Strike selection by delta

The fundamentals course built verticals from prices. Traders who do it every week build them from deltas, because delta is the one number that carries the strike's distance, its probability and its premium at the same time. Pick a delta and the rest of the spread follows; change the delta and you have changed the entire risk profile, not just the strike.

The menu

XYZ at $50, 45 days to expiration, IV 30%. Every row is a $5-wide bull put spread; only the short strike changes.

Look at the last column before anything else. With the crude approximation that the market's probability of max loss equals credit ÷ width, every spread has zero expectancy by construction. That is not a coincidence; it is what "fairly priced" means. The rows do not differ in edge. They differ in how the zero is packaged: many small wins and rare large losses at 9 delta, or a near coin-flip with a 1:2.6 payout at 35 delta.

The approximation is rough. A better probability estimate is the delta of the option at the breakeven price: for 45/40 the breakeven is $44.55, and a $44.55 put has a delta near 0.15, giving a probability of profit around 85% rather than 91%. Use the breakeven-delta method when you want a real number; use credit ÷ width when you want a fast sanity check.

Where the edge actually comes from

If the odds are fair, a credit spread makes money only if one of three things is true:

1. Implied volatility is too high. Historically, index and large-cap IV has run a few points above subsequently realized volatility most of the time. That gap, the volatility risk premium, means the market's 16% is often more like 13% in practice. It is a small, unreliable edge that disappears in some years entirely.
2. You manage losers better than "hold to expiration." The expectancy table assumed the full max loss whenever the short strike finished in the money. Closing at a defined loss changes the arithmetic (next lessons).
3. You have a directional or level-based view that the market does not: support at $45, say. If you do, delta selection is where you express it.

None of these is guaranteed by the strike you pick. What the delta does control is how often you will be tested.

Probability of touch

The delta of the short strike approximates the chance of finishing in the money. The chance of the stock touching the strike at some point before expiration is roughly twice that.

A 16-delta spread will see its short strike tested about one time in three. Each of those times you will be looking at a spread worth two or three times the credit you collected, with the stock sitting on your strike and gamma rising, and you will have to decide. The 9-delta spread is tested half as often but pays half as much and its worst case is nearly the full width. Your delta choice is a choice about how many of those decisions you want to make per year.

Bull put spread, $5 wide: credit vs. how often you are tested

  Credit
  1.40 |                                  * 35 delta
  1.05 |                        * 28 delta
  0.45 |          * 16 delta
  0.22 |    * 9 delta
       +----+-----+------+--------+--------
       18%  32%   56%    70%     chance of touch

Delta targets that practitioners use

• Credit spreads for income: short strike at 16–30 delta. Below 10 delta the credit rarely covers the bid-ask and the tail; above 30 it is a directional trade wearing an income costume.
• Debit spreads for direction: buy the 50–60 delta option, sell the 25–30 delta option. The debit comes out near half the width, so the trade is roughly 1:1 with a probability near 45–50%. Buying further out of the money makes it cheaper and much less likely.
• Spreads that express a level: put the short strike just beyond the level (below support for a put spread, above resistance for a call spread) and then check that the delta is inside 10–35. If the level puts you at 5 delta, the trade is not worth the bid-ask; if it puts you at 45 delta, the level is too close to matter.

Deltas move with IV: at IV 45% the 16-delta put is at $43, not $45. That is why "sell the 16 delta" is a stable rule and "sell the $45 put" is not.

Key idea: At fair prices every strike has the same expectancy, about zero. Delta chooses how that zero is packaged (win rate against payout) and how often you will be tested (about 2 × delta). Any edge comes from IV being too high, from managing losers, or from a view the market lacks, not from the strike itself.

Try it: On a stock you follow, list the $5-wide put spreads at roughly 35, 25, 16 and 9 delta with their real credits. Compute return on risk, the credit ÷ width probability and the expectancy using it. Then compute the touch probability. Decide which row you would take and write down why in one sentence; if the sentence is "because the return is higher," go back to the expectancy column.

Recap

• Same-width spreads at different deltas have roughly the same expectancy at market prices; they package it as different win rates and payouts.
• Probability of profit ≈ 1 − credit ÷ width (rough) or the delta at the breakeven (better).
• Probability of the short strike being touched before expiry ≈ 2 × its delta.
• Income credit spreads: 16–30 delta short strike; directional debit spreads: buy 50–60, sell 25–30.
• Edge comes from overpriced IV, loss management or a view, never from the delta alone.