Conversion and Reversal: Options Arbitrage Strategies Explained

Conversions and reversals are the foundational arbitrage strategies that keep options markets efficient. While primarily used by market makers and professional traders, understanding these strategies helps all traders grasp put-call parity and spot mispriced options. In this guide, we will demystify these essential concepts.

What Are Conversions and Reversals?

A conversion and reversal are mirror-image strategies that combine stock with options to create a position with locked-in profit potential. They exploit violations of put-call parity, the fundamental relationship between call prices, put prices, and stock prices.

Understanding Put-Call Parity

Put-call parity is the relationship that keeps conversions and reversals in check:

• Call price - Put price = Stock price - Present value of strike price
• When this equation is out of balance, arbitrage opportunities exist
• Conversions and reversals exploit these imbalances

The Conversion Strategy

A conversion involves three positions:

• Long 100 shares of stock
• Long 1 put option
• Short 1 call option (same strike and expiration as the put)

Why the Conversion Works

The combination of long stock, long put, and short call creates a synthetic bond:

• If stock falls to $80: Exercise put to sell at $100. Call expires worthless. You get $100.
• If stock rises to $120: Put expires worthless. Call is assigned, you sell at $100. You get $100.
• If stock stays at $100: Both options expire worthless. You have stock worth $100.

The Reversal Strategy

A reversal is the opposite of a conversion:

• Short 100 shares of stock
• Long 1 call option
• Short 1 put option (same strike and expiration as the call)

Why the Reversal Works

The combination of short stock, long call, and short put creates a synthetic obligation:

• If stock falls to $80: Call expires worthless. Put is assigned, you buy at $100.
• If stock rises to $120: Put expires worthless. Exercise call to buy at $100.
• In both cases: You pay $100 to close your short stock position.

Conversion vs Reversal: When to Use Each

The choice depends on the mispricing direction:

• Use conversion when: Puts are expensive relative to calls (buy cheap calls, sell expensive puts)
• Use reversal when: Calls are expensive relative to puts (buy cheap puts, sell expensive calls)
• Market makers: Constantly watch for either opportunity

Why Retail Traders Rarely Use These

Several factors make these strategies impractical for most traders:

• Tiny profit margins: Mispricings are usually pennies, not dollars
• Transaction costs: Commissions on three legs can exceed profits
• Execution difficulty: Getting all legs at favorable prices simultaneously is hard
• Capital intensive: Requires buying or shorting stock, tying up capital
• Competition: High-frequency traders capture opportunities in milliseconds

Interest Rates and Dividends

Two factors complicate conversions and reversals:

Interest Rate Effects

• Conversions require capital to buy stock (financing cost)
• Reversals generate cash from short sales (interest income)
• The "fair" profit margin includes these interest rate effects

Dividend Effects

• Conversion holders receive dividends (bonus income)
• Reversal holders pay dividends on short stock (extra cost)
• Expected dividends must be factored into fair value calculations

Early Exercise Considerations

American options add complexity:

• Conversion risk: Your short call may be assigned early, especially before dividends
• Reversal risk: Your short put may be assigned early
• Impact: Early assignment changes your cash flows and can eliminate profit

How Market Makers Use These Strategies

Professional traders use conversions and reversals for several purposes:

• Delta hedging: Offset directional risk while keeping option positions
• Inventory management: Adjust stock holdings without closing options
• Arbitrage: Capture small mispricings thousands of times
• Financing: Borrow or lend money at competitive rates

Spotting Arbitrage Opportunities

While rare, mispricings can occur. Here is how to check:

• Compare call price minus put price to the stock price minus present value of strike
• Account for any expected dividends
• Factor in your transaction costs
• If a profit remains after all costs, you may have found an opportunity

Why Understanding This Matters

Even if you never trade a conversion or reversal, knowing how they work helps you:

• Understand option pricing: See why calls and puts are related
• Spot unusual pricing: Recognize when something seems mispriced
• Build synthetic positions: Create stock-like payoffs with options
• Think like a market maker: See the market from a professional perspective

Summary

Conversions and reversals are arbitrage strategies that exploit violations of put-call parity. A conversion combines long stock with a long put and short call to lock in value. A reversal does the opposite with short stock, a long call, and short put. While these strategies are primarily used by market makers due to thin margins and execution challenges, understanding them helps all traders grasp fundamental options relationships and think about pricing more clearly.

Want to learn related concepts? Check out our guide on box spreads or explore synthetic stock positions for practical applications of these principles.