Estimated study time: 45 minutes
Content:
Options are uniquely powerful hedging instruments because they provide asymmetric payoffs — the holder can cap downside while preserving upside. At Level 3, the emphasis is on using options to manage portfolio risk rather than on option pricing theory (which was covered at Level 2). Key applications include protective puts, covered calls, collars, and portfolio insurance strategies.
A protective put combines a long stock (or portfolio) position with a long put option. The put gives the holder the right to sell at the strike price, capping downside loss at (purchase price − put strike price) + premium paid, while preserving unlimited upside. The cost is the put premium. For a portfolio manager concerned about a market decline, buying index puts on the portfolio's benchmark creates a "portfolio insurance" strategy. The tradeoff: premium paid reduces returns in flat or rising markets.
A covered call involves holding the underlying asset and selling a call option. The short call generates premium income, which partially offsets potential losses. However, the short call caps the portfolio's upside — if the asset rises above the strike, the gain is capped. Covered calls are appropriate for investors expecting sideways markets who want to generate income. Downside protection is limited to the call premium received.
A collar combines a protective put and a covered call: buy a put (floor) and sell a call (cap), creating a range within which the portfolio's value is "collared." A zero-cost collar occurs when the put premium equals the call premium — no net cost, but both upside and downside are capped. Collars are common when investors have a large concentrated equity position and want to hedge without selling (which would trigger capital gains).
Delta hedging is the continuous adjustment of option positions or underlying positions to maintain a target portfolio delta of zero (delta-neutral). As the underlying price moves, delta changes (gamma effect), requiring rebalancing. Gamma is the rate of change of delta — high gamma options require frequent rebalancing. A long options position has positive gamma (the position becomes more favorable as the underlying moves in either direction). Delta-neutral, long-gamma positions profit from large moves in either direction (used in volatility trading).
Portfolio insurance using options seeks to replicate a protective put synthetically using dynamic trading — selling the underlying when it falls (reducing exposure) and buying when it rises. The replication requires frequent rebalancing and works only if markets are liquid and price moves are continuous. Black Monday (October 1987) demonstrated the failure mode: markets gapped down faster than portfolio insurance strategies could rebalance, exacerbating the crash by adding systematic selling pressure.
Key Terms:
Quiz Questions:
Q1. A portfolio manager holds a $10 million equity portfolio. She buys put options on the S&P 500 with a strike 5% below the current index level, paying $150,000 in premiums. If the market falls 15%, the approximate maximum loss on the protected portfolio is:
A) 15% ($1,500,000) B) 5% ($500,000) plus the premium cost ($150,000) C) Zero — puts fully protect the portfolio D) 5% ($500,000) minus the premium earned
Answer: B — The put strike is 5% below current levels, so the portfolio absorbs the first 5% of losses. Below 5%, the puts compensate. Total maximum loss = 5% × $10M + $150,000 premium = $500,000 + $150,000 = $650,000. The puts protect below the strike but not for the first 5% (which represents the difference between current price and strike).
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Q2. An investor holds 1,000 shares of a stock currently trading at $50. She sells 10 call options (each representing 100 shares) with a strike price of $55, receiving $2 per share in premium. If the stock rises to $65 at expiration, the investor's profit is:
A) $15,000 (from the $15 stock gain) B) $7,000 (capped at $55 strike plus premium received) C) $17,000 (stock gain plus premium) D) $2,000 (premium only)
Answer: B — Stock value caps at $55 (the call is exercised by the counterparty). Gain per share = $55 − $50 = $5. Plus premium = $2. Total per share gain = $7. Total gain = 1,000 × $7 = $7,000. Without the covered call, the investor would have gained $15,000 — the covered call costs $8,000 in opportunity cost above $55.
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Q3. A delta-neutral portfolio has total delta = 0 and positive gamma. What happens if the underlying index moves up or down significantly?
A) The portfolio loses money in both directions because delta is zero B) The portfolio profits in both directions because positive gamma causes the position to become net long in a rising market and net short in a falling market C) The portfolio remains unchanged because delta = 0 means no sensitivity to price moves D) The portfolio profits only if implied volatility also increases
Answer: B — A delta-neutral, long-gamma position profits from large moves in either direction. As the underlying rises, positive gamma increases delta (position becomes net long), benefiting from further rises. As the underlying falls, delta becomes negative (position becomes net short), benefiting from further falls. This is the long straddle or strangle payoff profile.
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Q4. A zero-cost collar is best described as:
A) A long call and short put that requires no premium exchange B) A protective put and covered call where the premium received from the call equals the premium paid for the put, resulting in zero net cost C) An option strategy that eliminates all risk with no cost to the investor D) A futures hedge that requires no margin deposit
Answer: B — A zero-cost collar buys a put (floor, pays premium) and sells a call (cap, receives premium) where both premiums exactly offset. The net cost is zero, but the investor gives up upside above the call strike in exchange for protection below the put strike.
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Q5. Portfolio insurance using dynamic hedging (synthetically replicating a protective put) failed during the 1987 market crash primarily because:
A) Put options were too expensive to purchase during the crash B) The S&P 500 fell below all available put strikes, making hedging impossible C) Markets gapped down in discontinuous jumps, and systematic selling pressure from dynamic hedging strategies exacerbated the decline, making it impossible to rebalance at expected prices D) Portfolio insurance strategies were prohibited by the SEC following the crash
Answer: C — Dynamic replication of a put requires selling the underlying as prices fall. In 1987, the strategy's widespread adoption created a positive feedback loop: falling prices triggered selling, which caused more price declines. The assumption of continuous trading was violated by market gaps, and the model broke down precisely when it was needed most.
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