Vertical credit spreads

A credit spread is the same two-strike structure with the roles reversed: you sell the option closer to the money and buy a further-out one as protection. You receive cash up front, keep it if the stock stays on the right side of your short strike, and have a defined maximum loss if it does not. It is the cleanest way to sell premium without unlimited risk.

The bull put spread

XYZ at $50, 45 days to expiration. Sell the $45 put at $0.65, buy the $40 put at $0.20.

• Net credit: $0.65 − $0.20 = $0.45 per share, $45 per contract. This is the maximum profit, kept if XYZ is at or above $45 at expiration.
• Maximum loss: width minus credit = ($45 − $40) − $0.45 = $4.55 per share, $455 per contract, if XYZ is at or below $40.
• Breakeven at expiration: short strike minus credit = $45 − $0.45 = $44.55.
• Buying power required: the max loss, $455 (most brokers hold width minus credit).
• Return on buying power if it expires worthless: $45 ÷ $455 = 9.9% for 45 days.

The full table:

Bull put spread 45/40 for 0.45 credit
 P&L
  +45 |              _______________________________
      |             /
    0 |-----------X--------------------------------  X = 44.55
      |          /
 -455 |_________/
      +----+----+----+----+----+----+----+----
      38   40   42   44   46   48   50   52   XYZ at expiry

The arithmetic of "high probability"

The short $45 put has a delta of about −0.16, so roughly an 84% chance of expiring worthless by the market's estimate. Sounds good. Now compute expectancy the way Module 3 of the risk management course does:

• Win: 84% × $45 = +$37.80.
• Loss: 16% × (average loss when it happens). If the average loss in the losing cases is, say, $250 (some losses are partial, some are the full $455), that is 16% × $250 = −$40.00.
• Expectancy: about −$2 per trade before commissions.

Whether that number is slightly positive or slightly negative depends on whether the market's 16% is too high (the volatility risk premium says it usually is, a little) and on how you manage losers. The point is that a spread with an 84% win rate can easily have zero or negative expectancy, because the loss is ten times the win. High-probability credit spreads are a business of many small wins and rare large losses, and the large losses decide the year.

The bear call spread

Mirror image for a bearish or neutral view. XYZ at $50: sell the $55 call at $0.70, buy the $60 call at $0.20.

• Credit $0.50, max profit $50, kept if XYZ is at or below $55.
• Max loss $5 − $0.50 = $4.50, or $450, if XYZ is at or above $60.
• Breakeven $55.50.

Bear call spreads collect a little less than bull put spreads at the same delta, because of skew: OTM calls carry lower IV than OTM puts. They also face the risk that stocks can gap up on takeover news by far more than a $5 width, though the spread caps the damage at $450 regardless.

The Greeks of a credit spread

Small positive theta, small negative vega, mildly long delta. It earns about $0.90 a day per contract if nothing happens and loses if IV rises or the stock falls. As XYZ approaches $45, the short put's gamma and theta both grow: the position earns faster and is also more dangerous. That is the same gamma-theta trade as always, and it is why most credit-spread traders have a rule to close or roll when the short strike is tested rather than hoping.

Key idea: A credit spread sells the nearer option and buys a further one as insurance. Max profit is the credit; max loss is width minus credit; breakeven is the short strike adjusted by the credit. The win rate is high, the loss is a multiple of the win, and the losses decide the result.

Management rules that sellers use

• Take profit early. Closing at 50% of max profit (buy the spread back at $0.22 in the example) captures half the credit in far less than half the time, usually, and removes the position before gamma gets large. Many systematic sellers use exactly this rule.
• Define the loss in advance. Common choices: close when the loss equals the credit received (−$45 here), or when it reaches 2× the credit. Letting the spread run to max loss because "it is defined risk" means accepting a 10-to-1 loss on a trade that paid 1.
• Close before the last week. Gamma at the short strike near expiration can move the spread from near-max-profit to near-max-loss in a day.
• Know the assignment scenario. If XYZ is below $45 at expiry, the short put is assigned and you own 100 shares at $45; the long $40 put protects you below $40 but does not stop the assignment. Module 7 and Module 8 cover what happens next.

Run the numbers on the options profit calculator before entering, particularly the P&L at various dates before expiration, so you know what a 50% profit or a 1× credit loss looks like in stock terms.

Try it: Build a bull put spread on a stock you follow with the short strike at about 16 delta and a $5 width. Compute credit, max loss, breakeven and return on buying power. Then compute the expectancy assuming the market's delta is correct and the average losing trade costs half the max loss. Note whether it is positive.

Recap

• Bull put spread: sell a higher put, buy a lower put; bear call spread: sell a lower call, buy a higher call.
• Max profit = credit; max loss = width − credit; breakeven = short strike − credit (puts) or + credit (calls).
• High win rate does not mean positive expectancy; the loss is a multiple of the win.
• Manage: take profit near 50% of credit, cap the loss at 1× to 2× the credit, close before the last week.
• Assignment on the short leg still happens; the long leg limits the loss, not the mechanics.