FRM Exam Part I · Trading Strategies

Covered Calls and Protective Puts for FRM Part I

Updated 11 October 2026 · Fact-checked

A covered call is long stock plus a short call: you collect the premium but cap your upside. A protective put is long stock plus a long put: you pay a premium and floor your downside. Solve by adding the stock profit and the option profit at each final price, then subtract premium costs or add premium income.

Understand Covered Calls and Protective Puts

Both strategies pair one share of stock with one option on that share. The option changes the shape of the stock's payoff. You are no longer exposed to the full range of outcomes.

A covered call is long the stock and short a call. The short call is covered because you own the shares to deliver if the call is exercised. You receive the call premium up front. In return, you give up any gain above the strike. If the stock falls, you lose on the stock, but the premium cushions the loss a little. The payoff at expiry is S_T if S_T ≤ K, and K if S_T > K, before premium.

A protective put is long the stock and long a put. You pay the put premium. If the stock falls below the strike, the put gains one-for-one and offsets the stock loss. Your worst outcome is fixed. If the stock rises, you keep the gain minus the premium. It works like insurance: the premium is the cost, the strike is the deductible level. The payoff at expiry is K if S_T ≤ K, and S_T if S_T > K, before premium.

The two strategies have mirror-like shapes but are not opposites. The covered call has limited upside and a large downside. The protective put has limited downside and unlimited upside. Put-call parity links them: a protective put (stock + put) has the same payoff as a long call plus cash equal to the present value of the strike. A covered call has the same payoff profile as a short put (with the same strike and expiry) plus cash. Exam questions often test this equivalence.

Key formulas to remember

Covered call profit at expiry: Profit = (S_T − S_0) − max(S_T − K, 0) + C; S_0 is the purchase price, K the strike, C the call premium received. Maximum profit = K − S_0 + C. Breakeven = S_0 − C.
Protective put profit at expiry: Profit = (S_T − S_0) + max(K − S_T, 0) − P; P is the put premium paid. Maximum loss = S_0 − K + P. Breakeven = S_0 + P. Upside is unlimited.
Put-call parity (European, no dividends): c + K·e^(−rT) = p + S_0; Use K ÷ (1 + r)^T if discrete compounding is given. With dividends, subtract the present value of dividends from S_0.
Protective put equivalence: S_0 + p = c + K·e^(−rT); Stock plus put equals a call plus cash. This is why a protective put looks like a long call.
Covered call equivalence: S_0 − c = K·e^(−rT) − p; Stock minus call equals cash minus put. The covered call looks like a short put.

How to solve Covered Calls and Protective Puts questions

Use one routine for any question on covered calls or protective puts. It works for payoffs, profits, breakevens and parity links.

1Identify the positions: long stock, then long or short, call or put. Note S_0, K, the premium and whether the option is European.
2Decide whether the question asks for payoff (ignores the premium and the initial stock cost) or profit (includes them).
3Write the stock profit as S_T − S_0 and the option profit as payoff plus premium received (short) or payoff minus premium paid (long).
4Add the two lines at the key prices: S_T well below K, S_T equal to K, S_T well above K.
5Find the maximum gain, maximum loss and breakeven from the flat or sloped segments.
6For parity questions, replace the stock plus option with the equivalent call or put plus cash and check the present value of K.
7Sanity check: a covered call has capped profit, and a protective put has a floored loss. If your answer breaks this, recheck the signs.

Quickest way: Three-point shortcut

When to use it: Use it for multiple-choice questions asking for maximum profit, maximum loss or breakeven. You can finish in under a minute.

Covered call: max profit = K − S_0 + C. Breakeven = S_0 − C. Max loss = S_0 − C (stock goes to zero).
Protective put: max loss = S_0 + P − K. Breakeven = S_0 + P. Max profit is unlimited.
Check the strike against S_0. An in-the-money put or call changes the sign of K − S_0, so do not skip this.
If the question uses parity, move to the equivalent position: protective put = long call, covered call = short put.

Common mistakes in Covered Calls and Protective Puts

Treating a covered call as protection against large falls.
The word covered sounds like hedged.
Fix: The premium only offsets the first few points of loss. The downside is nearly the full stock loss, reduced by the premium.
Forgetting the premium in breakeven.
Students plot payoffs and read breakeven at S_0.
Fix: Covered call breakeven is S_0 − C. Protective put breakeven is S_0 + P.
Mixing up payoff and profit.
Textbooks use both terms and the formulas look similar.
Fix: Payoff ignores the cost of setting up. Profit subtracts the stock cost and includes the premium. Read the stem for the word used.
Using the wrong sign for the premium on a short call.
The writer receives the premium but students subtract it by habit.
Fix: Short option: add the premium. Long option: subtract the premium.
Applying put-call parity to American options as an equality.
The formula is memorised without conditions.
Fix: The equality holds for European options. For American options only bounds hold. Adjust S_0 for dividends before applying it.
Saying a protective put caps the profit.
Confusion with the covered call, which does cap it.
Fix: The put floors the loss only. The upside stays open, less the premium.

Worked examples

Example 1

An investor buys a share at $50 and writes a 3-month call with strike $55 for a premium of $2. Find the maximum profit, the breakeven price and the profit if the share ends at $60.

Show the solution

Maximum profit = K − S_0 + C = 55 − 50 + 2 = $7, which occurs for any S_T ≥ 55.
Breakeven = S_0 − C = 50 − 2 = $48.
At S_T = 60: stock profit = 60 − 50 = $10. Call payoff owed = 60 − 55 = $5. Net = 10 − 5 + 2 = $7.
This equals the maximum profit, as expected since the price is above the strike.

Answer: Maximum profit $7; breakeven $48; profit at $60 is $7.

Example 2

A share trades at $80. A European put with strike $75 costs $3.50. An investor buys the share and the put. Find the maximum loss and the profit if the share ends at $90.

Show the solution

Maximum loss = S_0 + P − K = 80 + 3.50 − 75 = $8.50, which occurs for any S_T ≤ 75.
Check at S_T = 70: stock loss = −10, put payoff = 75 − 70 = 5, premium = −3.50. Net = −10 + 5 − 3.50 = −$8.50. This matches.
At S_T = 90: stock profit = 90 − 80 = $10. Put expires worthless. Net = 10 − 3.50 = $6.50.

Answer: Maximum loss $8.50; profit at $90 is $6.50.

Exam tips

Draw the profit line at three prices before answering. It catches most sign errors.
Know that protective put = long call + cash, and covered call = short put + cash. Parity links are a favourite.
Check whether the question asks for payoff or profit, and per share or for a contract size.
Look for dividends in parity questions. Subtract their present value from the stock price.
Compare strategies by shape: covered call has capped gain and near-full downside, protective put has a floored loss and open upside.

Practice questions from Trading Strategies

Covered Calls and Protective Puts in other exams

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

Covered Calls and Protective Puts: frequently asked questions

What is the difference between a covered call and a protective put?

A covered call is long stock plus a short call. It earns premium but caps the upside. A protective put is long stock plus a long put. It costs premium but floors the downside and leaves the upside open.

How does put-call parity relate to a protective put?

Put-call parity says c + K·e^(−rT) = p + S_0 for European options without dividends. The right side is a protective put. So a protective put has the same payoff as a long call plus a zero-coupon bond paying K.

How do I draw a covered call profit diagram?

Plot the stock profit as a rising line, then subtract the short call payoff. The result rises with the stock up to the strike, then goes flat. The flat level is K − S_0 + C. The line crosses zero at S_0 − C.

Does a protective put have unlimited profit?

Yes, in theory. If the stock keeps rising, the put expires worthless and you keep the stock gain minus the premium paid. Your loss is limited to S_0 + P − K.