Protective Put

At expiration the combined position is worth the greater of the asset price or the strike: if the asset settles above the strike the put expires worthless and the holder keeps the asset outright; if it settles below, the put is exercised and the effective proceeds equal the strike. Value at expiry is therefore the maximum of the settlement price and the strike, and profit subtracts the original asset purchase price plus the premium paid.

Three quantities follow directly. Breakeven is the asset purchase price plus the premium, since the asset must rise by the cost of the insurance before the strategy turns profitable. Maximum loss is the purchase price plus the premium minus the strike, which is fixed and known at inception. Maximum gain is theoretically unlimited, because upside participation above breakeven is unimpaired. Candidates should be able to produce all three from a stated strike, spot and premium without drawing the diagram.

Put-call parity states that a long asset plus a long put on that asset equals a long call plus a risk-free bond maturing at the strike. The left side is the protective put; the right side is often called a fiduciary call. Both terminal payoffs equal the greater of the settlement price and the strike, so in a no-arbitrage market the two packages must cost the same today.

This equivalence is exam-relevant in two directions. It explains why a hedged long position behaves like a call: limited downside, convex upside, and value that decays with time as the embedded option loses premium. It also lets a candidate reprice one structure from another, or identify an arbitrage when quoted prices for the asset, put, call and discount bond are inconsistent. Recognising that a protective put is insurance with an option-like cost structure, not a costless guarantee, follows from the same relationship.

Protection is priced, not granted. A higher strike raises the floor but costs more premium, pushing breakeven further away and reducing expected upside; a lower strike is cheaper but tolerates a larger loss before the hedge engages. Longer-dated puts cost more in absolute terms but less per unit of time, which is why rolling short-dated protection repeatedly can be more expensive than buying a single longer contract.

Implied volatility is the dominant variable in practice. Put premiums rise sharply when markets are stressed, and equity index puts typically trade at implied volatilities above at-the-money levels because of persistent demand for downside insurance, the pattern known as the volatility skew. A candidate should therefore treat the drag from premium as a recurring cost of carry on the hedged portfolio, and be able to explain why hedging after a shock is markedly less efficient than hedging before one.

Asset managers buy index puts to floor the value of a diversified equity book without liquidating holdings, which preserves dividend income, avoids realising taxable gains and keeps transaction costs low relative to selling and repurchasing the underlying. Holders of concentrated single-stock positions, including executives subject to lock-ups, use puts to limit downside exposure they cannot otherwise sell. Commodity producers and importers apply the same logic to output or input prices.

Because the premium drag is unattractive over long horizons, the protective put is frequently converted into a collar by selling a call above the market to fund part or all of the put cost, accepting a cap on upside in exchange. Candidates should be able to compare these alternatives on floor level, cost, retained upside and breakeven, and to state clearly that basis risk remains when the put is written on an index rather than on the exact portfolio held.