expiration date you choose for an options position determines the trade's Greek profile. At the money, and with no rates or dividends, the formulas of Chapter 5C reduce to simple powers of the time to expiry $T$ , in years:

price: $C \approx 0.4\,S\sigma\sqrt{T}$
gamma: $\Gamma \approx 0.4/(S\sigma\sqrt{T})$
vega, per unit of volatility: $\nu \approx 0.4\,S\sqrt{T}$
theta, per year: $\Theta \approx -0.2\,S\sigma/\sqrt{T}$

Here $S$ is the price of the underlying and $\sigma$ the implied volatility, and 0.4 is the height of the normal curve at its center. Dividing theta by the price gives the share of the premium that decays each year, $1/(2T)$ . Divide by 365 for a calendar day, and write $D = 365\,T$ for the days to expiry (DTE):

\frac{|\Theta|/365}{C} \approx \frac{1}{2D}

(11M.1)

An at-the-money option loses about $1/(2D)$ of its value each day: 1.7% a day at 30 DTE and 7.1% at 7 DTE, and the rate keeps climbing until the last day takes all that is left. Since the price scales with $\sqrt{T}$ , an option held $h$ calendar days with nothing else changing keeps $\sqrt{(D-h)/D}$ of its value. The share lost to time over the hold is

L(D,h) = 1 - \sqrt{\frac{D-h}{D}}

(11M.2)

It reaches 100% when $h = D$ : an option that expires at your exit has lost all of its time value by then. Theta runs on calendar days, weekends included, so count the hold in calendar days (Chapter 5C).

Worked example: Two expiries, one SPY call

Step 1: the shortcut. Take SPY at 600 with an implied volatility of 16%. At 30 DTE, $\sqrt{T} = \sqrt{30/365} = 0.2867$ , so an at-the-money call costs about $0.4 \times 600 \times 0.16 \times 0.2867 = \$11.01$ . At 7 DTE, $\sqrt{T} = 0.1385$ and the call costs about $5.32.

Step 2: the full Greeks. Black-Scholes values, with no rates or dividends, are close to the shortcut:

At the money, SPY 600, IV 16%	30 DTE	7 DTE
Premium	$10.98	$5.30
Delta	0.51	0.50
Gamma	0.0145	0.0300
Theta per day	−$0.18	−$0.38
Theta as a share of premium	1.7%	7.1%
Vega per volatility point	$0.69	$0.33

Step 3: per dollar of premium. A $1 rise in SPY adds about $0.51 to either call: 4.6% of the 30-day premium and 9.5% of the 7-day one. Gamma and theta per dollar of premium are both $30/7 = 4.3$ times as high on the 7-day call.

2 · The DTE decision table

The source sorts expiries into seven bands by their Greek profile:

DTE range	Greek profile	Use case
0DTE	Gamma-dominant, tiny vega, charm-dominant	Intraday convexity plays only. Not appropriate for any swing thesis of 2 days or more
1 to 7 DTE	High gamma, rapid theta decay, low vega	Tactical event trades such as the FOMC vanna unwind, and short-duration mean reversion. High execution risk; requires very high conviction
8 to 21 DTE	Balanced gamma and theta, growing vega	The classic swing-options zone for tactical setups: Trend Pullback option expressions, post-earnings premium selling, the aftermath of a vanna unwind
21 to 45 DTE	Lower gamma, a lower daily rate of theta decay, meaningful vega	The default swing-options zone: pre-earnings momentum option overlays, multi-day setups, catalyst-driven positions
45 to 90 DTE	Low gamma, slow theta decay, high vega	A directional thesis with vega exposure: PMCC long legs, diagonal back-month legs
90 to 365 DTE	Very low gamma, minimal theta, very high vega and rho	Strategic positions, hedges, replacement-stock structures; horizons of a quarter or more
Over 365 DTE (LEAPS)	Near-stock delta, minimal theta, extreme vega	Equity replacement strategies

"Charm-dominant" means that on its last day an option's delta is moved most by the clock (Chapter 5D). Rho, the sensitivity to interest rates, grows with $T$ (Chapter 5C). PMCC is a poor man's covered call: a long-dated call bought in place of shares, with shorter calls sold against it. A diagonal spread pairs a front-month short with a back-month long. The source adds a warning: LEAPS are not "cheap lottery tickets". Their high vega means a change of implied-volatility regime can move the position 30% to 50% independent of the underlying.

Worked example: What a volatility regime does to a LEAPS call

Step 1: at the money. A one-year at-the-money SPY call at 20% implied volatility is worth $47.79 (Black-Scholes, no rates or dividends). With SPY unchanged, it is worth $33.48 at an implied volatility of 14%, 30% less, and $23.93 at 10%, 50% less.

Step 2: deep in the money. A one-year call struck at 450, with a delta of 0.94, is worth $153.49 at 20% and $150.53 at 14%, only 1.9% less. Most of its value is intrinsic, which volatility cannot touch.

So the table's LEAPS row describes two strikes at once. The near-stock delta belongs to a deep in-the-money LEAPS call, and the 30% to 50% swings to one near the money.

3 · The fit between strategy and expiry

The figure scores eight strategies against six DTE buckets. Each cell is a judgment score from 0 (avoid) to 5 (ideal), not a measurement. Green cells, 4 and 5, are good fits, yellow cells score 2 or 3, and red cells, 0 or 1, mark buckets whose Greek profile fights what the strategy is trying to do. Two rows of buttons choose a strategy and a bucket, with readouts of their fit, the strategy's whole row and the bucket's profile. The buckets are cut at different days from the table above: 0DTE, weekly (1 to 9 days), short-dated (10 to 30), mid-dated (31 to 60), long-dated (61 to 180) and LEAPS from 180 days, where the table starts LEAPS beyond 365. It opens on the credit spread in the short-dated bucket. Step the long call across the buckets, then compare the gamma scalp's row with the PMCC's.

strategy

DTE bucket

Fit 5 of 5 (ideal). Credit spread (premium-sell), short-dated (10-30 days). Its row, 0DTE to LEAPS: 2, 4, 5, 4, 2, 0.

Short-dated (10-30 days): balanced gamma/vega/theta, the standard zone.

Match the expiry to the strategy. Eight strategies against six DTE buckets, each cell a judgment score from 0 (avoid) to 5 (ideal), not a measurement. Green cells are good fits; red cells mark buckets whose Greek profile fights what the strategy is trying to do. Choose a strategy and a bucket to read their fit and the bucket's profile. The buckets are cut at different days from the table above: here LEAPS starts at 180 days.

The credit spread opens at 5 of 5, ideal, in the short-dated bucket, with a row reading 2, 4, 5, 4, 2, 0 from 0DTE to LEAPS. The long call's row, 3, 3, 4, 4, 4, 5, rises toward LEAPS. The gamma scalp's row, 5, 5, 4, 2, 1, 0, and the PMCC's, 0, 1, 2, 3, 4, 5, are near mirror images: one lives on short-dated gamma, the other on a long-dated leg's delta. The pre-earnings call spread scores 5 in the short-dated bucket, 10 to 30 days, while this chapter's setup table below asks for 30 to 45. Both keep the rule that the option must expire after the report.

Three rows need the Edge Book's view beside them. For the iron condor row, it rejects systematic condors, which Chapter 12C teaches (Chapter 10I). For the credit spread row, its one volatility-selling strategy is the VRP harvest: cash-secured at-the-money XSP puts sold 30 to 45 days out and closed at 21 (Chapters 10C and 13F). It treats weekly and 0DTE premium selling as a different strategy, with much higher operational risk. The gamma scalp row is the delta-hedged long option of gamma scalping (Chapter 6D), not the scalping of gamma-exposure levels that the Edge Book rejects.

4 · The matching principle

The cardinal rule: the DTE should match the thesis horizon, with a buffer for an adverse path. The source gives three theses:

"SPY bounces from the 21-EMA in 2 to 5 days." 0DTE options are a structural mismatch, since their gamma exposure and theta decay do not match a 5-day horizon. The right vehicle is 14 to 30 DTE options, which give the thesis time to play out without bleeding to zero through theta.
"NVDA drifts up over 2 weeks into earnings." 7 DTE options are wrong: they expire before earnings, and the theta burn over 14 days at 7 DTE is destructive. The right vehicle is 30 to 45 DTE options, which cover the thesis with a buffer.
"Tech leads for the next quarter." 30 DTE options are wrong, with too much short-dated gamma noise and too little vega capture for a multi-month horizon. The right vehicle is 90 to 120 DTE options or LEAPS-based structures.

Worked example: Theta over the holding period

Step 1: the bounce. A hold of 5 trading days spans 7 calendar days. By (11M.2), an at-the-money option at 14 DTE loses $1 - \sqrt{7/14} = 29\%$ of its value to time over the hold, at 21 DTE $1 - \sqrt{14/21} = 18\%$ and at 30 DTE 12%, while a 7 DTE option loses all of it.

Step 2: the dollars. At SPY 600 and 16%, those three options cost $7.50, $9.19 and $10.98, so the 7 days take $2.20, $1.69 and $1.37 from them. The longer expiry costs more to buy and less to hold.

Step 3: the drift into earnings. Over 14 days, a 30 DTE option loses $1 - \sqrt{16/30} = 27\%$ of its value to time and a 45 DTE option $1 - \sqrt{31/45} = 17\%$ .

The source gives each setup its own expiry:

Setup	DTE	Why
Trend Pullback	14 to 30 DTE with options; with shares, an immediate exit, since no expiry constrains it	Holds typically 2 to 5 days; needs a buffer for an adverse path
Compression Breakout	21 to 45 DTE	Holds up to 8 days; wants meaningful gamma without rapid theta burn
Undercut and Reclaim	14 to 21 DTE	Holds 2 to 3 days; a tighter DTE is acceptable because the hold is short
IBS + RSI Mean Reversion	Shares preferred; 7 to 14 DTE with options	Holds 1 to 2 days; very short duration
Pre-earnings momentum	Shares preferred; 30 to 45 DTE with options, expiring after earnings	The trade closes before earnings, but the vehicle's expiry must outlast them
FOMC vanna unwind	0 to 1 DTE	An intraday operation only (Chapter 11K)
Macro catalyst hedge	30 to 60 DTE	Wants vega exposure for a possible expansion of implied volatility

5 · The expires-before-exit trap

A common retail mistake is to buy short-dated options for a swing thesis without checking that the option expires after the planned exit. The source's example: on a Monday you enter a Trend Pullback with a 5-day time stop, buying options that expire this Friday, at 4 DTE. By Wednesday the thesis is playing out, but the position needs to hold through Friday's time stop. Friday is also expiration day. You are now forced into one of three choices:

Exit Thursday, one day early, sacrificing potential continuation.
Roll to next week's expiration, paying premium twice.
Hold to expiration, taking the maximum theta hit on Friday.

By (11M.2), an at-the-money option with 2 DTE on Wednesday has lost $1 - \sqrt{1/2} = 29\%$ of its value by Thursday, and all of its time value by Friday's close.

The structural fix is to choose a DTE such that your option expires at least 2 to 3 trading days after your latest planned exit. For a 5-day Trend Pullback time stop, that means at least 8 to 10 DTE. In practice, 14 to 21 DTE gives a clean buffer.

Worked example: Counting the minimum expiry

Step 1: the exit. Count the entry day as day 1, as the source's example does. A Monday entry with a 5-day time stop exits at Friday's close, 4 calendar days later.

Step 2: the buffer. Two or three trading days after Friday is the next Tuesday or Wednesday, 8 or 9 calendar days after entry: the source's minimum of 8 to 10 DTE.

Step 3: a longer setup. A Compression Breakout entered on a Tuesday with an 8-day time stop exits at the next Thursday's close, 9 calendar days later. The buffer carries the expiry to the Monday or Tuesday after, 13 or 14 DTE, comfortably inside the setup's 21 to 45.

6 · Why retail picks expiries that are too short

In the source's account, retail traders consistently choose shorter DTEs than is optimal for their stated thesis, for two reasons:

Cost. Shorter-DTE options cost less in absolute dollars: the source puts a 7 DTE call at 30% to 50% less than a 30 DTE call at the same strike, which makes it feel more affordable.
Leverage perception. Shorter-DTE options have higher gamma per dollar of premium, so small moves produce larger percent returns, which is psychologically attractive.

The discount depends on the strike: at the money, the square-root rule puts the 7-day price at $\sqrt{7/30} = 0.48$ of the 30-day one. A call in the money, whose intrinsic value does not decay, is discounted less:

SPY call, SPY 600, IV 16%	7 DTE	21 DTE	30 DTE	7 DTE below 30 DTE	21 DTE above 7 DTE
Strike 590, $10 in the money	$11.70	$14.97	$16.61	30%	28%
Strike 600, at the money	$5.30	$9.19	$10.98	52%	73%
Strike 610, $10 out of the money	$1.77	$5.11	$6.78	74%	189%

The source's 30% to 50% spans calls from $10 in the money, at 30%, to about the money, at 52%. The two-expiry worked example measured the leverage: a $1 move is 9.5% of the 7-day call's premium and 4.6% of the 30-day call's.

Both reasons confuse leverage with edge, the trap of Chapter 1E. Cheaper options are not better options. They are cheaper because they have less time for your thesis to develop and more daily theta cost as a percentage of premium.

The professional bias is toward a longer DTE than feels comfortable, accepting the higher absolute cost in exchange for structural buffer. The source states the asymmetry: paying 30% more for three times the time to develop is a fundamentally better risk-adjusted trade than paying less for an option that expires while your thesis is still developing. The table shows where that 30% holds: for the call $10 in the money, 21 days cost 28% more than 7. At the money, three times the time costs $\sqrt{3} = 1.73$ times as much, 73% more.

Familiar ground

Choosing an expiry is choosing a trial's follow-up. A trial of adjuvant therapy with six months of follow-up cannot show a benefit in recurrence that emerges at two years. The study ends before its endpoint can accrue, so a real effect goes unseen. Follow-up far longer than the endpoint needs costs money without adding information. An option that expires before your thesis resolves is the first design, while a LEAPS call for a three-day trade is the second.

In practice

Write the latest exit date on the order ticket. Take it from the time stop, then set the expiry at least 2 to 3 trading days later.
Count calendar days. DTE and theta run on calendar days, so a Friday-to-Monday weekend costs three days of decay (Chapters 5C and 7B).
Rolling costs twice. A roll closes one option and opens another, paying the spread on both and buying new time value (Chapter 2D).
Beyond 90 DTE, check vega. Before buying a LEAPS call, price it at an implied volatility several points lower. A fall like the worked example's can take 30% to 50% with no move in the underlying.

When it fails

Longer is not free. A long expiry costs more premium, while its larger vega exposes it to a fall in implied volatility. Chapter 11N counts a 90 DTE option for a 3-day trade as a horizon mismatch too. At SPY 600 and 16%, a 90 DTE at-the-money call costs $36.86 per unit of delta against $14.82 for a 14 DTE one, with 2.5 times the vega.
The buffer does not cover the thesis. An expiry after the exit protects the vehicle, not the idea. If the setup fails, the time stop and the invalidation close the trade whatever the expiry.
The matrix is judgment. The figure's scores are the source's opinion of fit, on buckets that differ from the table's.

Decision rule

Before buying an option for a swing trade:

Write the thesis horizon and the latest exit from the setup's time stop.
Set the expiry at least 2 to 3 trading days after the latest exit, and inside the setup's band from the table.
The bands: 14 to 30 DTE for the Trend Pullback, 21 to 45 for the Compression Breakout, 14 to 21 for the Undercut and Reclaim, and 7 to 14 for IBS + RSI.
If an event falls inside the horizon, the option must expire after it, as for pre-earnings momentum at 30 to 45 DTE.
Check the decay with (11M.2), and beyond 90 DTE check the vega against a regime change in implied volatility.
Prefer shares where the source does: for the IBS + RSI and pre-earnings setups.

Common mistake: buying the cheapest weekly

The weekly call is half the price of the monthly and doubles your return on a small move, so it feels like the better trade. It is the same bet with less time, decaying four times as fast per dollar. If the move comes a day late, the weekly has already paid for it.

What to carry forward

The expiry sets the Greeks: at the money, gamma and theta grow as $1/\sqrt{T}$ , while the premium and vega grow as $\sqrt{T}$ .
An at-the-money option loses about $1/(2D)$ of its value a day, and $1 - \sqrt{(D-h)/D}$ over a hold of $h$ days.
Match the DTE to the thesis horizon, with the option expiring at least 2 to 3 trading days after the latest planned exit.
Short expiries are cheaper because they buy less time. Longer ones cost more to buy and less to hold.
LEAPS carry high vega: a regime change in implied volatility can move them 30% to 50% with no move in the underlying.

7 · Check yourself

Question 1

An at-the-money option has 10 days to expiry. What share of its value does it lose each day, and over a 7-day hold?

Answer

By (11M.1), about $1/20 = 5\%$ a day. By (11M.2), over 7 days it loses $1 - \sqrt{3/10} = 45\%$ of its value to time, nearly half.

Question 2

You enter a Compression Breakout on a Tuesday, with its 8-day time stop. What is the shortest expiry the buffer rule allows, and what does the setup table suggest?

Answer

Counting Tuesday as day 1, the time stop is the next Thursday's close, 9 calendar days out. Two or three trading days later is the following Monday or Tuesday, 13 or 14 DTE, against the table's 21 to 45 DTE.

Question 3

A 30 DTE at-the-money SPY call costs $11. Roughly what does the 7 DTE call at the same strike cost, and why is that no bargain for a 5-day thesis?

Answer

It costs about $11 \times \sqrt{7/30} = \$5.31$ . It expires on the day the thesis matures, so by (11M.2) it loses all its time value over the hold, where a 30 DTE option loses 12%.

Question 4

A one-year at-the-money SPY call is priced at an implied volatility of 25%. Roughly how much does it lose if implied volatility falls to 20%, with SPY unchanged?

Answer

At the money the price scales with $\sigma$ , so about $1 - 20/25 = 20\%$ . Black-Scholes gives $59.69 falling to $47.79, a loss of 19.9%, from the fall in implied volatility alone.

Question 5

Why does the source's LEAPS row list both "near-stock delta" and "extreme vega", and which strikes carry each?

Answer

A deep in-the-money LEAPS call has a delta near 1, like the stock. Most of its value is intrinsic, so a fall in implied volatility barely moves it: 1.9% in the worked example. An at-the-money LEAPS call carries the large vega, losing 30% when implied volatility falls from 20% to 14%.