# The Concept of Relative Pricing

The essence of the conversion relationship is that given a strike price, costs, and a target profit, a constant difference between the time value of the call and the time value of the put always will exist.Relative pricing means that the price of a call, a put, or a stock can be calculated if prices of the other two are known.In Table 6-3, the time value of the 55 Call had to be 69 cents greater than the time value of the 55 Put.

Therefore, if the prices of the stock and the 55 Put are known,then the price of the 55 Call can be calculated.Also, if the prices of the stock and the 55 Call are known, then the price of the 55 Put can be calculated, and if the prices of the 55 Call and 55 Put are known,then the price of the stock can be calculated.

In the days when option trading was conducted in open outcry,market makers would start their days by calculating the relative prices of calls to puts by strike price. If trading the 60-strike options in row 4 of Table 6-9, for example, a market maker would note that the time value of the 60 Call must be 58 cents greater than the time value of the 60 Put in order to make a 5-cent-per-share profit on a conversion.

Then, during the day, if 60 Puts were offered at 3.10 when stock was offered at 60.47, the market maker would offer 60 Calls at 4.15. If someone were to buy the calls for 4.15 (and the market maker sold them), the market maker would then simply buy the stock at 60.47 and buy the puts at 3.10 to complete the conversion and thereby lock in a 5-cent-per-share profit.

As stock prices changed and as option orders entered the pit, the market maker would constantly use the 58-cent difference to calculate the relative prices of 60 Calls and 60 Puts and make bids and offers accordingly.In today’s electronic trading environment, computers handle the pricing of options—and therefore the pricing of conversions. Nevertheless,the same concepts apply, and today’s option traders must understand these concepts for those occasions when they need to override the computer or adjust its assumptions.

The Reverse Conversion:As its name implies, the reverse conversion or, simply, the reversal is the opposite of the conversion. It involves the purchase of synthetic stock and the sale of real stock. A reverse conversion is a three-part strategy consisting of short stock, short puts, and long calls on a share-forshare basis. The calls and puts have the same strike price and same expiration date.

A reverse conversion is established for a net credit,which is invested at the risk-free rate. To be profitable, the interest earned from the net credit must be greater than transaction costs plus the difference of call time value minus put time value.Table 6-10 and Figure 6-2 illustrate a reverse conversion that yields a gross profit of 75 cents per share before transaction costs and interest.

The three-part position consists of one share of stock sold short at \$102, one short 100 Put sold at 5.25, and one long 100 Call purchased for 6.50. As column 5 in Table 6-10 and the solid line in Figure 6-2 show, the final outcome at expiration, 75 cents per share profit, is the same regardless of the stock price.This example assumes that the net credit proceeds from the reverse conversion are invested. Consequently, the net profit or loss of a reverse conversion depends on the amount of interest earned.

Reverse Conversion—Outcomes at Expiration As with synthetic positions and conversions, there are three possible outcomes at expiration for reverse conversions. Table 6-11 summarizes the possibilities. If the stock price closes below the strike at expiration outcome 1, then the short put is in the money. It therefore will be assigned, and the stock will be purchased at the strike price.

If the stock price is above the strike price at expiration, outcome 3, then the long call is in the money. It therefore will be exercised, and the stock will be purchased at the strike price.It does not matter if the stock price closes above or below the strike price at expiration; the stock will be purchased, and the reverse conversion position will be closed. This result is the desired outcome because a profit will be realized, and the position will be closed.

Then there will be no open position with the attendant risk that could reduce the profit or create a loss.Reverse Conversion—Pin Risk Pin risk poses as much of a problem for the reverse conversion as it does for the conversion. When the stock price closes exactly at the strike price at expiration, the trader must make a difficult decision.The three-part position of short stock, short puts, and long calls produces uncertainty about how many puts, if any, will be assigned. If all the calls are exercised but only some of the puts are assigned, then a long stock position is created.