Conversion Arbitrage: Reverse Conversions
By John Summa
The related strategy of reverse conversions (or reversals) involves exactly what the name implies, the reverse of a conversion. Here the arbitrageur will be selling (instead of buying) the stock short, and then buying a call and selling a same-strike, same-month put. (Read more about arbitrage in Trading The Odds With Arbitrage.)
As with a conversion, if this can be executed for a net time-premium credit between the call sale and put purchase, you will have locked in a profit no matter where the stock trades before expiration day. To remind you, at this level we are abstracting from some complicating factors to provide a way to better grasp the basic idea.
Just as a conversion involves three legs in the strategy, so too does a reversal. The rule of thumb for determining profitability applies with one minor alteration. Recall that conversions can be explained in terms of the cost of establishing the positions (stock price plus put price minus sale of call), which is a debit price. Here we look to compare a credit price (received for the reversal) to the strike price used in the trade to look for potential profitablility.
When speaking of conversions, as long as the debit sale price is less than the strike price, a conversion profit exists (leaving aside the complicating factors we will turn to in subsequent sections). With a reversal, on the other hand, the same rule of thumb applies but the credit received for establishing the position must be greater than the strike price for a potential arbitrage profit to exist. (Learn more about options in Do Option Sellers Have A Trading Edge?)
Using Reversals to Capture Time-Value Credit
Unlike the conversion, where you have to pay for the position with a net cash outlay, a reversal involves selling short the stock and the put, which brings in a credit to the account. Leaving aside the interest earnings potential on this credit balance for now, the size of the credit must exceed the strike price for a reversal profit to be established. This reduced form model should allow for grasping the core concept of the reversal without overwhelming you with complicating details.
While a reversal involves selling stock short and then buying a call and selling a same-strike and same- month put, it must be executed for a net time-premium credit. This is simply stating, in a different way, that the overall pricing conditions (overall credit received from sale of reversals > the strike price) need to lock in a profit. Above we mentioned that the credit from the reversal must exceed the strike price, so we are simply boiling all this down to show that it amounts to establishing a net time-value credit between the put sold and call purchased.
Figure 7 shows some hypothetical prices (altered from our previous actual example) for ABC stock to illustrate the idea of a December 75 reverse conversion's potential arbitrage profit as a time-value credit.
|Option Month||Option Type
||Option Strike||Option Price||Intrinsic Value||Time Value|
|December||Long Call||75||4.90 (ask)||0||4.90|
|December||Short Put||75||5.85 (bid)||.90||4.95|
|Reversal Profit||Net Time Value=
|Figure 7: ABC\'s stock has an assumed ask price of $74.10 and options prices slightly altered to show how a reversal would generate a small arbitrage profit. The 5 cent net time-value credit translates into $5 per reverse conversion, which requires selling 100 shares short at $74.10, selling a December 75 put at $5.85 and buying a December 75 call at $4.90.|
Often the reversal is presented in terms of the price of selling the stock (credit cost) in relation to the strike of the options. If the credit received from selling it is greater than the strike price, then the arbitrage profit is established, as seen in Figure 8, where the position entry price shown is $75.05, which is greater than the strike of $75 by 5 cents.
For example, at the price of $25, the December 75 long call loses $4.90 and the December 75 short put loses $19.15 (for a total loss of $24.05), but that is offset by a gain of $24.10 on the short stock, leaving a per-share gain of 5 cents. As was seen in Figure 7, we arrived at the same profit we saw above by showing how this is simply the same as collecting a net time-premium (or extrinsic value) credit.
|Positions Settlement Prices @ 100/50||Position
Gain/Loss @ 100
Gain/Loss @ 50
|Dec 75 Long Call||4.90 (buy)||25/0||20.10
|Dec 75 Short Put||5.85 (sell)||0/25||5.85||-19.15|
|Short Stock||74.10 (sell)||100/50||-25.9||24.10|
|75.05 (> 75)||$.05 ($5)||$.05 ($5)|
|Figure 8:Here we demonstrate the same profit of $5 is available at any price for this reversal. We take only two prices, however, to simulate the outcomes (it would be true for any prices on the scale). Wecalculate results based on an assumed stock price of $50 and $100 for the stock at options expiration day. The table above shows the same gains at the two assumed expiration day prices for ABC stock.|
|Reversal Profit Calculation|
|(Stock Price + Put Price)||(Strike Price - Call Price)|
|74.10 + 5.85 = 79.95||Minus(-)||75.00 + 4.90 = $79.90||Profit=$0.05|
|Figure 9: Reversal arbitrage profit in this model assumes no carrying costs and no dividend paid or received. Here you can see that the position establishes a $5 arbitrage profit as was demonstrated inthe other calculation methods shown in Figure 7 and Figure 8.|
As the reader will see, when moving to a more complex understanding of a conversion and reversal, dividends can play a key role in determining potential profit and loss. While it is possible to reduce the dividend risk from the strategy through the proper assessment of trades, it will remain a potential risk.
Additionally, the cost of carry is a feature of this strategy that will be incorporated as we move through the different parts. It comes into play in the conversion but not the reversals. Reversals create a credit balance and are thus free of a cost of carry (defined as the interest paid on a debit balance).
In fact, reversals are strategies than allow for capturing interest payments on the cash proceeds of the short sale (put plus short stock) in the reversal itself. These interest earnings are then factored into the equation for determining ultimate profitability. However, like with dividend payments in conversions, there is no guarantee that these variables will remain fixed once in a conversion or reversal, thus opening a window of risk to the arbitrageur. (Learn more in Using Options Instead of Equity.)
Reversals on stocks involve selling the shares short, selling a put and buying a same-strike call with the same expiration dates. Here we demonstrated how such a strategy could make a profit if the sale price of the reversal is above the strike price used. When this condition is met, there is a locked in time-value credit that represents an arbitrage profit. However, we are still excluding the possibility of dividends in the equation, a subject to which we now turn.
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