Conversion Arbitrage: How Does It Work?
By John Summa
In the previous section of this tutorial, we saw that conversions and reversals are three-legged strategies combining stock and options positions. Still remaining with the simplified model, the workings of the conversion strategy will be explained in more detail.
Because a conversion trader buys stock, sells calls and buys same-strike puts (with the same expiration dates), directional risk is removed from the equation. Actually, a conversion is a long stock position combined with a synthetic short stock position, which is created from the short sale of the call and purchase of a same-strike put. (For related reading, see Short Selling Can Be Similar To Buying Long.)
Synthetic Short Stock Combined With Long Stock
As an example, if we constructed an at-the-money conversion, the deltas would be -50 (short call) and -50 (long put), or -100 deltas taken together, and would be exactly opposite the long stock position of 100 shares. This offers a perfect hedge, as gains and losses are offsetting. It is displayed in Figure 1, below.
As mentioned previously, if this can be executed for a net time-premium credit (extrinsic value collected from selling the call is greater than the extrinsic value of the put), an arbitrage profit is available. (Learn more about options strategies in Gamma-Delta Neutral Option Spreads.)
|Conversion||Long Stock||Short Call||Long Put|
|Figure 1: Any long stock gains are offset by short call/long put losses, leaving a net time-value credit for the conversion arbitrageur. Meanwhile, any long stock losses are offset by short call/long put gains, but also leaving the same net time-value credit for the arbitrageur.|
Expiration Day Outcomes
Now we'll break this down for expiration day. If the stock trades higher by options expiration day, the short call expires in the money (ITM) with zero time value; the put expires out of the money (OTM) (assuming the conversion was done using at- or in-the-money calls). The put time value is lost and the call time value becomes profit. The difference between the two is the profit on the trade. The call gets exercised and the stock is called away leaving the trader flat all legs, left with just his or her arbitrage profit.
If the stock trades lower by expiration (again making the assumption of a conversion done at the money) the call expires OTM with zero time-premium and the put expires ITM (also with zero time-premium). The put is exercised and the stock is put to sellers of the puts, leaving the trader flat, with the initial time value credit turned into a profit. (Help increase your success when trading options; read Stock Option Trading Cycles.)
Regarding reversals, the same is true in terms of the net time value (extrinsic value) credit conditions outlined above. Recall that the reverse conversion involves selling the stock short, selling puts and buying same-strike calls (with the same expiration date). Here we have a synthetic long created with the short put/long call options, and this perfectly hedges the short stock position.
|Reversal||Short Stock||Short Put||Long Call|
|Figure 2: Any short stock up losses are hedged by the short put/long call gains, leaving a net time-value credit for the conversion arbitrageur. Any short stock down gains are offset by short put/long call losses, leaving the same net time-value credit for the conversion arbitrageur.|
As displayed in Figure 2, if the stock trades lower by the time of the expiration of the options, the short put expires ITM with zero time premium and is exercised, thus removing the short position. The call expires worthless, out of the money. Again, if the reversal was established for a time-value credit (put extrinsic value > call extrinsic value), this will leave a profit (assuming no commissions, as we do throughout this tutorial) equal to the size of the time-value credit.
Finally, if the stock trades higher by the expiration date of the options, the long call expires in the money with zero time value and is exercised, thus removing the short stock positions. When you exercise a call you get a long stock position. Since you are already short stock, this flattens out the short stock position. (Try a new approach to covered calls, read An Alternative Covered Call: Adding A Leg.)
In this tutorial section, general outcomes for conversions and reversals were summarized. For a conversion where you are long stock, we looked at the results of a stock trading higher or lower by expiration. For reversals where you are short stock, we walked through the same two scenarios. We explained that the resulting profit would depend on the size of the time-value credit obtained in the initial setup of the strategies. In the next section, we will begin working with an example of a conversion with actual prices to demonstrate why this occurs.
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