Choose option protection by payoff, cost and risk exposure

Learning goals

• Compare protective puts, covered calls, spreads and collars.
• Relate option sensitivities and volatility views to implementation.

Draft · approximately 60 minutes, excluding further revision.

Decision case · fictional facts

A fictional investor owns one share at 100. A 95 put costs 3 and a 110 call can be sold for 2, same expiry. Ignore interest, dividends, taxes and trading fees. A collar combines the stock, long put and short call. Compare terminal stock prices 80,100,120. The investor also considers a long 100 call/short 110 call spread at net premium 4.

Translate the mandate into a terminal payoff

A protective put limits expiry downside while retaining upside, at a premium cost. A covered call exchanges some upside for premium and retains substantial stock downside; it is not full insurance. A collar finances some put cost by capping upside with a short call. Compare total initial cost, expiry value, profit, break-even and assignment obligations on the same per-share basis.

Vertical spreads limit both gain and loss; a debit bull call spread buys the lower strike and sells the higher. Straddles and strangles seek large moves but pay time value, while short volatility strategies can have severe tail losses. Calendar spreads depend on the term structure and changing volatility, so a simple directional label is insufficient.

Manage sensitivities before expiry

Delta approximates small price sensitivity; gamma measures its change, vega sensitivity to implied volatility, theta time decay and rho rate sensitivity under a model. Long vanilla options are generally long gamma/vega; a locally delta-neutral hedge still faces gamma, discrete rebalancing, cost and model error. Implied volatility is a market price input, not a guarantee of future realized volatility.

Contract multiplier, exercise style, early assignment, dividend dates, liquidity and collateral can change implementation. Payoff diagrams at maturity omit path-dependent margin demands. Stress jumps and volatility shifts, obtain suitable permissions, and confirm how protection matches the investor’s actual holding and horizon.

Protective put: price the floor and insurance cost

One share costs 100 and a same-horizon put with strike 95 costs 4. Ignore financing, dividends, fees and early exercise. Total initial cost 104; expiration value=max(ST,95). Maximum loss 9, upside profit is uncapped, and upside breakeven 104. The put limits loss over its life but protection expires and renewal can be costly.

At ST 80, the stock loses 20 and put pays 15, so net loss after premium is 9. At ST 120, put expires and combined profit 16. The hedge does not guarantee a positive return.

Delta compares local exposure, not full downside

With call delta.6, a covered call has delta 1−.6=.4. With put delta−.4, a protective put has delta.6. Assume a short forward has delta−1 in the same zero-carry units; long stock plus short forward then has delta 0. These local sensitivities differ from nonlinear expiration outcomes and change as spot, time and volatility change.

A delta-neutral position can retain gamma, vega, funding and basis risk. Do not treat current delta as a permanent hedge ratio.

Calls and short puts change a short-stock profile differently

A short stock plus a long call at strike 100 has expiration liability min(ST,100)before premiums: the call caps the loss from rising stock. A short stock plus a short put at 100 has liability max(ST,100): downside-stock gains are capped while losses as stock rises remain unbounded. Premiums, borrow, dividends and financing still affect profit.

At ST 150, the long call pays 50 against the short stock’s 150 repurchase liability; the short put pays nothing. Buying a call is therefore not economically interchangeable with selling a put on a short-stock position.

Compare spread, straddle and collar payoff shapes

Ignore financing and fees; all options below share expiry and one-share coverage. Bull call: buy K 100 call for 8, sell K 110 call for 3; net debit 5, max gain 5, max loss 5, breakeven 105. Bear put: buy K 110 put for 12, sell K 100 put for 6; debit 6, max gain 4, max loss 6, breakeven 104. Each vertical trades capped reward for bounded loss.

Long straddle at K 100 with total premium 10 has breakevens 90 and 110, max loss 10, and benefits from sufficiently large movement in either direction. Long stock 100 with put K 95 cost 4 and short call K 110 receipt 2 forms a collar: initial net cost 102, expiration floor 95, ceiling 110, max loss 7, max gain 8, and breakeven 102. The collar gives up extreme upside to help finance a floor.

Calendar spreads trade the term structure

A long calendar sells a near-dated option and buys a longer-dated option of the same type and strike. It can express relative time-decay and volatility-term-structure views. At the short option’s expiry, the long option still has time value; subtracting two final intrinsic payoffs at that date is invalid. Assignment, margin and a large spot move can create risk.

Evaluate both implied volatilities, remaining maturity, spot path and exit policy. A cheap initial debit does not make the strategy a guaranteed income trade.

Smile and skew are strike-dependent implied volatility

For a fixed expiry, implied volatility can differ across strikes. A smile has relatively high volatilities in both wings; a skew can make downside protection especially expensive. Implied volatility is inferred from prices through a model, not a directly guaranteed future realized volatility. Compare matched maturities and delta/strike conventions.

A put-spread or collar can reduce premium but changes tail protection or upside rights. Price each leg on the relevant surface rather than using one ATM volatility for every option.

Select an option strategy from objectives

A client insisting on a defined short-horizon floor and retaining all upside can consider a protective put if the premium is affordable. A covered call earns premium while retaining substantial downside and caps upside; it is not equivalent insurance. A collar can fund some protection by surrendering upside. A long straddle requires movement large enough to overcome both premiums.

Check mandate, coverage, horizon, cost, liquidity and assignment before choosing the attractive payoff diagram. Use the same unit coverage and maturity when comparing strategies.

Target delta with stated contract size

Hold 500 shares, delta 500. A call contract covers 100 shares and has option delta.6, so each short call contributes−60 delta. To target delta 200, short five matching calls:(500−200)/60=5 contracts. This is a local hedge; spot and time changes require monitoring and can change delta materially.

Contract rounding, basis, dividend and exercise risk matter; delta targeting does not establish a guaranteed loss limit or remove margin obligations.

Formula and assumptions

Collar expiry value=S+max(Kput−S,0)−max(S−Kcall,0); profit=expiry value−net initial cost

Errors to catch

• Calling a covered call downside insurance.
• Confusing payoff with profit after premium.

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Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.optionseducation.org
• Reference · www.cmegroup.com