Risk Management and Trading Strategies with Options
Protective put, covered call, stradle, bull call spread
1 Introduction
Options are among the most versatile instruments in finance. Unlike stocks or bonds, which provide straightforward exposure to price movements or interest payments, options give investors the ability to sculpt their risk-return profiles with remarkable precision. Want to amplify your returns when you’re confident about a stock’s direction? Options can do that. Worried about a market downturn but don’t want to sell your holdings? Options have you covered. Think a stock will move dramatically but aren’t sure which direction? There’s an options strategy for that too.
This flexibility stems from the fundamental asymmetry built into options contracts. A call option gives you the right but not the obligation to buy at a specified price, while a put option gives you the right but not the obligation to sell. This asymmetric payoff structure—where your downside is limited to the premium paid but your upside can be substantial—is what makes options so powerful for both speculation and hedging.
In this lecture, we explore how investors use options strategically. We begin by examining how options can be used to amplify risk and potential returns, then turn to protective strategies that limit downside exposure. We then explore strategies that allow you to profit from your views on volatility itself, regardless of market direction. Along the way, we’ll work through numerical examples that illustrate exactly how these strategies perform under different market scenarios. By the end, you should understand not just the mechanics of these strategies but why an investor might choose one approach over another.
2 Using Options to Increase Risk and Potential Returns
One of the most straightforward uses of options is to take a leveraged position in a stock. When you buy call options instead of shares, you control more shares for the same initial investment—but you also take on substantially more risk. This leverage works in your favor when you’re right about the stock’s direction, but it can be devastating when you’re wrong.
To understand why, consider what happens when you buy a stock versus buying call options on that stock. With stock ownership, your investment moves dollar-for-dollar with the stock price. If the stock rises 10%, your investment rises 10%. But with call options, a 10% move in the stock price can translate into a much larger percentage gain—or a complete loss of your investment.
The key insight is that options provide leverage. For a relatively small premium, you gain exposure to the full upside of a stock above the strike price. However, this leverage comes with a critical trade-off: if the stock doesn’t rise above your strike price before expiration, you lose your entire investment. There’s no partial recovery, no dividend income along the way—just the binary outcome of profit or total loss of premium.
Let’s work through a concrete example to see exactly how this leverage works in practice.
Example 1: Comparing Stock Investment vs. Call Option Investment
Consider an investor with $9,000 to invest who is bullish on Stock A, currently trading at $90 per share. The investor is considering two strategies:
| Strategy | Description | Initial Position |
|---|---|---|
| Strategy A | Buy shares directly | 100 shares × $90 = $9,000 |
| Strategy B | Buy call options | 900 calls × $10 = $9,000 |
The call options in Strategy B have a strike price of $90 and expire in one year. Calculate the percentage return for each strategy if the stock price in one year is: (a) $75, (b) $90, or (c) $105.
Scenario (a): Stock price = $75
Strategy A (Stock): \[\text{Return} = \frac{P_1 - P_0}{P_0} = \frac{\$75 - \$90}{\$90} = -16.67\%\]
Strategy B (Call Options): At expiration, the call options are out-of-the-money since $75 < $90 (strike price). The options expire worthless. \[\text{Return} = \frac{\$0 - \$9,000}{\$9,000} = -100\%\]
Scenario (b): Stock price = $90
Strategy A (Stock): \[\text{Return} = \frac{\$90 - \$90}{\$90} = 0\%\]
Strategy B (Call Options): At expiration, the call options are at-the-money. Since $90 = $90 (strike price), the options expire worthless. \[\text{Return} = \frac{\$0 - \$9,000}{\$9,000} = -100\%\]
Scenario (c): Stock price = $105
Strategy A (Stock): \[\text{Return} = \frac{\$105 - \$90}{\$90} = 16.67\%\]
Strategy B (Call Options): Each call option has an intrinsic value of $105 - $90 = $15 at expiration. Total value = 900 options × $15 = $13,500 \[\text{Return} = \frac{\$13,500 - \$9,000}{\$9,000} = 50\%\]
Summary Table:
| Stock Price | Strategy A Return | Strategy B Return |
|---|---|---|
| $75 | -16.67% | -100% |
| $90 | 0% | -100% |
| $105 | +16.67% | +50% |
The leverage effect is clear: the option strategy produces returns that are roughly 3× the magnitude of the stock strategy, both on the upside and downside. This is why options are described as “leveraged” instruments—small percentage moves in the underlying asset translate into much larger percentage moves in the option position.
The example above reveals a critical concept: options provide leverage, but leverage amplifies both gains and losses. The stock investor who experienced a 16.67% loss still has $7,500 remaining. The options investor who was wrong about the direction—or even right about direction but wrong about magnitude—lost everything. This asymmetry is essential to understand before using options speculatively.
3 Using Options to Decrease Risk: The Protective Put
While options can amplify risk, they can also be used to manage and reduce it. The most intuitive hedging strategy is the protective put, sometimes called “portfolio insurance.” The logic is simple: if you own a stock and are worried about downside risk, you can buy a put option that guarantees you the right to sell at a specified price. This creates a floor under your potential losses while preserving your upside.
The protective put is particularly valuable when you want to maintain your stock position—perhaps for tax reasons, because you believe in the company’s long-term prospects, or because you want to retain voting rights—but you’re concerned about short-term volatility. Rather than selling the stock and potentially missing out on gains, you pay a premium for downside protection.
Think of it like buying insurance on your home. You pay a premium hoping you’ll never need to file a claim, but the protection gives you peace of mind. Similarly, the put premium is the cost of sleeping well at night during volatile markets.
The payoff and profit functions for a protective put help us understand exactly how this insurance works:
| Component | Payoff at Expiration | Cost |
|---|---|---|
| Long Stock | \(S_T\) | \(S_0\) |
| Long Put | \(\max(X - S_T, 0)\) | \(P\) |
| Protective Put | \(\max(S_T, X)\) | \(S_0 + P\) |
Where \(S_T\) is the stock price at expiration, \(S_0\) is the initial stock price, \(X\) is the strike price, and \(P\) is the put premium.
The profit formula for the protective put is: \[\text{Profit} = \max(S_T, X) - S_0 - P\]
Notice that the combined payoff is \(\max(S_T, X)\)—you receive either the stock price or the strike price, whichever is higher. This elegant result shows that the protective put effectively converts your stock position into one with a guaranteed minimum value of \(X\).
Example 2: The Protective Put in Action
You purchase one share of AMZN for $100 and simultaneously buy a put option on AMZN for $5. The put has a strike price of $95 and expires in 3 months. Compare this protective put strategy to simply holding the stock.
| Strategy | Initial Investment | Position |
|---|---|---|
| Strategy A (Stock only) | $100 | 1 share AMZN |
| Strategy B (Protective Put) | $105 | 1 share AMZN + 1 put option (X = $95) |
Calculate the percentage return for each strategy if the stock price in 3 months is: (a) $0, (b) $90, (c) $95, (d) $105, or (e) $150.
Scenario (a): Stock price = $0
Strategy A: \[\text{Return} = \frac{\$0 - \$100}{\$100} = -100\%\]
Strategy B: The put is deep in-the-money. You exercise the put and sell the share for $95. Portfolio value = $95 \[\text{Return} = \frac{\$95 - \$105}{\$105} = -9.52\%\]
Scenario (b): Stock price = $90
Strategy A: \[\text{Return} = \frac{\$90 - \$100}{\$100} = -10\%\]
Strategy B: The put is in-the-money ($90 < $95). You exercise and sell for $95. Portfolio value = $95 \[\text{Return} = \frac{\$95 - \$105}{\$105} = -9.52\%\]
Scenario (c): Stock price = $95
Strategy A: \[\text{Return} = \frac{\$95 - \$100}{\$100} = -5\%\]
Strategy B: The put is at-the-money. Whether you exercise or not, portfolio value = $95. \[\text{Return} = \frac{\$95 - \$105}{\$105} = -9.52\%\]
Scenario (d): Stock price = $105
Strategy A: \[\text{Return} = \frac{\$105 - \$100}{\$100} = +5\%\]
Strategy B: The put expires worthless (out-of-the-money). Portfolio value = $105. \[\text{Return} = \frac{\$105 - \$105}{\$105} = 0\%\]
Scenario (e): Stock price = $150
Strategy A: \[\text{Return} = \frac{\$150 - \$100}{\$100} = +50\%\]
Strategy B: The put expires worthless. Portfolio value = $150. \[\text{Return} = \frac{\$150 - \$105}{\$105} = +42.86\%\]
Summary Table:
| Stock Price | Strategy A Return | Strategy B Return |
|---|---|---|
| $0 | -100% | -9.52% |
| $90 | -10% | -9.52% |
| $95 | -5% | -9.52% |
| $105 | +5% | 0% |
| $150 | +50% | +42.86% |
The protective put creates a “floor” for returns at -9.52%, regardless of how far the stock falls. However, this insurance comes at a cost: the protective put strategy underperforms the stock-only strategy in every scenario where the stock rises. The $5 premium is the price of peace of mind.
The payoff diagram for a protective put has a distinctive kinked shape. Below the strike price, the payoff is flat—that’s your insurance kicking in. Above the strike price, the payoff rises one-for-one with the stock price, just as if you held unhedged stock (but starting from a lower base due to the premium paid).
4 Generating Income: The Covered Call
While the protective put involves buying options to hedge risk, investors can also sell options to generate income. The most common such strategy is the covered call, where an investor who owns shares sells call options against that position. The strategy is “covered” because if the option buyer exercises their right, you already own the shares to deliver.
The covered call represents a fundamental trade-off: you receive premium income today in exchange for capping your upside potential. This strategy is popular among investors who hold stocks for the long term and want to generate additional income, particularly when they believe the stock will trade sideways or rise modestly in the near term.
Think of it this way: you’re essentially renting out the upside potential of your shares. If the stock stays flat or rises moderately, you keep the rental income (the premium) plus any gains up to the strike price. If the stock soars, you miss out on gains above the strike price—the “renter” exercises their option and takes those gains instead.
The payoff and profit for a covered call are:
| Component | Payoff at Expiration | Premium Received |
|---|---|---|
| Long Stock | \(S_T\) | — |
| Short Call | \(-\max(S_T - X, 0)\) | \(+C\) |
| Covered Call | \(\min(S_T, X)\) | \(+C\) |
The profit formula for the covered call is: \[\text{Profit} = \min(S_T, X) - S_0 + C\]
Where \(C\) is the call premium received. Notice that the combined payoff is \(\min(S_T, X)\)—you receive either the stock price or the strike price, whichever is lower. This is the mirror image of the protective put.
Example 3: The Covered Call Strategy
You own one share of XYZ stock, currently trading at $50. You sell a call option with a strike price of $55 for a premium of $3. The option expires in one month. Calculate your profit for the covered call strategy if the stock price at expiration is: (a) $45, (b) $50, (c) $55, or (d) $65.
Your initial position: Own 1 share at $50, received $3 premium from selling the call.
Scenario (a): Stock price = $45
The call expires worthless (out-of-the-money since $45 < $55). You keep the share (worth $45) and the premium ($3). \[\text{Profit} = (\$45 - \$50) + \$3 = -\$2\]
Without the covered call, your loss would have been $5. The premium reduced your loss.
Scenario (b): Stock price = $50
The call expires worthless. \[\text{Profit} = (\$50 - \$50) + \$3 = +\$3\]
You earned $3 on a flat stock—pure income generation.
Scenario (c): Stock price = $55
The call is at-the-money and may or may not be exercised (assume not exercised for simplicity). \[\text{Profit} = (\$55 - \$50) + \$3 = +\$8\]
This is actually the maximum profit for this strategy.
Scenario (d): Stock price = $65
The call is in-the-money and will be exercised. You must sell your share for $55. \[\text{Profit} = (\$55 - \$50) + \$3 = +\$8\]
Note: If you had simply held the stock without selling the call, your profit would have been $15. By selling the call, you capped your upside at $8.
Summary Table:
| Stock Price | Stock-Only Profit | Covered Call Profit |
|---|---|---|
| $45 | -$5 | -$2 |
| $50 | $0 | +$3 |
| $55 | +$5 | +$8 |
| $65 | +$15 | +$8 |
The covered call outperforms when the stock is flat or down, but underperforms when the stock rises significantly.
The covered call is particularly attractive in low-volatility environments or when an investor has a neutral-to-moderately-bullish outlook. If implied volatility is high (meaning options are expensive), selling calls generates more premium income. However, high implied volatility often presages large price moves, which means the likelihood of the stock being called away increases.
5 Trading Volatility: The Straddle
So far, we’ve discussed strategies that profit from directional moves—up or down—in the underlying stock. But what if you have a view on volatility itself rather than direction? Options allow you to express opinions about how much a stock will move, regardless of which way it moves.
The long straddle is the classic volatility bet. You simultaneously buy a call and a put at the same strike price and expiration. This position profits when the stock makes a large move in either direction, and loses when the stock stays near the strike price.
When would you use a long straddle? Consider a pharmaceutical company awaiting FDA approval, an earnings announcement, or a pending court ruling. You might believe the outcome will move the stock significantly, but you have no edge in predicting which direction. A long straddle lets you bet on the magnitude of the move without taking a directional stance.
The payoff and profit for a long straddle are:
| Component | Payoff at Expiration | Cost |
|---|---|---|
| Long Call | \(\max(S_T - X, 0)\) | \(C\) |
| Long Put | \(\max(X - S_T, 0)\) | \(P\) |
| Long Straddle | \(|S_T - X|\) | \(C + P\) |
The profit formula for the long straddle is: \[\text{Profit} = |S_T - X| - C - P\]
The straddle has two breakeven points: \[\text{Upper Breakeven} = X + C + P\] \[\text{Lower Breakeven} = X - C - P\]
The stock must move beyond one of these breakeven points for the straddle to be profitable.
Example 4: Betting on Volatility with a Long Straddle
You buy a call option on stock X for $10 and a put option on stock X for $5. Both options have a strike price of $100 and the same expiration date. For what stock prices would you make a positive profit?
Setup:
- Call premium (C) = $10
- Put premium (P) = $5
- Strike price (X) = $100
- Total cost = $10 + $5 = $15
Breakeven Analysis:
For the straddle to break even, the payoff must equal the cost: \[|S_T - X| = C + P\] \[|S_T - 100| = 15\]
This gives us two solutions: \[S_T - 100 = 15 \implies S_T = 115 \text{ (Upper breakeven)}\] \[100 - S_T = 15 \implies S_T = 85 \text{ (Lower breakeven)}\]
Profit Regions:
- Profitable when \(S_T < 85\) or \(S_T > 115\)
- Loss when \(85 < S_T < 115\)
- Maximum loss of $15 occurs when \(S_T = 100\) (both options expire worthless)
Example Calculations:
At \(S_T = 70\): \[\text{Profit} = |70 - 100| - 15 = 30 - 15 = +\$15\]
At \(S_T = 100\): \[\text{Profit} = |100 - 100| - 15 = 0 - 15 = -\$15\]
At \(S_T = 130\): \[\text{Profit} = |130 - 100| - 15 = 30 - 15 = +\$15\]
The profit diagram is V-shaped, with the vertex (maximum loss) at the strike price. Profits increase linearly as the stock moves away from the strike in either direction.
The short straddle is the opposite bet—you profit when the stock stays near the strike price. By selling both a call and a put, you collect premium income but expose yourself to unlimited potential losses if the stock makes a large move.
6 Taking Directional Bets with Limited Risk: The Bull Call Spread
The strategies we’ve discussed so far involve either buying or selling individual options, or combining calls and puts. But traders frequently combine options of the same type to create spread strategies that offer defined risk-reward profiles.
The bull call spread involves buying a call option at a lower strike price and simultaneously selling a call option at a higher strike price, both with the same expiration. This strategy profits when the stock rises moderately, but both the maximum gain and maximum loss are capped.
Why use a spread instead of simply buying a call? The main reason is cost reduction. Buying calls can be expensive, especially on volatile stocks. By selling a higher-strike call against your long call, you reduce your net cost but also cap your upside. The bull call spread is ideal when you’re moderately bullish—you expect the stock to rise, but not dramatically.
The payoff and profit for a bull call spread are:
| Component | Payoff at Expiration | Premium |
|---|---|---|
| Long Call (strike \(X_1\)) | \(\max(S_T - X_1, 0)\) | \(-C_1\) (paid) |
| Short Call (strike \(X_2\), where \(X_2 > X_1\)) | \(-\max(S_T - X_2, 0)\) | \(+C_2\) (received) |
| Bull Call Spread | See below | \(C_2 - C_1\) (net debit) |
The profit depends on where the stock price ends up:
\[\text{Profit} = \begin{cases} -\text{Net Debit} & \text{if } S_T \leq X_1 \\ (S_T - X_1) - \text{Net Debit} & \text{if } X_1 < S_T < X_2 \\ (X_2 - X_1) - \text{Net Debit} & \text{if } S_T \geq X_2 \end{cases}\]
Where Net Debit = \(C_1 - C_2\) (the net premium paid).
Example 5: The Bull Call Spread
You are moderately bullish on stock ABC, currently trading at $100. You implement a bull call spread by buying a call with a strike price of $100 for $8 and selling a call with a strike price of $110 for $3. Both options expire in two months. Calculate your profit if the stock price at expiration is: (a) $95, (b) $105, (c) $110, or (d) $120.
Setup:
- Long call: \(X_1 = 100\), Premium paid = $8
- Short call: \(X_2 = 110\), Premium received = $3
- Net debit = $8 - $3 = $5
- Maximum profit = \((X_2 - X_1) - \text{Net Debit} = (110 - 100) - 5 = \$5\)
- Maximum loss = Net Debit = $5
- Breakeven = \(X_1 + \text{Net Debit} = 100 + 5 = \$105\)
Scenario (a): Stock price = $95
Both calls expire worthless (both are out-of-the-money). \[\text{Profit} = 0 - 0 - 5 = -\$5\]
This is the maximum loss.
Scenario (b): Stock price = $105
Long call payoff = $105 - 100 = $5 Short call payoff = $0 (out-of-the-money) \[\text{Profit} = 5 - 0 - 5 = \$0\]
This is exactly at breakeven.
Scenario (c): Stock price = $110
Long call payoff = $110 - 100 = $10 Short call payoff = $0 (at-the-money, assume no exercise) \[\text{Profit} = 10 - 0 - 5 = +\$5\]
This is the maximum profit.
Scenario (d): Stock price = $120
Long call payoff = $120 - 100 = $20 Short call payoff = $120 - 110 = $10 (you owe this amount) \[\text{Profit} = 20 - 10 - 5 = +\$5\]
Even though the stock went higher, your profit is still capped at $5.
Summary Table:
| Stock Price | Long Call Payoff | Short Call Payoff | Net Profit |
|---|---|---|---|
| $95 | $0 | $0 | -$5 |
| $105 | $5 | $0 | $0 |
| $110 | $10 | $0 | +$5 |
| $120 | $20 | $10 | +$5 |
The bull call spread has a defined maximum gain ($5) and defined maximum loss ($5), making it a conservative bullish strategy compared to buying a call outright.
The bull call spread exemplifies a key principle in options trading: you can often reduce costs by accepting limits on your potential gains. For investors who have moderate convictions about direction and magnitude, spreads offer an efficient way to express their views without paying for upside they don’t expect to realize.
7 Key Takeaways
Options provide investors with a powerful toolkit for managing risk and expressing market views that goes far beyond simple buying and selling of stocks. The core insight is that options allow you to separate and trade different aspects of a security’s behavior—its direction, its volatility, and your risk tolerance—independently.
When used to increase risk, options provide leverage that amplifies both gains and losses. An investor buying call options instead of stock controls more shares for the same capital outlay, but faces the possibility of losing their entire investment if the stock doesn’t move favorably. This leverage is a double-edged sword that demands respect and careful position sizing.
When used to decrease risk, options function as insurance. The protective put strategy creates a floor under potential losses while preserving unlimited upside, at the cost of the premium paid. The covered call takes the opposite approach—capping upside in exchange for premium income that cushions downside losses and enhances returns in flat markets.
Volatility strategies like the long straddle allow investors to profit from large price movements without predicting direction. These strategies are particularly useful around binary events like earnings announcements or regulatory decisions. The key is understanding that you’re not betting on which way the stock moves, but on how much it moves relative to what the market expects.
Spread strategies like the bull call spread offer a middle ground, allowing directional bets with clearly defined maximum gains and losses. By combining long and short options, investors can reduce costs and tailor their risk-reward profiles to match their specific market views and risk tolerances.
Understanding these strategies isn’t just academic—it’s practical knowledge that helps you interpret market activity, evaluate investment products, and make informed decisions about whether and how to incorporate options into your own portfolio.
8 Key Formulas Summary
| Concept | Formula | When to Use |
|---|---|---|
| Call Option Payoff | \(\max(S_T - X, 0)\) | Calculating value of call at expiration |
| Put Option Payoff | \(\max(X - S_T, 0)\) | Calculating value of put at expiration |
| Protective Put Payoff | \(\max(S_T, X)\) | Finding combined stock + put value at expiration |
| Protective Put Profit | \(\max(S_T, X) - S_0 - P\) | Evaluating protective put performance |
| Covered Call Payoff | \(\min(S_T, X)\) | Finding combined stock + short call value at expiration |
| Covered Call Profit | \(\min(S_T, X) - S_0 + C\) | Evaluating covered call performance |
| Long Straddle Payoff | \(\|S_T - X\|\) | Finding straddle value at expiration |
| Long Straddle Profit | \(\|S_T - X\| - C - P\) | Evaluating straddle performance |
| Straddle Breakevens | \(X + C + P\) (upper), \(X - C - P\) (lower) | Finding prices where straddle breaks even |
| Bull Call Spread Max Profit | \((X_2 - X_1) - \text{Net Debit}\) | Calculating best-case spread outcome |
| Bull Call Spread Max Loss | \(\text{Net Debit} = C_1 - C_2\) | Calculating worst-case spread outcome |
| Percentage Return | \(\frac{\text{Final Value} - \text{Initial Investment}}{\text{Initial Investment}}\) | Comparing strategy performance |
9 Practice Problems
Practice Problem 1: Leveraged Options Position
An investor has $12,000 to invest and is bullish on Stock B, currently trading at $60 per share. She is considering two strategies:
| Strategy | Description |
|---|---|
| Strategy A | Buy shares directly at $60 per share |
| Strategy B | Buy call options at $4 per option with a strike price of $60, expiring in 6 months |
Calculate the percentage return for each strategy if the stock price in 6 months is: (a) $50, (b) $60, (c) $70, or (d) $80.
Setup:
- Strategy A: $12,000 ÷ $60 = 200 shares
- Strategy B: $12,000 ÷ $4 = 3,000 call options
Scenario (a): Stock price = $50
Strategy A: \[\text{Return} = \frac{\$50 - \$60}{\$60} = -16.67\%\]
Strategy B: Calls are out-of-the-money ($50 < $60). Options expire worthless. \[\text{Return} = \frac{\$0 - \$12,000}{\$12,000} = -100\%\]
Scenario (b): Stock price = $60
Strategy A: \[\text{Return} = \frac{\$60 - \$60}{\$60} = 0\%\]
Strategy B: Calls are at-the-money. Options expire worthless. \[\text{Return} = \frac{\$0 - \$12,000}{\$12,000} = -100\%\]
Scenario (c): Stock price = $70
Strategy A: \[\text{Return} = \frac{\$70 - \$60}{\$60} = +16.67\%\]
Strategy B: Each call is worth $70 - $60 = $10. Total value = 3,000 × $10 = $30,000 \[\text{Return} = \frac{\$30,000 - \$12,000}{\$12,000} = +150\%\]
Scenario (d): Stock price = $80
Strategy A: \[\text{Return} = \frac{\$80 - \$60}{\$60} = +33.33\%\]
Strategy B: Each call is worth $80 - $60 = $20. Total value = 3,000 × $20 = $60,000 \[\text{Return} = \frac{\$60,000 - \$12,000}{\$12,000} = +400\%\]
Summary Table:
| Stock Price | Strategy A Return | Strategy B Return |
|---|---|---|
| $50 | -16.67% | -100% |
| $60 | 0% | -100% |
| $70 | +16.67% | +150% |
| $80 | +33.33% | +400% |
Practice Problem 2: Protective Put Strategy
You purchase 100 shares of Tesla (TSLA) at $250 per share and simultaneously buy 1 put option contract (covering 100 shares) with a strike price of $230 for a total premium of $800. The option expires in 2 months. Calculate your total dollar profit and percentage return if the stock price in 2 months is: (a) $180, (b) $230, (c) $250, or (d) $300.
Setup:
- Stock investment: 100 shares × $250 = $25,000
- Put premium: $800
- Total investment: $25,000 + $800 = $25,800
- Put strike price: $230 (protects 100 shares)
Scenario (a): Stock price = $180
Stock value = 100 × $180 = $18,000 Put is in-the-money: Exercise and sell shares for $230 each. Portfolio value = 100 × $230 = $23,000 \[\text{Dollar Profit} = \$23,000 - \$25,800 = -\$2,800\] \[\text{Return} = \frac{-\$2,800}{\$25,800} = -10.85\%\]
Without the put, loss would have been: \((18,000 - 25,000) / 25,000 = -28\%\)
Scenario (b): Stock price = $230
Stock value = 100 × $230 = $23,000 Put is at-the-money. Portfolio value = $23,000 \[\text{Dollar Profit} = \$23,000 - \$25,800 = -\$2,800\] \[\text{Return} = \frac{-\$2,800}{\$25,800} = -10.85\%\]
Scenario (c): Stock price = $250
Stock value = 100 × $250 = $25,000 Put is out-of-the-money and expires worthless. Portfolio value = $25,000 \[\text{Dollar Profit} = \$25,000 - \$25,800 = -\$800\] \[\text{Return} = \frac{-\$800}{\$25,800} = -3.10\%\]
Scenario (d): Stock price = $300
Stock value = 100 × $300 = $30,000 Put expires worthless. Portfolio value = $30,000 \[\text{Dollar Profit} = \$30,000 - \$25,800 = +\$4,200\] \[\text{Return} = \frac{\$4,200}{\$25,800} = +16.28\%\]
Summary Table:
| Stock Price | Dollar Profit | Return |
|---|---|---|
| $180 | -$2,800 | -10.85% |
| $230 | -$2,800 | -10.85% |
| $250 | -$800 | -3.10% |
| $300 | +$4,200 | +16.28% |
Practice Problem 3: Covered Call Strategy
You own 100 shares of Intel (INTC) currently trading at $35 per share. You sell 1 call option contract (covering 100 shares) with a strike price of $40 for a total premium of $150. The option expires in one month. Calculate your total dollar profit if the stock price at expiration is: (a) $30, (b) $35, (c) $40, or (d) $50.
Setup:
- Current stock position: 100 shares × $35 = $3,500
- Call premium received: $150
- Strike price: $40
Scenario (a): Stock price = $30
Stock loss = 100 × ($30 - $35) = -$500 Call expires worthless. Keep premium of $150. \[\text{Dollar Profit} = -\$500 + \$150 = -\$350\]
Without the covered call, loss would have been $500.
Scenario (b): Stock price = $35
Stock gain = 100 × ($35 - $35) = $0 Call expires worthless. Keep premium of $150. \[\text{Dollar Profit} = \$0 + \$150 = +\$150\]
Pure income generation on a flat stock.
Scenario (c): Stock price = $40
Stock gain = 100 × ($40 - $35) = $500 Call is at-the-money (assume no exercise). \[\text{Dollar Profit} = \$500 + \$150 = +\$650\]
This is the maximum profit.
Scenario (d): Stock price = $50
Call is exercised. You must sell shares at $40. Stock gain = 100 × ($40 - $35) = $500 Plus premium = $150 \[\text{Dollar Profit} = \$500 + \$150 = +\$650\]
You missed out on the additional $10/share ($1,000 total) upside.
Summary Table:
| Stock Price | Stock P/L | Premium | Total Profit |
|---|---|---|---|
| $30 | -$500 | +$150 | -$350 |
| $35 | $0 | +$150 | +$150 |
| $40 | +$500 | +$150 | +$650 |
| $50 | +$500 | +$150 | +$650 |
Practice Problem 4: Long Straddle
You are expecting a major announcement from a biotech company. You buy a call option for $7 and a put option for $8, both with a strike price of $50 and expiring right after the announcement. Calculate the breakeven points and your profit if the stock price after the announcement is: (a) $35, (b) $50, or (c) $70.
Setup:
- Call premium (C) = $7
- Put premium (P) = $8
- Strike price (X) = $50
- Total cost = $7 + $8 = $15
Breakeven Analysis:
Upper breakeven = \(X + C + P = 50 + 15 = \$65\) Lower breakeven = \(X - C - P = 50 - 15 = \$35\)
Scenario (a): Stock price = $35
This is exactly at the lower breakeven. Put payoff = $50 - $35 = $15 Call payoff = $0 \[\text{Profit} = \$15 - \$15 = \$0\]
Scenario (b): Stock price = $50
Both options expire at-the-money (worthless). \[\text{Profit} = \$0 - \$15 = -\$15\]
This is the maximum loss.
Scenario (c): Stock price = $70
Call payoff = $70 - $50 = $20 Put payoff = $0 \[\text{Profit} = \$20 - \$15 = +\$5\]
Note: The stock needs to move beyond $65 (upper breakeven) or below $35 (lower breakeven) for positive profits.
Summary Table:
| Stock Price | Call Payoff | Put Payoff | Total Profit |
|---|---|---|---|
| $35 | $0 | $15 | $0 |
| $50 | $0 | $0 | -$15 |
| $70 | $20 | $0 | +$5 |
Practice Problem 5: Bull Call Spread
You implement a bull call spread on a stock trading at $75 by buying a call with a strike of $75 for $6 and selling a call with a strike of $85 for $2. Both options expire in one month. Calculate: (a) the net cost of the spread, (b) the maximum profit, (c) the maximum loss, (d) the breakeven point, and (e) your profit if the stock is at $80 at expiration.
Setup:
- Long call: \(X_1 = 75\), Premium = $6 (paid)
- Short call: \(X_2 = 85\), Premium = $2 (received)
(a) Net cost of the spread: \[\text{Net Debit} = \$6 - \$2 = \$4\]
(b) Maximum profit: \[\text{Max Profit} = (X_2 - X_1) - \text{Net Debit} = (85 - 75) - 4 = \$6\]
This occurs when \(S_T \geq 85\).
(c) Maximum loss: \[\text{Max Loss} = \text{Net Debit} = \$4\]
This occurs when \(S_T \leq 75\).
(d) Breakeven point: \[\text{Breakeven} = X_1 + \text{Net Debit} = 75 + 4 = \$79\]
(e) Profit at $S_T = $80:
Long call payoff = $80 - $75 = $5 Short call payoff = $0 (out-of-the-money) \[\text{Profit} = \$5 - \$4 = +\$1\]
Summary:
| Metric | Value |
|---|---|
| Net Cost | $4 |
| Maximum Profit | $6 |
| Maximum Loss | $4 |
| Breakeven | $79 |
| Profit at $80 | $1 |
10 Ask an LLM
Here are three questions you might ask an AI assistant to deepen your understanding of these concepts:
- How would the protective put and covered call strategies compare in a high-volatility versus low-volatility market environment? Which strategy benefits more from high implied volatility?
- Can you explain what happens to a long straddle position as time passes (time decay) if the stock doesn’t move? How should this affect when I enter and exit straddle positions?
- Walk me through how I would construct a “bear put spread” as the opposite of a bull call spread, and explain when I might choose it over simply buying a put option.
- What is the relationship between the protective put and the covered call? Can you show me how they are related through put-call parity?
- If I wanted to bet on low volatility but with less risk than a short straddle, what strategy could I use and how does it limit my potential losses?