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Width, probability, and credit-debit equivalence

Lesson 6 · about 12 min

Once the short strike is chosen, two questions remain: how far away to put the long strike, and whether to build the spread with calls or puts. The first changes the shape of the risk in a way most people underestimate; the second, it turns out, barely changes anything at all.

Width at a fixed short strike

XYZ at $50, 45 days to expiration, IV 30%. Keep the short $45 put (16 delta, $0.65) and vary the long put.

Spread Long put cost Net credit Max loss Credit ÷ width Return on risk Loss if XYZ = $42 at expiry
45/43 0.40 0.25 1.75 12.5% 14% −$175 (max)
45/40 0.20 0.45 4.55 9.0% 9.9% −$255
45/35 0.10 0.55 9.45 5.5% 5.8% −$245
Naked $45 put 0.65 44.35 (margin-based) −$235

Three things show up:

  • Wider collects more per spread but less per dollar of risk. Going from $5 to $10 wide adds $0.10 of credit and $4.90 of max loss. The 45/35 spread is 85% of a naked put with a sixth of the buying power efficiency lost.
  • Narrow spreads have the best ratio and the worst execution. The $2-wide spread's $0.25 credit has to survive perhaps $0.05–0.10 of bid-ask on entry and exit; that is 20–40% of the credit gone to friction. And because the max loss is small, traders scale up the contract count until the dollar risk matches a wider spread, which puts the same dollars at risk with far more friction.
  • The long wing only helps once the stock is past it. At $42, the $5-wide and $10-wide spreads lose almost the same as the naked put. The wing's value is entirely in the tail: the 45/40 spread's loss stops at $455 while the naked put's continues to $4,435.

The practical rule is to choose the width from the dollar loss you are willing to accept per position, and then the contract count from that. Someone who accepts $500 of risk might trade one 45/40 or two 45/43 spreads (2 × $175 = $350, with room to spare) but not the 45/35. Wider spreads on high-priced stocks are natural; narrow spreads on cheap stocks are where the friction lives.

Credit and debit spreads are the same trade

Now the second question. Here are two bullish spreads on XYZ at $50 using the $45 and $50 strikes.

Bull call spread (debit): buy the $45 call at $5.75, sell the $50 call at $2.40. Debit $3.35. Max profit $1.65.

Bull put spread (credit): sell the $50 put at $2.30, buy the $45 put at $0.65. Credit $1.65. Max loss $3.35.

XYZ at expiry Call spread value Call spread P&L Put spread value (owed) Put spread P&L
40 0.00 −3.35 5.00 −3.35
45 0.00 −3.35 5.00 −3.35
46.65 1.65 −1.70 3.35 −1.70
48 3.00 −0.35 2.00 −0.35
48.35 3.35 0.00 1.65 0.00
50 5.00 +1.65 0.00 +1.65
55 5.00 +1.65 0.00 +1.65

Identical at every price. Same breakeven ($48.35), same max profit, same max loss, same buying power ($335 either way, because a broker holds the max loss on the credit version). This is put-call parity applied to a spread: a call spread plus a put spread at the same strikes always sums to the width, so the debit of one and the credit of the other must add to $5.00. In practice the two differ by a few cents of interest and by the bid-ask on each side.

45/50 bull call spread  ==  45/50 bull put spread

  +1.65 |                 __________________
        |                /
    0   |--------------X-------------------   X = 48.35
        |             /
  -3.35 |____________/
        +----+----+----+----+----+----+
        42   44   46   48   50   52   54   XYZ

The credit version feels different. Cash arrives in the account, and "getting paid" is more pleasant than paying. Nothing about the risk is different. The cash is a deposit against a maximum loss of $335, exactly as the debit was.

So which one do you trade?

Use the version whose strikes are out of the money:

  • Bullish with strikes below the current price (like 45/50 above): the puts are OTM, the calls are ITM. Trade the put credit spread.
  • Bullish with strikes above the current price (50/55): the calls are OTM. Trade the call debit spread.
  • Bearish, mirror image: strikes above price → call credit spread; strikes below → put debit spread.

The reasons are practical. OTM options are more liquid with tighter markets, so you give up less on entry and exit. ITM short legs carry early assignment risk (lesson 4) and ITM long legs tie up more cash. And OTM spreads are what most other traders quote, so fills at the mid are more realistic.

The one thing this does not mean is that a "credit strategy" and a "debit strategy" are different approaches to the market. A trader who "only sells premium" with 45/50 put spreads and a trader who "only buys" 45/50 call spreads hold the same position and will have the same year.

Key idea: Width sets the dollar risk per spread, not the edge; choose it from the loss you accept, then set contracts. A call vertical and a put vertical at the same strikes are the same trade to within a few cents, so pick the one whose strikes are out of the money for liquidity and assignment reasons, not because credit feels better than debit.

Try it: Pick any stock and any two strikes. Look up the bid-ask of the call spread and the put spread at those strikes and confirm debit + credit ≈ width. Then compare the bid-ask width of each version and note which one is OTM. That is the one to trade.

Recap

  • Wider spreads collect more credit per spread and less per dollar risked; the wing only matters once the stock is past it.
  • Narrow spreads have the best credit ÷ width and the worst friction; scaling up contracts recreates the risk with more slippage.
  • Choose width from the dollar loss you accept per position, then choose contract count.
  • Call and put verticals at the same strikes have identical payoffs; debit + credit = width.
  • Trade the version whose strikes are OTM for liquidity and to avoid early assignment on an ITM short leg.

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

Bid-ask spread in an order bookSell orders stacked above buy orders with a gap between the best of each.SELLERS (asks)50.0690050.051,40050.0460050.011,10050.002,30049.99800spread = 0.03BUYERS (bids)
The bid-ask spread. Buy orders sit below, sell orders above, and the gap between the best bid (50.01) and best ask (50.04) is the spread you pay to cross. Bar length shows the size resting at each price.
Payoff of a long call at expiryA flat loss equal to the premium below the strike, turning upward at 45 degrees above it.Profit / loss per share08595115125Strike 105Max loss 3 — the premium paidBreakeven 108Profit keeps growingUnderlying price at expiry
Buying a call: payoff at expiry. A 105-strike call bought for 3 loses that whole 3 if the price finishes at or below 105, breaks even at 108, then gains a dollar for every dollar higher. The loss is capped at the premium; the upside is not capped.
Payoff of a bull call spread at expiryA flat loss below the lower strike, a rising middle section, and a flat capped profit above the upper strike.Profit / loss per share08895115122100110buy the 100 callsell the 110 callBreakeven 103Max profit 7capped above 110Max loss 3 — the net debitUnderlying price at expiry
Vertical spread: payoff at expiry. Buying the 100 call and selling the 110 call costs 3 net. Below 100 that 3 is the whole loss; above 110 the gain stops at 7, because the sold call gives back every dollar the bought call earns beyond 110.