Skip to content

FRM Exam Part I · Options Markets

Combinations and Covered Strategies in Options Markets

Updated 11 October 2026 · Fact-checked

Combinations mix calls and puts on the same asset to express a view on volatility. A straddle is a long call and put at one strike. A strangle uses two strikes. Strips and straps tilt a straddle. Covered calls and protective puts pair an option with the stock. Solve by adding payoffs and subtracting the premium.

Understand Combinations and Covered Strategies

A single option bets on direction. A combination holds calls and puts on the same underlying, so you can bet on how far the price moves instead of which way. That is a view on volatility.

A long straddle is a long call and a long put with the same strike and expiry. You pay two premiums. You profit if the price ends far from the strike in either direction. You lose the most if it ends exactly at the strike. A long strangle uses an out-of-the-money put (lower strike) and an out-of-the-money call (higher strike). It costs less, but the price must move further before you profit. Selling these (short straddle, short strangle) is the opposite view: you expect low volatility, you collect premium, and your loss is large if the price moves a lot.

A strip is a long call and two long puts at the same strike. It is a straddle that pays more if the price falls, so you are bearish and expect a big move. A strap is two long calls and one long put at the same strike. It pays more if the price rises, so you are bullish and expect a big move. Both cost more than a straddle.

A covered call is a long stock position plus a short call. You earn the premium but give up gains above the strike. Its shape looks like a short put. A protective put is a long stock position plus a long put. It sets a floor on your loss at the cost of the premium. Its shape looks like a long call. Put-call parity explains these resemblances.

In all cases, build the total payoff by adding each leg at expiry, then subtract the net premium paid (or add the net premium received) to get profit.

Key formulas to remember

Long straddle profit (strike K)
Profit = max(S_T − K, 0) + max(K − S_T, 0) − (c + p) = |S_T − K| − (c + p)
Break-evens: K + (c + p) and K − (c + p). Maximum loss is c + p at S_T = K. Gain is unlimited on the upside.
Long strangle profit (put strike K1 < call strike K2)
Profit = max(S_T − K2, 0) + max(K1 − S_T, 0) − (c + p)
Break-evens: K2 + (c + p) and K1 − (c + p). Maximum loss is c + p for any S_T between K1 and K2.
Strip (1 call + 2 puts, strike K)
Profit = max(S_T − K, 0) + 2 × max(K − S_T, 0) − (c + 2p)
Bearish tilt. Break-evens: K + (c + 2p) above, and K − (c + 2p) ÷ 2 below.
Strap (2 calls + 1 put, strike K)
Profit = 2 × max(S_T − K, 0) + max(K − S_T, 0) − (2c + p)
Bullish tilt. Break-evens: K + (2c + p) ÷ 2 above, and K − (2c + p) below.
Covered call profit
Profit = (S_T − S_0) − max(S_T − K, 0) + c
Maximum profit = K − S_0 + c, reached when S_T ≥ K. Loss is large if the stock falls.
Protective put profit
Profit = (S_T − S_0) + max(K − S_T, 0) − p
Maximum loss = S_0 − K + p, when S_T ≤ K. Upside is unlimited.
Put-call parity link (European, no dividends)
S_0 + p = c + K × e^(−rT)
Shows a protective put is equivalent to a long call plus cash. A covered call is equivalent to a short put plus cash.

How to solve Combinations and Covered Strategies questions

Use the same routine for any combination question. Work at expiry, leg by leg, and keep premiums separate until the end.

  1. 1List every leg: long or short, call or put, strike, and quantity.
  2. 2Compute the net premium. Long legs cost money, short legs bring it in.
  3. 3Write the payoff of each leg for the three zones: below the lowest strike, between strikes, above the highest strike.
  4. 4Add the leg payoffs in each zone, then subtract net premium paid to get profit.
  5. 5Find break-evens by setting profit to zero in the zone where it crosses zero. Check that each answer lies in that zone.
  6. 6Find maximum loss and maximum gain from the end points and the strike points.
  7. 7Match the shape to the view: long volatility, short volatility, bullish, bearish, or hedged.

Quickest way: Shape and break-even shortcut

When to use it: Use when options give a view or a break-even and you need an answer in under a minute.

  1. Identify the strategy from the legs: same strike with call and put is a straddle, strip or strap; different strikes is a strangle.
  2. Use total premium as the distance. For a straddle, break-evens are K ± (c + p).
  3. For strips and straps, the heavier side divides the premium: the doubled leg gives a break-even closer to K.
  4. For stock plus option, remember the lookalike: covered call is a short put shape, protective put is a long call shape.
  5. Eliminate options whose view conflicts with the shape, then confirm with one calculation.

Common mistakes in Combinations and Covered Strategies

  • Treating a straddle as a directional bet.

    Students see a call and assume a bullish view.

    Fix: A straddle holds both a call and a put. It gains from a large move in either direction and is a bet on high volatility.

  • Forgetting to subtract the premium when finding break-evens.

    Payoff and profit get mixed up.

    Fix: Break-even is where payoff equals the total premium paid. Always compute profit, not just payoff.

  • Mixing up strip and strap.

    The names sound alike.

    Fix: Strap has more calls (bullish). Strip has more puts (bearish). Think: a strap pulls the price up.

  • Using c + p as the distance for strips and straps.

    Students copy the straddle rule.

    Fix: Only one side has doubled payoff. Divide the total premium by 2 on that side, as the formulas show.

  • Saying a covered call protects against a fall.

    The word covered suggests safety.

    Fix: The call premium only cushions a small fall. The stock downside stays. A protective put is the one that sets a floor.

  • Getting strangle strikes the wrong way round.

    Students put the call strike below the put strike.

    Fix: A long strangle buys an out-of-the-money put (low strike) and out-of-the-money call (high strike). Flat zone sits between them.

Worked examples

Example 1

A trader buys a 3-month straddle on a stock with strike $50. The call costs $4 and the put costs $3. Find the break-even prices and the maximum loss. What is the profit if the stock ends at $62?

Show the solution
  1. Total premium = 4 + 3 = $7.
  2. Upper break-even = 50 + 7 = $57.
  3. Lower break-even = 50 − 7 = $43.
  4. Maximum loss occurs at S_T = 50 and equals the premium, $7.
  5. At S_T = 62: payoff = |62 − 50| = 12.
  6. Profit = 12 − 7 = $5.

Answer: Break-evens are $43 and $57. Maximum loss is $7. Profit at $62 is $5.

Example 2

An investor holds a stock bought at $80 and sells a call with strike $85 for $3. What are the maximum profit and the break-even price at expiry? Then compare with buying a put with strike $75 for $2 instead of selling the call: what is the maximum loss?

Show the solution
  1. Covered call maximum profit = K − S_0 + c = 85 − 80 + 3 = $8, reached when S_T ≥ 85.
  2. Break-even: stock price falls by the premium, so 80 − 3 = $77.
  3. Protective put maximum loss = S_0 − K + p = 80 − 75 + 2 = $7.
  4. This loss applies for any S_T ≤ 75. Above 75 the loss is smaller, and gains are unlimited above the break-even of 80 + 2 = $82.

Answer: Covered call: maximum profit $8, break-even $77. Protective put: maximum loss $7, break-even $82.

Exam tips

  • Check whether the question asks for payoff or profit. Many wrong options are the payoff answer.
  • Draw the three zones quickly. It prevents break-even errors on strangles, strips and straps.
  • Link views to strategies: long straddle, strangle, strip and strap expect a big move. Short versions expect little movement.
  • Remember the lookalikes from put-call parity. Questions often ask which option position a covered call or protective put resembles.
  • Use the stated units and dollar values. Avoid rounding until the last step.

Practice questions from Options Markets

Combinations and Covered Strategies in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Combinations and Covered Strategies: frequently asked questions

What is the difference between a straddle and a strangle?

A straddle uses the same strike for the call and put. A strangle uses a lower strike put and a higher strike call. The strangle costs less but needs a bigger price move to profit.

When should you use a long straddle?

Use it when you expect a large price move but are unsure of the direction, such as before an earnings release or a major announcement. It loses the full premium if the price stays near the strike.

What is the difference between a strip and a strap?

A strip is one call and two puts at the same strike, so it is bearish. A strap is two calls and one put at the same strike, so it is bullish. Both profit from large moves.

Why does a covered call look like a short put?

Put-call parity shows that stock minus a call equals a short put plus cash, in the European, no-dividend case. Both positions earn limited premium and lose when the stock falls.