Tutorials › Exam FM - Financial Mathematics › Choosing Vertical Spread Strikes For A Target View

Exam FM · Spreads, Collars, and Short Sales · Tutorial 846 of 998

Choosing Vertical Spread Strikes For A Target View

Match a bull or bear vertical spread to a target expiration-price range by checking its breakeven, profit region, and risk limits.

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What You'll Learn

  • Translate a stated price view into an expiration-price interval.
  • Compare candidate vertical spreads using their strikes and net premiums.
  • Identify where a spread earns a profit and where it reaches maximum gain or loss.
  • Apply breakeven formulas to bull call, bear put, bear call, and bull put spreads.
  • Distinguish a close match to a target view from a universally superior strategy.

Start With the Price View

Choosing strikes for a vertical spread begins with a precise statement of the view: what range of underlying prices is anticipated at expiration, and which price movements should produce a profit? A spread that is bullish in direction may still be a poor match for a view of only a small increase if its breakeven is too high. A bearish spread may have the right direction but place its maximum-gain region far below the anticipated price.

The comparison is made at expiration. For the calculations here, profit per share equals the spread’s expiration payoff plus its initial net credit, or minus its initial net debit. This convention ignores financing, transaction costs, and taxes. All options in a spread have the same underlying and expiration, and each option is for one share. A contract multiplier would scale both cash flows and profit, but would not change the breakeven price.

Definition: A target price view is a stated expectation for the underlying price at expiration, often given as a range rather than a single price. A spread matches that view when its expiration profit regions and breakeven are consistent with the range. A match to the view does not, by itself, establish that the spread is appropriate for every investor or that the view will be correct.

A disciplined comparison uses the same sequence for each candidate:

1
Write the target range.
State the anticipated expiration prices, not just “bullish” or “bearish.”
2
Calculate the net premium.
For a debit spread, subtract the premium received from the premium paid. For a credit spread, subtract the premium paid from the premium received.
3
Locate breakeven and payoff regions.
Check whether the target range falls in a profit region, and whether it approaches a maximum-gain or maximum-loss region.
4
Compare the trade-offs.
Consider the amount at risk, the maximum possible gain, and how much the spread’s profit changes across the target range.

Four Common Vertical-Spread Choices

For a bull call spread, buy a call with lower strike \(K_1\) and sell a call with higher strike \(K_2\), where \(K_1<K_2\). If the net debit is \(D\), its expiration profit per share is

$$ \min\bigl(\max(S_T-K_1,0),K_2-K_1\bigr)-D. $$

Here \(S_T\) is the underlying price at expiration. The spread’s breakeven is \(K_1+D\), provided that breakeven lies between the strikes. Below \(K_1\), the loss is the debit. At or above \(K_2\), the profit is \(K_2-K_1-D\).

For a bear put spread, buy a put with higher strike \(K_2\) and sell a put with lower strike \(K_1\), where \(K_1<K_2\). With net debit \(D\), the breakeven is \(K_2-D\). The maximum loss is \(D\), while the maximum gain is \(K_2-K_1-D\).

Credit spreads express the same directional views with a different premium structure. A bear call spread sells a call at lower strike \(K_1\) and buys a call at higher strike \(K_2\). If its net credit is \(C\), its breakeven is \(K_1+C\). A bull put spread sells a put at higher strike \(K_2\) and buys a put at lower strike \(K_1\); its breakeven is \(K_2-C\). For either credit spread, maximum gain is \(C\), and maximum loss is \(K_2-K_1-C\).

SpreadDirectional viewBreakevenMaximum gain
Bull call, debit \(D\)Rise\(K_1+D\)\(K_2-K_1-D\)
Bear put, debit \(D\)Fall\(K_2-D\)\(K_2-K_1-D\)
Bear call, credit \(C\)Fall or stay below\(K_1+C\)\(C\)
Bull put, credit \(C\)Rise or stay above\(K_2-C\)\(C\)

Why Breakeven Depends on the Net Premium

Breakeven is found by setting expiration payoff plus the net premium cash flow equal to zero. The result is useful for comparing strikes, but it must be interpreted with the payoff regions: a calculated price outside the active strike interval would not be a relevant interior breakeven.

For a bull call spread, when \(K_1<S_T<K_2\), the lower-strike call pays \(S_T-K_1\) and the higher-strike call expires without value. Profit is therefore \(S_T-K_1-D\). Setting this equal to zero gives the breakeven.

$$ S_T-K_1-D=0 \quad\Longrightarrow\quad S_T=K_1+D. $$

For a bull put spread, in the interval \(K_1<S_T<K_2\), the short put has payoff obligation \(K_2-S_T\), while the lower-strike long put expires without value. Adding the initial credit \(C\), profit is \(C-(K_2-S_T)\). Thus its breakeven is \(K_2-C\). The credit lowers the price at which the spread breaks even; it does not eliminate the loss if the price falls far enough.

$$ C-(K_2-S_T)=0 \quad\Longrightarrow\quad S_T=K_2-C. $$

Worked Example: Choosing a Bull Call for a Moderate Rise

An underlying asset is trading at \(102\). A trader’s stated view is that its expiration price will be between \(108\) and \(110\). Two same-expiration bull call spreads are available. Candidate A buys the \(100\)-strike call for \(11.60\) and sells the \(110\)-strike call for \(5.00\). Candidate B buys the \(104\)-strike call for \(8.00\) and sells the \(110\)-strike call for \(3.20\). Compare their net debit, breakeven, maximum gain and loss, and profit across the target range. Which is the closer fit if a profit throughout the stated range is required?

Method. For each bull call spread, subtract the premium received from the premium paid. Then use \(K_1+D\) for breakeven and \(K_2-K_1-D\) for maximum gain.

Candidate A. The net debit is \(11.60-5.00=6.60\). Its breakeven is \(100+6.60=106.60\). Its strike width is \(110-100=10\), so its maximum gain is \(10-6.60=3.40\), and its maximum loss is the debit, \(6.60\).

At \(S_T=108\), the spread payoff is \(108-100=8\), so profit is \(8-6.60=1.40\). At \(S_T=110\), the payoff is capped at \(10\), so profit is \(10-6.60=3.40\). Candidate A is profitable across the full target range because its breakeven is below \(108\).

Candidate B. The net debit is \(8.00-3.20=4.80\). Its breakeven is \(104+4.80=108.80\). Its width is \(110-104=6\), so maximum gain is \(6-4.80=1.20\), and maximum loss is \(4.80\).

At \(S_T=108\), the payoff is \(108-104=4\), giving profit \(4-4.80=-0.80\). At \(S_T=110\), the payoff is \(6\), giving profit \(6-4.80=1.20\). Candidate B is not profitable throughout the target range.

Conclusion and check. Candidate A is the closer fit when the requirement is a profit throughout \(108\) to \(110\). Its loss is larger if the price finishes below \(100\), so the lower breakeven and higher target-range profit come with a larger maximum loss. The calculation also checks at \(110\): each spread’s profit equals its stated maximum gain.

Common mistake to avoid. Using \(K_2-D\) as Candidate A’s breakeven would give \(110-6.60=103.40\). That is the wrong strike for a bull call breakeven. The long call’s lower strike is the starting point, so the correct calculation is \(100+6.60=106.60\).

Match the Spread to the Depth of a Bearish View

A target interval can distinguish between spreads that have the same directional label. A bear call spread can reach its maximum gain when the price stays at or below its short-call strike. A bear put spread, in contrast, reaches maximum gain only when the price falls to or below its lower put strike. If the expected decline is modest, the credit spread may already be in its maximum-gain region; if a substantial fall is expected, a put spread’s lower breakeven may be more relevant.

Worked Example: Comparing Bear Call and Bear Put Spreads

An asset is trading at \(50\), and a trader expects an expiration price between \(46\) and \(48\). A bear call spread sells the \(48\)-strike call for \(4.60\) and buys the \(53\)-strike call for \(1.50\). A bear put spread buys the \(50\)-strike put for \(6.20\) and sells the \(45\)-strike put for \(2.00\). Compare their profit in the target range and explain which better matches a moderate decline.

Bear call spread. The net credit is \(4.60-1.50=3.10\). Its breakeven is \(48+3.10=51.10\). Its width is \(53-48=5\), so maximum gain is \(3.10\) and maximum loss is \(5-3.10=1.90\).

At every target price from \(46\) through \(48\), both calls expire without value, so the spread keeps its full \(3.10\) credit as profit. At \(S_T=49\), the short call costs \(49-48=1\) and the long call is out of the money; profit is \(3.10-1=2.10\). At or above \(53\), the spread’s loss is capped at \(1.90\).

Bear put spread. Its debit is \(6.20-2.00=4.20\). Its breakeven is \(50-4.20=45.80\). The strike width is \(50-45=5\), so maximum gain is \(5-4.20=0.80\), and maximum loss is \(4.20\).

At \(S_T=46\), the put payoff is \(50-46=4\), with the \(45\)-strike put expiring without value. Profit is \(4-4.20=-0.20\). At \(S_T=48\), the payoff is \(50-48=2\), so profit is \(2-4.20=-2.20\). If the price falls to \(44\), the payoff is capped at \(5\), giving maximum profit \(5-4.20=0.80\).

Conclusion and check. The bear call spread better matches a moderate decline to \(46\)–\(48\): it earns its full \(3.10\) maximum gain throughout that range. The bear put spread is not yet at breakeven anywhere in the target interval, but it can gain from a deeper decline. At \(44\), its profit equals its calculated maximum gain of \(0.80\).

Common mistake to avoid. A bearish direction alone does not make the put spread the better choice. Check where its breakeven falls: here \(45.80\) is below the whole stated target range.

Compare Credit and Debit Structures for a Bullish Range

A bull put credit spread can suit a view that the underlying will stay above a selected level, because it earns its maximum gain once the price finishes at or above the short-put strike. A bull call debit spread generally benefits from a rise through its long-call strike, but its breakeven may sit above much of a modest target range. Neither structure is automatically preferable: the target-price fit must be weighed against its maximum loss, maximum gain, and the range of prices at which those outcomes occur.

Worked Example: A Bull Put Spread for a Price Expected to Hold Up

An asset is trading at \(75\). A trader expects an expiration price between \(78\) and \(80\). Candidate A is a bull put spread that sells the \(72\)-strike put for \(2.80\) and buys the \(67\)-strike put for \(0.90\). Candidate B is a bull call spread that buys the \(75\)-strike call for \(7.40\) and sells the \(82\)-strike call for \(3.10\). Compare their breakevens and profits at \(78\) and \(80\).

Candidate A: bull put. Its credit is \(2.80-0.90=1.90\). Its breakeven is \(72-1.90=70.10\). The spread width is \(72-67=5\), so maximum gain is \(1.90\) and maximum loss is \(5-1.90=3.10\). Since both puts expire without value for prices of \(78\) and \(80\), profit is \(1.90\) at both prices.

Candidate B: bull call. Its debit is \(7.40-3.10=4.30\). Its breakeven is \(75+4.30=79.30\). Its width is \(82-75=7\), so maximum gain is \(7-4.30=2.70\) and maximum loss is \(4.30\).

At \(S_T=78\), the call spread payoff is \(78-75=3\), so its profit is \(3-4.30=-1.30\). At \(S_T=80\), the payoff is \(80-75=5\), so profit is \(5-4.30=0.70\). Thus the bull put spread earns more at both endpoints of the target range, while the bull call spread is profitable only above \(79.30\).

Conclusion and check. If the view is specifically that the price will remain between \(78\) and \(80\), the bull put spread has the closer profit-region fit: it earns its full \(1.90\) gain throughout. The bull call spread has a higher maximum gain, \(2.70\), if the price reaches or exceeds \(82\). The bull put spread’s maximum loss is \(3.10\), compared with \(4.30\) for the bull call spread. The breakeven check is consistent with the results: \(78\) is above the bull put breakeven but below the bull call breakeven.

Common mistake to avoid. Do not infer that the lower debit of a credit spread means lower risk. Candidate A can lose \(3.10\), which is greater than its \(1.90\) maximum gain.

Use the Target Range, Not Just the Direction

Strike selection is a comparison of possible terminal outcomes, not a forecast guarantee. Before choosing, check more than one price in the stated range—especially the endpoints and any breakeven inside it. For example, a spread that profits at the range’s upper endpoint may still lose at its lower endpoint. Also compare what happens outside the range: a credit spread may have a narrow maximum-gain region and a larger maximum loss, while a debit spread’s maximum loss is its debit but its maximum gain is limited by the strike width.

The examples use expiration profit per share. For a position containing multiple contracts, multiply the per-share profit and loss by the contract multiplier and number of contracts. That scaling changes the dollar amounts, not the strike-based breakeven or the price regions in which the spread gains or loses.

Key takeaway: A spread is aligned with a price view when its breakeven and expiration-profit regions fit the stated target range. Confirm that fit with the net premium and both strike levels, then compare maximum gain and maximum loss. Direction alone is not enough to choose strikes.

Check Your Understanding

For each problem, use the expiration-profit convention stated above. Treat all premiums as per share, and ignore financing and transaction costs.

  1. A bull call spread buys the \(90\)-strike call for \(13.20\) and sells the \(100\)-strike call for \(7.40\). Find its debit, breakeven, maximum gain, maximum loss, and profit if \(S_T=97\). (Answer: Debit \(5.80\); breakeven \(95.80\); maximum gain \(4.20\); maximum loss \(5.80\); profit at \(97\) is \(1.20\).)
  2. A bear put spread buys the \(65\)-strike put for \(8.10\) and sells the \(58\)-strike put for \(2.60\). Find its debit and breakeven, then calculate profit at \(S_T=57\) and \(S_T=60\). (Answer: Debit \(5.50\); breakeven \(59.50\); profit at \(57\) is \(1.50\); profit at \(60\) is \(-0.50\).)
  3. A bear call spread sells the \(44\)-strike call for \(5.20\) and buys the \(49\)-strike call for \(2.00\). Find its credit, breakeven, maximum gain, maximum loss, and profit at \(S_T=47\). (Answer: Credit \(3.20\); breakeven \(47.20\); maximum gain \(3.20\); maximum loss \(1.80\); profit at \(47\) is \(0.20\).)
  4. A bull put spread sells the \(110\)-strike put for \(6.30\) and buys the \(103\)-strike put for \(2.10\). Find its credit, breakeven, and maximum loss. Then calculate profit at \(S_T=107\) and \(S_T=104\). (Answer: Credit \(4.20\); breakeven \(105.80\); maximum loss \(2.80\); profit at \(107\) is \(4.20\); profit at \(104\) is \(-1.80\).)
  5. An asset is expected to finish between \(122\) and \(124\). Candidate A is a bull call spread that buys the \(118\)-strike call for \(9.50\) and sells the \(126\)-strike call for \(4.00\). Candidate B is a bull put spread that sells the \(114\)-strike put for \(3.80\) and buys the \(108\)-strike put for \(1.20\). Which earns more at both endpoints of the target range, and what is its maximum loss? (Answer: Candidate B earns more at both endpoints, with its full \(2.60\) maximum gain at each; its maximum loss is \(3.40\).)
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