Conversion Arbitrage: Forward Conversions
By John Summa
With a forward conversion (herein, referred to as a conversion), it is possible to achieve a riskfree profit if samestrike calls and puts are priced out of line (defined here as time value not equal). This means that a call can be sold and a put purchased at the same strike and in the same month, but at different time values (call time value > put time value). The different time values on the call and put options offer an opportunity to lock in a profit by use of a conversion. Here we will look at an example to illustrate the point. (To read more about time value, check out The Importance Of Time Value.)
Let's take a look at a forward conversion on a stock we will call ABC. The inner workings of the strategy will be revealed when we start working with some numbers. However, we will keep the example simplified (leaving out dividends, interest and a few other issues) until later.
Forward Conversion Example
Suppose ABC stock last traded at $73.95 with an ask price of $74.10. Meanwhile, ABC's December 75 calls and puts were showing a bid and ask respectively of $4.95 (call) and $5.80 (put). At the bid/ask pricing of the options, a conversion could be purchased for $74.95. Recall that there are two ways to assess whether a profit exists at these prices. We will now walk through both.
First, the quickest way to look at the pricing is to ask if the purchase price for the conversion, $74.95, is less than the strike price, $75. If it is, then a conversion profit exists. If you fill it for 5 cents under the strike price, there would be a profit of $5 per conversion. (Learn about other investing strategies in Profit On Any Price Change With Long Straddles.)
Let's take a second look from our timevalue perspective. Another way to think of this conversion is to compare time value (extrinsic value) on the call and put options. Figure 3 provides a breakdown of the two types of value in options. There is both intrinsic and extrinsic value in each option, the latter being the basis for potential arbitrage profit with a conversion.
Option Month  Option Type 
Option Strike  Option Price  Intrinsic Value  Time Value 
December  Short Call  75  4.95 (bid)  0  4.95 
December  Long Put  75  5.80 (ask)  .90  4.90 
Net Time Value=  $.05 
Figure 3: ABC stock last traded at $73.95, with an ask price of $74.10. The example above uses the ask price for the purchase price of the stock. As can be seen, this produces a 5 cent net timevalue credit per share, which translates into $5.00 per conversion (buy 100 shares, sell Dec. 75 call and buy Dec. 75 put). 
If the price of ABC stock at the expiration of December options is $100, the profit on the position is $5. If the price of the stock at expiration of the December options is $50, the profit is still $5. This is presented inFigure 4. For example, at the price of $100, the Dec. 75 call would lose $20.05, the Dec. 75 put would lose $5.80 (total loss of $25.85), but the stock position would gain $25.90, leaving a 5 cent per share gain. Figure 1, furthermore, presents the profit/loss payoff diagram of this conversion at all prices, showing $5 in profit at any price. (Learn more in Stock Option Expiration Cycles.)
Conversion Legs 
Position Entry Price 
Settlement Prices @ 100/50 
Position Gain/Loss @ 100 
Position Gain/Loss @ 50 
Dec 75 Short Call  4.95 (sale)  25/0  20.05  4.95 
Dec 75 Long Put  5.80 (buy)  0/25  5.80  19.20 
Long Stock  74.10 (buy)  100/50  25.90  24.10 
74.95 < 75  $.05 ($5.00)  $.05 ($5.00) 
Figure 4: Calculation of profit/loss with stock price at $50 and $100. The table above shows the gains and losses at the two assumed expiration prices for ABC stock and the associated same outcomes for the three legs of the conversion. 
Figure 5: Profit/loss diagram for ABC stock December 75 conversion 
Copyright © 2009 Investopedia.com 
Again, this outcome results from having an initial net timepremium credit (extrinsic value collected from selling the call is greater than the extrinsic value on the put) that amounts to an arbitrage profit.
In the ABC stock example, Figure 6 shows an alternative calculation to determine profitability of a conversion. The purchase price we know must be less than the strike used in the conversion. But here, we see that the strike price plus call price, minus the stock price plus put price arrives at the same 5cent per share profit. This is seen in both the timevalue based calculation and the purchasepricegreaterthanstrikeprice calculation.
Conversion Profit Calculation  
(Strike Price + Call Price)  (Stock Price + Put Price)  
75 + 4.95 = $79.95  Minus()  74.10 + 5.80 = $79.90  Profit=$0.05 
Figure 6: Conversion profit assumes carrying costs and no dividend payment. 
In the calculation inFigure 6, the conversion profit assumes no carry costs or dividend payments. The reality of trading is not so simple and actual profitability includes such things as dividend payments (if any), interest paid on debit balances (carrying costs) and any transaction costs (commissions/fees).
Conclusion
This section of the tutorial provided an example of a December 75 conversion on a hypothetical stock, which was used to flesh out the bare bones approach with which we began. By selling the December 75 call for more time premium, then purchasing the December samestrike put, a small arbitrage profit was secured, but here we saw two additional calculation methods used to arrive at this same outcome. Before relaxing key assumptions in our simple conversion story, let's take a closer look at a reversal to examine its inner workings.
Conversion Arbitrage: Reverse Conversions

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