Conversions and reversals are options arbitrage strategies that exploit pricing inefficiencies between calls, puts, and the underlying stock. These strategies are used primarily by market makers and institutional traders to lock in risk-free profits when options become mispriced relative to each other.
Understanding Put-Call Parity
Before diving into conversions and reversals, you need to understand put-call parity. This fundamental options pricing relationship states that:
Call Price - Put Price = Stock Price - Strike Price (adjusted for interest and dividends)
When this relationship is violated, arbitrage opportunities exist.
Simple version: A call and put at the same strike and expiration should be priced so that combining them with stock creates a risk-free position. When they are not priced correctly, traders can lock in guaranteed profits.
What is a Conversion?
A conversion is an arbitrage strategy that combines:
- Long 100 shares of stock
- Long 1 put option at strike price X
- Short 1 call option at strike price X
Both options have the same strike and expiration. This creates a position with no directional risk.
Conversion Example
Stock ABC is trading at $100. The $100 strike options show mispricing:
- Buy 100 shares at $100 ($10,000)
- Buy 1 $100 put for $4.00 ($400)
- Sell 1 $100 call for $5.50 ($550 credit)
Net cost: $10,000 + $400 - $550 = $9,850
At expiration (any stock price): Position is worth exactly $10,000 (strike price)
Risk-free profit: $10,000 - $9,850 = $150
This works because:
- If stock above $100: Call is assigned, you sell shares at $100, put expires worthless
- If stock below $100: Put exercised, you sell shares at $100, call expires worthless
- Either way, you receive $10,000
What is a Reversal?
A reversal (or reverse conversion) is the opposite of a conversion:
- Short 100 shares of stock
- Long 1 call option at strike price X
- Short 1 put option at strike price X
This also creates a position with no directional risk.
Reversal Example
Stock ABC is trading at $100. The options show the opposite mispricing:
- Short 100 shares at $100 ($10,000 received)
- Buy 1 $100 call for $4.50 ($450)
- Sell 1 $100 put for $5.00 ($500 credit)
Net credit: $10,000 + $500 - $450 = $10,050
At expiration (any stock price): Position costs exactly $10,000 to close
Risk-free profit: $10,050 - $10,000 = $50
Why These Strategies Work
Conversions and reversals exploit violations of put-call parity:
- Conversion profits when: Calls are overpriced relative to puts
- Reversal profits when: Puts are overpriced relative to calls
The combined position has zero delta (no directional exposure) and a guaranteed value at expiration equal to the strike price.
Interest Rate and Dividend Considerations
True arbitrage calculations must account for:
- Cost of carry: Interest paid to hold long stock or received from short stock proceeds
- Dividends: Long stock receives dividends; short stock pays dividends
- Time to expiration: Longer duration means more interest and dividend impact
Professional traders use sophisticated models to calculate whether apparent mispricings are real after accounting for these factors.
Who Uses Conversions and Reversals?
Market Makers
Market makers are the primary users of these strategies. They:
- Continuously monitor for pricing discrepancies
- Execute trades in milliseconds when opportunities arise
- Make small profits on large volume
- Help keep options markets efficient
Institutional Traders
Large institutions use conversions and reversals for:
- Risk-free returns on capital
- Synthetic borrowing or lending
- Tax optimization strategies
- Hedging existing positions
Retail Traders
Retail traders rarely profit from true conversions and reversals because:
- Mispricings are usually too small to overcome transaction costs
- Professional traders have faster execution
- Margin requirements can be prohibitive
- Opportunities disappear in seconds
Practical Applications for Retail Traders
While pure arbitrage may not be practical, understanding these concepts helps with:
1. Identifying Mispriced Options
If you notice calls seem unusually expensive compared to puts (or vice versa), it may indicate:
- High demand for directional speculation
- Upcoming dividends not yet priced in
- Hard-to-borrow stock affecting synthetic positions
2. Choosing Between Strategies
If calls are expensive relative to puts:
- Sell calls instead of buying puts for bearish views
- Use put spreads instead of call spreads for bullish views
3. Understanding Synthetic Positions
Conversions and reversals are built from synthetics:
- Long stock + synthetic short = conversion
- Short stock + synthetic long = reversal
Key insight: Even if you never trade a conversion or reversal, understanding them helps you evaluate whether options are fairly priced and choose the most efficient way to express your market view.
Risks of Conversions and Reversals
Despite being called "risk-free," these strategies have operational risks:
1. Early Assignment (American Options)
If the short option is assigned early, the arbitrage can be disrupted:
- Conversion: Early call assignment forces early sale of stock
- Reversal: Early put assignment forces early purchase of stock
2. Execution Risk
All three legs must be executed at the expected prices. Slippage on any leg can eliminate the profit.
3. Dividend Risk
Unexpected dividend changes can affect the expected payoff.
4. Pin Risk
If the stock closes exactly at the strike at expiration, there is uncertainty about assignment.
5. Capital Requirements
Conversions require capital to buy stock. Reversals require margin for the short stock position.
Conversion and Reversal vs Box Spread
- Conversion/Reversal: Involves stock plus two options
- Box Spread: Involves four options, no stock
- Both: Are arbitrage strategies that lock in risk-free returns
- Difference: Box spreads can use European options to avoid early assignment
How Market Makers Use These Strategies
- Inventory management: Convert unwanted positions to neutral
- Price discovery: Help establish fair value for options
- Risk reduction: Eliminate directional exposure while holding positions
- Profit capture: Lock in small gains from pricing inefficiencies
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Summary
Conversions and reversals are arbitrage strategies that combine stock with options to create risk-free positions. Conversions use long stock, long put, and short call. Reversals use short stock, long call, and short put. While these strategies are primarily used by market makers and institutions, understanding them helps all traders evaluate option pricing and choose efficient strategies. Remember that true risk-free arbitrage opportunities are rare and fleeting in modern markets.
Learn about related strategies: box spreads and synthetic stock positions.