Directional Butterflies

Trading a butterfly can be an excellent way to establish a low-cost, relatively low-risk directional trade when a trader has a specific price target in mind.Wing Spreads 195 For example, a trader, Ross, has been studying Walgreen Co. (WAG) and believes it will rise from its current level of $33.50 to $36 per share over the next month. Ross buys a butterfly consisting of all OTM January calls with 31 days until expiration. He executes the following legs:

Buy 1 January 35 call at 1.15 Sell 2 January 36 calls at 0.80 each Buy 1 January 37 call at 0.55 Net debit 0.10As a directional trade alternative, Ross could have bought just the January 35 call for 1.15. As a cheaper alternative, he could have also bought the 3536 bull call spread for 0.35. In fact, Ross actually does buy the 3536 spread, but he also sells the January 3637 call spread at 0.25 to reduce the cost of the bull call spread, investing only a dime.

The benefit of lower cost, however, comes with trade-offs.Exhibit 10.5 compares the bull call spread with a bullish butterfly.The butterfly has lower nominal risk—only 0.10 compared with 0.35 for the call spread. The maximum reward is higher in nominal terms, too—0.90 versus 0.65.The trade-off is what is given up. With both strategies, the goal is to have Walgreen Co. at $36 around expiration.

But the bull call spread has more room for error to the upside. If the stock trades a lot higher than expected, the butterfly can end up being a losing trade.Given Ross’s expectations in this example, this might be a risk he is willing to take. He doesn’t expect Walgreen Co. to close right at $36 on theexpiration date. However, he’d have to be wildly wrong to have the trade be a loser on the upside. It would be a much larger move than expected for the stock to rise significantly above $36.

If Ross strongly believes Walgreen Co. can be around $36 at expiration, the cost benefit of 0.10 vs. 0.35 may offset the upside risk above $37. As a general rule, directional butterflies work well in trending, low-volatility stocks.When Ross monitors his butterfly, he will want to see the greeks for this position as well. Exhibit 10.6 shows the trade’s analytics with Walgreen $33.50.

When the trade is first put on, the delta is small—only 10.008. Gamma is slightly negative and theta is very slightly positive. This is important information if Walgreen Co.’s ascent happens sooner than Ross planned. The trade will show just a small profit if the stock jumps to $36 per share right away. Ross’s theoretical gain will be almost unnoticeable. At $36 per share, the position will have its highest theta, which will increase as expiration approaches. Ross will have to wait for time to pass to see the tradereach its full potential.

This example shows the interrelation between delta and theta. We know from an at-expiration analysis that if Walgreen Co. moves from $33.50 to $36, the butterfly’s profit will be 0.90 (the spread of $1 minus the 0.10 initial debit). If we distribute the 0.90 profit over the 2.50 move from $33.50 to $36, the butterfly gains about 0.36 per dollar move in Walgreen Co. (0.90/(36 2 33.50).

This implies a delta of about 0.36.But the delta, with 31 days until expiration and Walgreen Co. at $33.50, is only 0.008, and because of negative gamma this delta will get even smaller as Walgreen Co. rises. Butterflies, like the vertical spreads of which they are composed, can profit from direction but are never purely directional trades.

Time is always a factor. It is theta, working in tandem with delta, that contributes to profit or peril.A bearish butterfly can be constructed as well. One would execute the trade with all OTM puts or all ITM calls. The concept is the same:sell the guts at the strike at which the stock is expected to be trading at expiration, and buy the wings for protection.