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FRM Part I · FRM Exam Part I

Trading Strategies for FRM Part I: Options Combinations Explained

Trading strategies combine options, the underlying asset and bonds to create a chosen payoff. To solve questions, list each position's payoff at expiry, add them, then subtract the net premium paid or add the premium received. Read off profit, breakeven and maximum loss from the result.

What this chapter covers

This chapter shows how you build a payoff shape from simple pieces: a long or short asset, calls, puts and zero-coupon bonds. You study principal-protected notes, covered calls, protective puts, bull and bear spreads, box and butterfly spreads, and straddles, strangles and other combinations.

The method is the same every time. Write the payoff of each leg at expiry, add the legs together, then adjust for the premiums. Once you can do this, you can handle any strategy, even one you have not seen before.

The chapter connects to Financial Markets and Products, where you learn how options are priced and how put-call parity links calls, puts, the asset and a bond. It also supports Valuation and Risk Models, where payoff shapes explain why option positions have nonlinear risk. The questions are quantitative, so you need accuracy with numbers under time pressure.

FRM Part I has 100 equally weighted questions in 4 hours, so every question is worth the same. Strategy questions are usually mechanical: you compute a payoff, a profit or a breakeven. If you know the method, they are fast and reliable points. They also reinforce put-call parity and option payoffs, which help in neighbouring chapters. GARP revises the curriculum every year, so check the current Study Guide and Learning Objectives for exact coverage.

Trading Strategies: topics in the order to study them

  1. 1Covered Calls and Protective PutsStart here. These add one option to one asset, so you learn payoff addition and premium adjustment in the simplest setting.
  2. 2Bull and Bear SpreadsNext you combine two options of the same type. You learn how a spread caps both profit and loss.
  3. 3Straddles, Strangles and Other CombinationsNow you mix calls and puts to bet on volatility rather than direction. Breakevens now come in pairs.
  4. 4Box Spreads and Butterfly SpreadsThese use four options or three strikes, so they come after you are fluent with two-leg payoffs. A box links to arbitrage and put-call parity.
  5. 5Principal-Protected Notes and Structured ProductsFinish with notes that bundle a zero-coupon bond with options. You need payoff building and discounting together.

How to prepare Trading Strategies

Use one repeatable method for every strategy, and practise it until it takes under two minutes.

  1. Learn the payoff of each basic position at expiry: long and short asset, long and short call, long and short put. Sketch each one.
  2. For every strategy, write the legs, add their payoffs in each price region (below the lower strike, between strikes, above the upper strike), and then include premiums.
  3. Compute breakeven, maximum profit and maximum loss by hand for at least two numeric examples per strategy.
  4. Match each strategy to a market view: bullish, bearish, expecting large moves, or expecting little movement. Exam questions often describe the view in words.
  5. Practise put-call parity (c + K·e^(−rT) = p + S₀ with continuous compounding) and use it to see why a box spread is risk-free and how a protective put relates to a call plus bond.
  6. For structured products, work out the bond value by discounting, then see how much is left to buy the option. Use your financial calculator for present values.
  7. Finish with timed mixed questions. Check that you subtracted premiums and used the right strikes.

Common mistakes in Trading Strategies

  • Reporting payoff when the question asks for profit.

    Fix: Write profit = payoff − net premium paid on the last line of every solution. Check the question wording first.

  • Mixing up which strike is bought and which is sold in a spread.

    Fix: Reason from the view. A bull spread wants gains when the price rises, so you hold the lower-strike long position. Test by checking the payoff at a high price.

  • Finding only one breakeven for a straddle or strangle.

    Fix: Find one breakeven on each side. For a long straddle they are K minus and K plus the total premium.

  • Treating a box spread as a directional bet.

    Fix: Remember the payoff is the same in every price outcome. Compare its price with the discounted strike difference.

  • Ignoring discounting in principal-protected notes.

    Fix: Price the zero-coupon bond as principal ÷ (1 + r)^T or with continuous compounding, as stated. The remainder funds the option.

  • Thinking a covered call limits losses substantially.

    Fix: The premium only cushions the loss. The downside is still large if the asset falls. Only a protective put sets a floor.

Last-day revision: Trading Strategies

  • Covered call = long asset + short call; it caps upside and the premium cushions small falls.
  • Protective put = long asset + long put; it sets a floor at the strike, less the premium paid.
  • Protective put payoff resembles a long call plus a bond, by put-call parity.
  • Bull call spread = long low-strike call + short high-strike call; maximum profit = strike difference − net premium.
  • Bear spreads profit when the price falls; a bear put spread buys the higher strike put and sells the lower strike put.
  • Long straddle = long call + long put at the same strike; profit needs a large move either way. Two breakevens: K ± total premium.
  • A strangle uses different strikes (out-of-the-money put and call), so it costs less but needs a bigger move.
  • Long butterfly (calls) = long low and high strike calls, short two middle strike calls; profits if the price stays near the middle.
  • A box spread combines a bull call spread and a bear put spread with the same strikes; its payoff is fixed at the strike difference.
  • A box spread's fair value is the strike difference discounted at the risk-free rate; a different price implies arbitrage.
  • Principal-protected note = zero-coupon bond + option; the option budget is the amount left after buying the bond.
  • Always add premiums to the payoff to get profit, and check the maximum loss against the net premium.

Trading Strategies practice questions

Trading Strategies in other exams

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

Trading Strategies: frequently asked questions

How do I find the maximum profit of an option spread?

Add the payoffs of the legs in the region where the price is beyond both strikes, then subtract the net premium. For a bull call spread, maximum profit is the strike difference minus the net premium paid.

What is the difference between a straddle and a strangle?

A straddle uses a call and a put at the same strike. A strangle uses different strikes, usually an out-of-the-money put and call. The strangle costs less but needs a larger price move to profit.

Do I need a financial calculator for this chapter?

It helps mainly for discounting, such as pricing the bond in a principal-protected note or the present value of a box spread's payoff. Payoff questions need only basic arithmetic.

Why is put-call parity relevant to trading strategies?

It shows that a protective put and a call plus a bond have the same payoff. It also explains why a box spread is risk-free. Knowing it lets you move between equivalent strategies.