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The Series 7 asks you for three numbers on every strategy: maximum gain, maximum loss and breakeven. If you can produce them for the positions in this chapter, with the arithmetic, you have the option questions that account for a large share of the exam. All examples use standard 100-share contracts and ignore commissions. Premiums are per share; multiply by 100 for dollars.

Start with the four basic positions

Two reflexes make the rest easy. First, the breakeven for any single option is strike ± premium (plus for calls, minus for puts), whether you bought or sold it. Second, the buyer's maximum loss is the writer's maximum gain, and the reverse.

Covered call writing (and the covered put)

A covered call is long 100 shares plus a short call on the same shares. The stock covers the call: if the call is assigned, the customer delivers shares already owned.

The purpose is income and a small cushion against loss. The cost is that upside is capped at the strike.

Worked example. A customer buys 100 XYZ at 48 and sells one XYZ 50 call for 3.

If XYZ finishes at 52 the call is assigned: the customer sells at 50 and keeps the 3. The gain is $500, not the $700 the stock alone would have produced. If XYZ finishes at 47, the call expires, the customer keeps the $300, and the stock has lost $100: net +$200. Maximum gain occurs at any price from 50 up.

A covered call is considered a conservative strategy but not a risk-free one. The loss on the stock is cushioned only by the premium. The risk the exam wants named is opportunity cost: giving up gains above the strike.

A covered put is the mirror image: short 100 shares plus a short put. The short put is "covered" in the sense that if it is assigned, the customer buys the stock at the strike and uses it to close the short position. The short stock is unprotected on the upside, so the loss is unlimited if the stock rises. The gain is limited to the premium plus any gap between the short-sale price and the strike: maximum gain = premium + (short price − strike) × 100.

Example. Short 100 at 40, sell one 40 put at 2. Breakeven = 40 + 2 = 42. Maximum gain = $200 (the premium) if the stock falls: the put is assigned at 40, the customer buys 100 at 40 and uses them to close the short position, which was opened at 40, leaving only the premium. Maximum loss is unlimited above 42.

A cash-secured put (short put with cash set aside to buy the stock) is not a "covered put" in the exam's sense, but its numbers equal those of a short put.

Protective put and protective call (hedging with options)

A protective put is long stock plus long put. It sets a floor under a position: the customer can sell at the strike no matter how far the stock falls. Think of it as insurance: the premium is the price of the policy.

Example. A customer owns 100 XYZ bought at 60 and buys a 55 put for 2.50.

• Breakeven = 60 + 2.50 = 62.50.
• Maximum loss = (60 − 55 + 2.50) × 100 = $750, no matter how low the stock goes.
• Maximum gain: unlimited (stock rises, put expires).

Compare with a covered call: the covered call pays the customer premium and limits gains; the protective put costs the customer premium and limits losses.

A protective call is short stock plus long call. It caps the loss on a short sale. Example: short 100 at 40, buy a 45 call for 1.50. Breakeven = 40 − 1.50 = 38.50. Maximum loss = (45 − 40 + 1.50) × 100 = $650. Maximum gain = (40 − 1.50) × 100 = $3,850 if the stock goes to zero.

Hedging a portfolio with index options

Index puts hedge a diversified portfolio because the index moves with it. The number of contracts is:

Contracts = portfolio value ÷ (index level × multiplier), then adjusted for the portfolio's beta.

Illustration (hypothetical index level). A $1,000,000 portfolio that tracks the broad market, with a broad-based index at 5,000 and a $100 multiplier. Each contract covers 5,000 × 100 = $500,000 of index value, so 2 puts hedge the portfolio. If the portfolio's beta against the index is 1.2, the hedge ratio is 1,000,000 × 1.2 ÷ 500,000 = 2.4, or about 2 or 3 contracts. The hedge is imperfect (basis risk): the portfolio may fall by more or less than the index. Index options are cash-settled, which is convenient, and if the market rises the portfolio profits while the puts lose their premium.

Collars

A collar is long stock, long put (below the market), short call (above the market). The short call premium pays for all or part of the put. The customer gives up upside above the call strike in return for a floor under the put strike.

Example. A customer buys 100 XYZ at 50, buys one 45 put for 1.50, and sells one 55 call for 2.

• Net option cost = 1.50 − 2.00 = a 0.50 credit. Effective cost per share = 50 − 0.50 = 49.50.
• Maximum gain = 55 − 49.50 = 5.50, or $550.
• Maximum loss = 49.50 − 45 = 4.50, or $450.
• Breakeven = $49.50.

When the premiums are equal, the collar costs nothing: a "zero-cost" collar. Collars are used for concentrated stock positions where the customer wants protection without cash outlay. Note that a collar is a hedge, not a speculation: both gain and loss are capped.

Spreads

A spread is the purchase of one option and sale of another of the same type (both calls or both puts) on the same underlying stock. The classification:

A debit spread costs money to open (the long option is the more expensive). A credit spread receives money (the short option is the more expensive). A trader with a debit spread wants the spread to widen; a trader with a credit spread wants it to narrow.

For a vertical spread, maximum gain + maximum loss = difference between the strikes (× 100). Use this to check your work.

Debit spreads

Bull call spread. Buy the lower-strike call, sell the higher-strike call. Example: buy 50 call at 6, sell 55 call at 3.

• Net debit = 6 − 3 = 3, or $300. This is the maximum loss, reached if the stock is at or below 50 at expiration.
• Maximum gain = (55 − 50 − 3) × 100 = $200, reached at or above 55.
• Breakeven = 50 + 3 = 53.
• Check: 300 + 200 = 500 = 5 points × 100.

Bear put spread. Buy the higher-strike put, sell the lower-strike put. Example: buy 55 put at 4, sell 50 put at 1.50.

• Net debit = 2.50, or $250 (maximum loss, at or above 55).
• Maximum gain = (55 − 50 − 2.50) × 100 = $250, at or below 50.
• Breakeven = 55 − 2.50 = 52.50.

Credit spreads

Bear call spread. Sell the lower-strike call, buy the higher-strike call. Example: sell 50 call at 5, buy 55 call at 2.

• Net credit = 3, or $300 (maximum gain, if the stock is at or below 50).
• Maximum loss = (55 − 50 − 3) × 100 = $200, at or above 55.
• Breakeven = 50 + 3 = 53.

Bull put spread. Sell the higher-strike put, buy the lower-strike put. Example: sell 50 put at 3, buy 45 put at 1.

• Net credit = 2, or $200 (maximum gain, stock at or above 50).
• Maximum loss = (50 − 45 − 2) × 100 = $300, at or below 45.
• Breakeven = 50 − 2 = 48.

A quick way to classify. For calls, buying the lower strike is a debit and bullish; selling the lower strike is a credit and bearish. For puts, buying the higher strike is a debit and bearish; selling the higher strike is a credit and bullish. The exam tests this by giving you positions and asking whether the spread is a debit or credit and bullish or bearish.

Margin. A debit spread requires the customer to pay the net debit in full. A credit spread requires a deposit of the difference between the strikes less the credit, which equals the maximum loss: the bear call spread above needs ($500 − $300) = $200 in addition to the credit received.

Calendar and diagonal spreads

A calendar (time or horizontal) spread sells a near-term option and buys a longer-dated option of the same strike. It profits from the faster decay of the near-term option. It is a debit spread because the longer-dated option is worth more.

Example. Sell the March 50 call at 1.50, buy the June 50 call at 3.50. Net debit = 2.00 ($200), which is the maximum loss for the position at the time the near-term option expires. The best result occurs if the stock is near 50 when the March option expires: the short option expires worthless and the long June call retains time value.

A diagonal spread changes both strike and month (for example, buy the June 50 call, sell the March 55 call). It combines a vertical and a calendar view and is a debit or credit depending on the prices.

Straddles, strangles and combinations

A straddle is a call and a put on the same stock with the same strike and same expiration. A strangle is a call and a put with the same expiration but different strikes, usually both out of the money. A combination is any other call-and-put pair, including different strikes and/or different expirations.

A long position is a bet on volatility: the customer profits if the stock moves a lot in either direction. A short position is a bet on little movement.

Long straddle. Buy a 50 call at 3 and a 50 put at 2.50.

• Total premium = 5.50, or $550: the maximum loss, at exactly 50 at expiration.
• Upper breakeven = 50 + 5.50 = 55.50; lower breakeven = 50 − 5.50 = 44.50.
• Maximum gain: unlimited on the upside; (50 − 5.50) × 100 = $4,450 on the downside.

Short straddle. Sell both: maximum gain $550 (stock at 50), unlimited loss on the upside, and loss down to (50 − 5.50) × 100 = $4,450 on the downside. The breakevens are the same 44.50 and 55.50.

Long strangle. Buy a 55 call at 1.50 and a 45 put at 1.00.

• Total premium = 2.50, or $250 (maximum loss, anywhere between 45 and 55).
• Upper breakeven = 55 + 2.50 = 57.50; lower breakeven = 45 − 2.50 = 42.50.

A strangle costs less than a straddle but needs a larger move to profit. A short strangle collects less, but has a wider zone where the writer keeps the whole premium; the risk is large moves either way and, on the upside, unlimited.

For a long straddle, strangle or combination: breakeven points = strikes ± total premium. For a short one, the same points apply, but they bound the profit zone instead of the loss zone.