Describe how combination strategies are used and explain their payoff functions.
The idea
Combinations mix calls and puts on the same underlying. A straddle is a long call and a long put with the same strike and expiry. It profits from a large move in either direction, with breakevens at the strike plus and minus the total premium paid. A strangle uses an out-of-the-money put and an out-of-the-money call. It costs less but needs a bigger move, with breakevens at the put strike minus the total premium and the call strike plus the total premium. A strip is one call and two puts, a volatility bet with a bearish tilt. A strap is two calls and one put, with a bullish tilt. Selling these positions collects premium and profits if the price stays quiet, but exposes the seller to large losses on a big move. The usual error is to forget that the premium on both options must be recovered before the position shows a profit.
Formulas
Breakevens of a long straddle
breakevens = K − (c + p) and K + (c + p)
- K
- the strike shared by the call and the put
- c
- the call premium
- p
- the put premium
Both premiums must be recovered before the position shows a profit. For a short straddle the same points bound the profit zone.
Breakevens of a long strangle
breakevens = K₁ − (c + p) and K₂ + (c + p)
- K₁
- the strike of the out-of-the-money put
- K₂
- the strike of the out-of-the-money call
- c
- the call premium
- p
- the put premium
Cheaper than a straddle, so the premium is smaller, but the price must move beyond a strike by more than the total premium.
A practice question
A trader buys a call and a put on the same stock with the same strike and expiry. Which view does this position express?
- A large price move is expected, but the direction is uncertain - correct
- The price is expected to remain close to the strikeWhy not: That view is expressed by a short straddle or a butterfly; a long straddle loses most at the strike.
- The price is expected to rise moderatelyWhy not: A bull call spread or a single call expresses that; the added put loses in a rise.
- The holder of the stock wants protection against a fallWhy not: A protective put hedges a stock holding; the extra call only adds cost to a hedge.
Long call plus long put at one strike is a long straddle: it gains on a big move up or down and loses the premium if the price finishes near the strike.
A harder one
A trader buys a call at 3.80 and a put at 3.20, both with strike 75 and the same expiry. If the stock is 85 at expiry, the profit per share is closest to:
- 10.00Why not: Ignores the total premium of 7.00 paid for both options.
- 3.00 - correct
- 6.20Why not: Subtracts only the call premium and forgets the premium paid for the put.
- 17.00Why not: Adds the premium instead of subtracting it; premiums paid are a cost.
Only the call is in the money: payoff = 85 - 75 = 10. Total premium = 3.80 + 3.20 = 7.00. Profit = 10 - 7.00 = 3.00.
The hardest tier
A trader buys a strip on a stock: one call and two puts, all with strike 100 and the same expiry. The call costs 6 and each put costs 5. If the stock is 88 at expiry, the profit on the strip is closest to:
- 24Why not: Counts the payoff of both puts but ignores the 16 premium paid for the strip.
- -4Why not: Counts only one put's payoff while still paying the premium for both puts.
- 8 - correct
- -5Why not: This is the result of a strap (two calls, one put), which is the opposite tilt to a strip.
Strip cost = 6 + 2 x 5 = 16. At 88 the call expires worthless and each put pays 12, so payoff = 24. Profit = 24 - 16 = 8.
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