### What is a Reverse Conversion

A reverse conversion is a form of arbitrage that enables options traders to profit from an overpriced put option. The trade consists of selling a put and buying a call to create a synthetic long position while shorting the underlying stock. As long as the put and call have the same underlying strike price and expiration date, the synthetic long position will have the same risk/return profile as ownership of an equivalent amount of underlying stock.

### BREAKING DOWN Reverse Conversion

Reverse conversion arbitrage is a type of put-call parity, which says that put and call option positions should be roughly equal when paired with the underlying stock and T-bills, respectively.

To illustrate this concept, consider two scenarios:

- A trader that purchases one call option with a strike price of $100 and a T-bill with a face value of $10,000 that matures on the call's expiration date will always have a minimum portfolio value equal to $10,000.
- A trader that purchases one put option with a strike price of $100 and $10,000 worth of stock will always have a minimum value equal to the strike price of the put option.

Since traders are unlikely to have an impact on interest rates, arbitrageurs take advantage of option price dynamics to ensure that the put and call values equal out for a given asset. In fact, the put-call parity theorem is central to determining the theoretical price of a put option using the Black-Scholes model.

A reverse conversion is a form of arbitrage that enables traders to capitalize on situations where the put is overpriced by selling a put, buying a call, and shorting the underlying stock. The call covers the short stock if it rises above the strike price and the put is covered by the shorted stock if the stock price is less than the strike price. The profit when initiating these positions is the theoretical arbitrage gain from the position that comes from an overpriced put option.

### Example of a Reverse Conversion

In a typical reverse-conversion transaction or strategy, a brokerage firm short sells stock and hedges this position by buying its call and selling its put. Whether the brokerage firm makes money depends on the borrowing cost of the shorted stock and the put and call premiums, all of which may render a return better than the low risk money market. In the context of futures markets, a trader would be synthetically long and short the underlying futures when looking for arbitrage opportunities.