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Synthetic Options



I have explained in past articles, volatility trading and how re-hedging the delta of long options by trading stock captures daily profits against time premium losses (re-hedging the delta of short options by trading the stock captures losses against time premium profits). If in effect re-hedging the delta of options offsets the profit/loss profile of an actual option position, it follows that the re-hedging of the delta with stock creates synthetic options, and thus, the same profit/loss profile of an option position can be created by trading the stock in a certain way. Let's take a close look at one of the primary stock trading methodologies, momentum trading, to illustrate.

Momentum trading attempts to profit from the statistical observation that trends have a certain degree of persistence: a trend can be viewed as a wave, a pattern with a trough and a crest (the crest being the beginning of the break-down of the pattern). It is mostly technical and short term in nature and is characterized by buying high and selling higher or shorting low and buying lower (we will only look at long positions, although the same applies to short positions).

The riskiest strategy for a short term trader is trying to pick a bottom in a stock (determine the trough): oversold conditions are best left to longer term buyers who commit larger amounts of money based on fundamentals and who average down to accumulate positions. Momentum trading effectively avoids this risky endeavor by waiting for the trough to form independently (and then some). The technician recognizes buying and rising stock prices as the earlier stages of accumulation and as such, devises a strategy to "ride" that part of the wave with the highest probability of continuing (between the trough and the crest). The most important element of staying on the wave is controlling risk: the trader uses a methodology of trailing stops, which should be pre-set based on the volatility of the stock (and closely adhered to). The following example will illustrate how this type of trading re-creates the profile of a long call option.

Stock X has risen 15% from its 12 month low and is currently trading at $50. Sheryl determines based on technicals that the stock is breaking out on the upside and that the current price is an excellent entry point. Before trading the position, she first determines the total maximum loss she is willing to incur and the amount of stock to buy based on the expected target price (this effectively creates leverage). She decides that she is willing to risk $5,000 in losses and based on a target price of $55, buys 3,000 shares, for an expected profit of $15,000: this gives her a return to risk profile of 3 to 1 ((3,000 x $5)/ $5,000).

Sheryl buys 1,000 shares at $50 for a third of a position and sets a sell stop at $48. She bases the stop on the fact that the stock normally trades at 30% volatility; this allows for two days of normal activity (2% per day). The logic is that if it breaks $48 that will signal that more than just two days of normal volatility is affecting the stock, that something else is going on to break the trend. If that happens, Sheryl will sell her long at $48. If the stock rises back from any level above $48 she buys the same 1,000 shares back at $50.

As the stock rises, to say $51 she decides to add another third to the position and places a $48 stop on 1,000 shares and a $49 stop on 1,000 shares. Once the stock rises to $52 she adds another third to the position: she has a full position now of 3,000 shares at an average cost of $51.67 (((1,000 x ($50 - $48)) + (1,000 x $50) + (1,000 x $51) + (1,000 x $52))/3,000)) with stops on 1,000 shares each at $48, $49, and $50 respectively. Sheryl is buying more as the stock rises as she gains confidence that the stock will reach the target price. Notice that what Sheryl is trying to do is limit her loss by selling the stock as it goes down and maximize her gain by increasing her exposure as the stock rises. As the stock continues to rise she will maintain her full exposure, but maintain the same maximum loss by raising her stops. Once she either loses her $10,000 (maximum "stop loss") or sells the entire position at the target price (crest), she is out of the trade.

I could go into much more detail, for there are many variation of this, but my purpose is only to introduce momentum trading and to illustrate that just like in buying a call option, there is a maximum loss (premium paid) and more exposure to a stock as it rises (the delta of a call option increases as well as the total premium as the stock rises). All of the cumulative losses in trading the stock to protect risk can be viewed as the premium for the option. Sheryl has effectively re-created a call option by the way she trades the stock. The only difference is that a call option has a hard stop: there is always a chance when trading the stock that it gaps down and Sheryl cannot effectively stop her position, or chooses to do so because of a lack of discipline.

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No positions in stocks mentioned.

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