Learning Module 13: Options Strategies

Position Equivalencies

LOS: Demonstrate how an asset’s returns may be replicated by using options.

Derivatives serve as fundamental building blocks in portfolio construction. Put-Call Parity forms the cornerstone of many option equivalencies: \[S_0 + p_0 = c_0 + \frac{X}{(1+r)^T}\]

  • Fiduciary Call: A long call option combined with a risk-free bond (with a present value of \(X/(1+r)^T\)).
  • Protective Put: A long position in the underlying stock combined with a long put option.

Synthetic Forward Positions

  • Synthetic Long Forward: Created by buying a call and selling a put, both with the same strike price (\(X\)) and expiration (\(T\)).
    • Payoff: The payoff profile is identical to directly owning the stock or a long forward contract.
    • Usage: Can be used to exploit arbitrage opportunities or to create a leveraged position.
  • Synthetic Short Forward: Created by selling a call and buying a put, both with the same strike price (\(X\)) and expiration (\(T\)).
    • Payoff: The payoff profile is identical to shorting the stock or a short forward contract.
    • Usage: Allows for short exposure without the need to borrow shares.

Synthetic Put and Call

  • Synthetic Long Put: Achieved by shorting the underlying stock and simultaneously buying a call option.
    • This structure profits if the underlying asset declines (like a traditional put) but limits losses if the asset price rises due to the long call.
  • Synthetic Long Call: Created by holding a long position in the underlying stock and buying a put option.
    • Payoff: Offers unlimited upside potential (from the stock) with a limited downside risk (provided by the put option floor).

Example 1 & 2 (Synthetics): A market maker hedges a short forward position by constructing a synthetic long forward (buying a call and selling a put). If the stock price increases, the call is exercised to acquire shares for delivery. Conversely, if the stock price falls, the put is exercised against them, obligating them to acquire shares for delivery.

Covered Calls

LOS: Discuss the investment objective(s), structure, payoff, risk(s), value at expiration, profit, maximum profit, maximum loss, and breakeven underlying price.

  • Structure: Consists of holding a long position in the underlying stock (\(S_0\)) and simultaneously selling (writing) a call option (\(c_0\)) against it.
  • Objectives:
    1. Yield Enhancement: To generate income from the premium received, particularly suitable for a neutral to slightly bullish market outlook.
    2. Reducing Position at Favorable Price: Effectively allows the investor to sell their stock at the strike price plus the premium received.
    3. Target Price Realization: The strike price can be set at a desired sell price for the underlying stock.
  • Formulas:
    • Maximum Gain: \((X - S_0) + c_0\) (Represents the appreciation limit on the stock plus the premium received).
    • Maximum Loss: \(S_0 - c_0\) (Occurs if the stock price falls to zero, offset by the premium received).
    • Breakeven: \(S_0 - c_0\)
    • Profit at Expiration: \(S_T - \text{Max}(0, S_T - X) - S_0 + c_0\)
  • Greeks:
    • Delta: Portfolio Delta = \(1 - \Delta_{\text{call}}\). This significantly reduces upside sensitivity.
    • Gamma: The position has short Gamma (negative), meaning the portfolio Delta drops more rapidly as the stock price (\(S\)) rises above the strike price (\(X\)).
  • Risk: The primary risk is opportunity loss if the stock price significantly skyrockets. The strategy also still bears the full downside risk of the stock, partially offset by the premium received.

Example 3 (Covered Call): Assume a stock price of $25. An investor writes a Call option with a strike price of $30 for a premium of $1.55. * Max Gain: \((30 - 25) + 1.55 = 6.55\). * Breakeven: \(25 - 1.55 = 23.45\). * Max Loss: \(25 - 1.55 = 23.45\) (if the stock price declines to zero).

Protective Puts

LOS: Discuss the investment objective(s), structure, payoff, risk(s)… of a protective put.

  • Structure: Consists of holding a long position in the underlying stock (\(S_0\)) and simultaneously buying a put option (\(p_0\)).
  • Objective: Acts as an insurance policy for wealth preservation, protecting against significant downside risk while retaining unlimited upside potential.
  • Formulas:
    • Maximum Gain: Unlimited (derived from the stock’s upside potential, less the premium paid for the put).
    • Maximum Loss: \((S_0 - X) + p_0\) (Represents the “deductible” up to the strike price plus the premium paid).
    • Breakeven: \(S_0 + p_0\)
    • Expiration Value: \(S_T + \text{Max}(0, X - S_T)\)
  • Greeks:
    • Delta: Portfolio Delta = \(1 + \Delta_{\text{put}}\) (where \(\Delta_{\text{put}}\) is negative). The overall delta remains positive but is less than 1.
    • Theta: Negative, as the investor is paying for time value (insurance) which erodes over time.

Example 4 (Protective Put): Assume a stock price of $25. An investor buys a Put option with a strike price of $20 for a premium of $1.15. * Breakeven: \(25 + 1.15 = 26.15\). * Max Loss: \((25 - 20) + 1.15 = 6.15\).

Risk Reduction on Short Positions

LOS: Compare the effect of buying a call on a short underlying position with the effect of selling a put on a short underlying position.

  1. Long Call + Short Stock (Synthetic Long Put):
    • Goal: Primarily used for hedging and protection against upside movements.
    • Effect: Caps the potential loss on the short stock position if the price of the underlying asset rises significantly.
    • Payoff: Offers an asymmetrical payoff profile, providing limited loss potential while allowing profit if the stock price falls.
  2. Short Put + Short Stock:
    • Goal: Primarily used for yield enhancement or generating income.
    • Effect: Provides a partial hedge. The premium received from selling the put cushions losses if the stock price rises, but the potential for loss remains unlimited beyond that cushion.
    • Payoff: Offers a capped profit (maximum gain occurs if the stock declines to the strike price plus the premium received) but unlimited loss potential if the stock rises significantly.

Spreads

LOS: Discuss… bull spread, bear spread, straddle, and collar.

Bull Spreads

  • View: Suitable for a moderately bullish market outlook.
  • Bull Call Spread: Involves buying a call with a low strike price (\(X_L\)) and selling a call with a high strike price (\(X_H\)).
    • Type: A debit spread, meaning there is a net cost to enter the position (\(c_L - c_H\)).
    • Max Profit: \((X_H - X_L) - \text{Net Premium Paid}\).
    • Max Loss: Equal to the Net Premium Paid.
    • Breakeven: \(X_L + \text{Net Premium Paid}\).
  • Bull Put Spread: Involves buying a put with a low strike price (\(X_L\)) and selling a put with a high strike price (\(X_H\)).
    • Type: A credit spread, meaning a net premium is received upon entry.

Bear Spreads

  • View: Suitable for a moderately bearish market outlook.
  • Bear Put Spread: Involves buying a put with a high strike price (\(X_H\)) and selling a put with a low strike price (\(X_L\)).
    • Type: A debit spread, meaning there is a net cost to enter the position.
    • Max Profit: \((X_H - X_L) - \text{Net Premium Paid}\).
    • Max Loss: Equal to the Net Premium Paid.
    • Breakeven: \(X_H - \text{Net Premium Paid}\).
  • Bear Call Spread: Involves buying a call with a high strike price and selling a call with a low strike price.
    • Type: A credit spread, meaning a net premium is received upon entry.

Straddle

  • Structure: Involves simultaneously buying a call and buying a put on the same underlying asset, with the same strike price (\(X\)), and the same expiration (\(T\)).
  • View: Highly volatile market conditions are expected, but the direction of the move is uncertain (direction neutral).
  • Formulas:
    • Max Loss: Limited to the Total Premium Paid (\(c + p\)).
    • Max Profit: Unlimited.
    • Breakevens: Two breakeven points: \(X \pm (c + p)\).
  • Greeks: Has a long Vega (benefits from increasing implied volatility) and negative Theta (experiences high time decay).

Collar

  • Structure: Consists of a long position in the underlying stock, a long put option (\(X_L\)), and a short call option (\(X_H\)).
  • Objective: To achieve low-cost portfolio protection. A “Zero-Cost Collar” is achieved when the premium received from the short call equals the premium paid for the long put.
  • Payoff: The payoff is bounded within a specific range.
    • Max Gain: \((X_H - S_0) - p_0 + c_0\).
    • Max Loss: \((S_0 - X_L) + p_0 - c_0\).
  • Usage: Commonly used to lock in profits on an existing long stock position while limiting downside exposure.

Example 6 (Spreads): Consider a Bull Call Spread 45/50 (Buy a 45 Call at $2.55, Sell a 50 Call at $1.45). The Net Cost is $1.10. * Max Gain: \((50 - 45) - 1.10 = 3.90\). * Breakeven: \(45 + 1.10 = 46.10\).

Calendar Spreads

LOS: Describe uses of calendar spreads.

  • Structure: Involves selling a near-term option and simultaneously buying a longer-term option with the same strike price.
  • Objective: To capitalize on the decay of time value (Theta).
  • Mechanism: The near-term option experiences time decay at a faster rate than the longer-term option.
  • Max Profit: Occurs if the underlying stock price is exactly at the strike price at the near-term option’s expiration (the short option expires worthless, while the long option retains maximum time value).
  • View: Suitable for a neutral or range-bound market outlook in the short term, with a bullish or bearish view (depending on whether calls or puts are used) for the long term.

Volatility Skew and Smile

LOS: Discuss volatility skew and smile.

  • Implied Volatility (IV): The market’s expectation of future volatility, derived from option prices.
  • Volatility Smile: A pattern where implied volatility is higher for out-of-the-money (OTM) puts and out-of-the-money (OTM) calls compared to at-the-money (ATM) options. This pattern is commonly observed in foreign exchange markets.
  • Volatility Skew (Smirk):
    • Equity Skew: In equity markets, OTM puts typically exhibit higher implied volatility than OTM calls.
    • Reason: This reflects a high demand for crash protection (puts) among investors.
    • Implication: Bear spreads using puts can be cheaper to implement, as they involve selling expensive low-strike volatility.
  • Term Structure: Implied volatility can also vary across different expiration dates. During periods of market stress, the term structure can invert, meaning short-term implied volatility becomes higher than long-term implied volatility.

Strategy Selection

LOS: Identify and evaluate appropriate option strategies consistent with given investment objectives.

Exhibit 32: Selection Matrix

View on Direction Expected Volatility: Decrease Expected Volatility: Stable Expected Volatility: Increase
Bullish Short Put Bull Spread Long Call
Neutral Short Straddle / Strangle Calendar Spread Long Straddle / Strangle
Bearish Short Call Bear Spread Long Put
  • Aggressive vs. Conservative:
    • Buying options: Typically implies a long Vega position (benefits from increasing volatility) and involves a debit (an upfront cash outlay).
    • Selling options: Typically implies a short Vega position (benefits from decreasing volatility) and results in a credit (income received upfront).

Portfolio Management Applications

LOS: Demonstrate the use of options to achieve targeted equity risk exposures.

  • Hedging Tail Risk: Can be achieved by purchasing VIX Calls or Put Options on a relevant equity index.
  • Managing Volatility:
    • Long Variance Swap: A pure bet on whether realized variance will exceed implied variance, offering a convex payoff.
    • VIX Futures/Options: Used to hedge against equity market drawdowns, given the typically negative correlation between the VIX (volatility index) and stock prices.
  • Rebalancing:
    • Options can be used to adjust equity exposure by leveraging their delta.
    • Example: To increase portfolio Beta, one might buy Calls (which have high delta) or implement Bull Spreads. To decrease Beta, one could buy Puts or establish Collars.