## What Is Conversion Arbitrage?

Conversion arbitrage is an options trading strategy employed to exploit perceived inefficiencies that may exist in the pricing of certain options. Conversion arbitrage is considered to be a risk-neutral strategy, whereby a trader buys a put and writes a covered call (on a stock that the trader already owns) with identical strike prices and expiration dates.

A trader will attempt to profit through a conversion arbitrage strategy when the call option is overpriced or the put is relatively underpriced. This can be due to market inefficiencies, or from the effects of mispriced interest rate assumptions. This strategy is most often achieved through an options spread called a reverse conversion (or reversal conversion).

Conversion arbitrage should not be confused with convertible arbitrage, which is a strategy involving apparent mispricings in a convertible bond and its components.

### Key Takeaways

- Conversion arbitrage attempts to profit from relative mispricings between call and put options in the same underlying security.
- Put-call parity suggests that there is a direct relationship between the prices of calls and puts for the same strike price and expiration.
- If this parity relationship is out of whack in the market, traders can utilize a conversion arbitrage strategy.
- There are still important risk factors to bear in mind when considering arbitrage conversions, including a shift in interest rates or a change in dividends.

## Understanding Conversion Arbitrage

Conversion arbitrage in options is an arbitrage strategy that can be undertaken for the chance of a riskless profit when options are either theoretically overpriced or underpriced relative to each other and the underlying stock—as determined by the trader's pricing model.

To implement the strategy, the trader will sell short the underlying stock and simultaneously offset that trade with an equivalent synthetic long stock position (long call + short put). The short stock position carries a negative 100 delta, while the synthetic long stock position using options has a positive 100 delta, making the strategy delta neutral, or insensitive to the direction of the market.

## Example of How Conversion Arbitrage Works

For example, if the price of the underlying security falls, the synthetic long position will lose value at the exact same rate that the short stock position gains value; and vice-versa. In either situation, the trader is risk-neutral, but profits may accrue as expiration approaches and the options' intrinsic value (time value) changes.

Conversion arbitrage works because of the theoretical claim of put-call parity, based on the Black-Scholes options pricing formula. Put-call parity suggests that, once fully hedged, calls and puts of the same underlying, same expiration date, and same strike price—should be theoretically identical (parity). This is expressed by the following expression, where PV is the present value:

*Call - Put = Price of underlying - PV(Strike)*

If the left side of the equation (call minus put price) is different than the right side of the equation, a potential conversion arbitrage opportunity exists.

## Special Considerations

It is important to note that just because it is called arbitrage, conversions are not without risks. Interest rates impact both carry costs and earnings on credit balances. Carrying costs also include the amount of interest charged on debit balances.

As with all arbitrage opportunities, conversion arbitrage is rarely available in the market. This is because any opportunity for risk-free money is acted on very quickly by those who can spot these opportunities quickly and push the market back in line. Additionally, since executing options and short-selling stock involves transaction costs such as broker fees and margin interest, apparent arbitrage opportunities may not exist in practicality.

There are important risk factors to bear in mind when considering arbitrage conversions; a few of these include a hike to interest rates and the elimination of dividends.