Conversion
Long stock plus a long put and short call at the same strike. An arbitrage strategy that locks in a risk-free profit when options are mispriced.
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What is a Conversion?
A conversion is an arbitrage strategy that combines three positions: long stock, a long put, and a short call at the same strike and expiration. The long stock plus the long put is equivalent to a long call (via put-call parity). By simultaneously selling a call, you lock in any difference between the theoretical and actual prices.
In plain terms, you own the stock, you buy insurance on it (the put), and you sell someone else the right to buy it from you (the call). If the options are priced perfectly, there is no profit and no loss — the whole thing is a wash. But when options are slightly mispriced, the conversion captures that edge.
This is not a strategy for making big directional bets. It is a precision tool used by market makers and institutional traders to capture tiny mispricings between stock and options. It relies on the principle of put-call parity.
How to Set It Up
- Buy 100 shares of the stock
- Buy 1 put at strike A
- Sell 1 call at the same strike A
- Same expiration for both options
- Strike selection: Any strike works, but at-the-money is most common because it has the most liquidity and the tightest spreads.
- Expiration: Any expiration. Longer expirations have more potential for mispricing due to interest rate and dividend effects.
- Net cost: The total outlay is the stock price minus the call premium plus the put premium. This should approximately equal the present value of the strike price.
The position is delta-neutral. No matter what the stock does, the outcome is locked in from the start.
When to Use This Strategy
Use a conversion when:
- You spot a pricing discrepancy between the stock and its options
- Put-call parity is violated and you can capture the difference
- You are a market maker managing inventory
- You want to earn the interest rate differential on a stock position
- You need a hedged position that carries no directional risk
Retail traders almost never use conversions because the profit is tiny (often pennies per share) and gets eaten by commissions and bid-ask spreads. It is mainly a professional and algorithmic trading strategy. But understanding it helps you understand how options are priced.
Example Trade
Stock XYZ is trading at $100. The $100 strike options with 60 days to expiration are available.
- Buy 100 shares of XYZ at $100.00
- Buy 1 XYZ $100 put for $3.50
- Sell 1 XYZ $100 call for $3.80
- Net credit from options: $3.80 - $3.50 = $0.30 ($30)
- Total invested: $10,000 (stock) + $350 (put) - $380 (call) = $9,970
If XYZ rallies to $110 at expiration: You sell stock at $100 via the call. You receive $10,000. Put expires worthless. You invested $9,970 and received $10,000. Profit: $30.
If XYZ drops to $90 at expiration: You sell stock at $100 via the put. You receive $10,000. Call expires worthless. You invested $9,970 and received $10,000. Profit: $30.
If XYZ stays at $100: Both options expire worthless. You still own stock worth $10,000. You invested $9,970. Profit: $30.
The profit is the same no matter what happens. That is the definition of arbitrage.
Risk and Reward
- Max profit: The arbitrage edge, which is minimal. In our example, $30.
- Max loss: Minimal. If executed correctly, there is essentially no loss scenario. However, execution risk (slippage, partial fills) can turn a small profit into a small loss.
- Breakeven: The position is already locked in. There is no breakeven in the traditional sense — you either capture the arbitrage or you do not.
The profit comes from the violation of put-call parity. In efficient markets, this edge is very small and often disappears before retail traders can capture it.
Tips and Common Mistakes
- Transaction costs kill the profit. With a $30 profit on a $10,000 position, even a few dollars in commissions wipes out the edge. This is why it is mainly an institutional strategy.
- Dividend risk matters. If the stock pays a dividend before expiration, the short call may be assigned early (the call buyer wants the dividend). Factor dividends into your calculations.
- Interest rates affect pricing. The conversion profit is closely tied to the cost of carry (interest rates). Higher rates can create more opportunities.
- Learn it for the theory. Even if you never trade a conversion, understanding it teaches you put-call parity, which is foundational to all options pricing.
- Use it to check option pricing. If you see a "free money" conversion, something is wrong — either your data is stale, there is a dividend you missed, or the execution risk exceeds the theoretical profit.
Related Strategies
- Reversal — the opposite: short stock + short put + long call
- Synthetic Long Stock — the options-only component (long call + short put)
- Collar — similar structure but with different strikes (not arbitrage)
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