Creating a Synthetic Long Straddle

Long synthetic straddles are easy to put together and easier to understand than most traders think. To create a long synthetic straddle, you purchase 2 put options for every 100 shares of the underlying stock you own. Let's look at an example using a hypothetical stock called XYZ Corp which has become much more volatile lately.
  
Buy 100 shares of stock @ $94.25
Buy 2 September 95 puts @ $13.80 

Notice that the trade exhibits the same familiar V-shape risk-reward profile as a standard straddle.  It has two breakeven points on expiration day of $68.63 on the downside and $121.36 on the upside.  The movement from today (T+0, the dotted line) to expiration day (T+98, the solid line that represents the trade on the September expiration day) shows the effect of time decay, the loss due to the passage of time for the puts in the position.

So why would you do this trade rather than a standard straddle? One reason would be if you already have a position in the underlying stock that you don't want to sell. There are others, of course. Let's take a look at a standard versus a synthetic straddle and see what some of the other advantages (and disadvantages) are between the two trades.

Comparing Standard and Synthetic Straddles

A standard long straddle consists of simultaneously buying a put option and a call option with the same strike price in the same expiration month.  For the long synthetic straddle, you purchase 2 put options for every 100 shares of the underlying stock.  Below is a Graphic Analysis comparing a standard straddle to the same synthetic straddle we just looked at in XYZ Corp.  Note that we used the at-the-money (ATM) options with a $95 strike price for both of the trades.

The risk graphs of the two trades are nearly identical.  In fact they are so close it may be hard for you to see that there are actually two different trades superimposed on each other, the standard long straddle in red and the synthetic long straddle in blue. 

One disadvantage of using the synthetic straddle is that it requires more capital since you have to buy the stock.  The synthetic straddle cost $12,191 (Using 100% margin on the stock) versus only $2,682 for the standard straddle. The long stock position is why it is called synthetic, and buying the stock always costs more than buying the options.

But there are also advantages to using a synthetic straddle. The first is that since you own the stock with the synthetic straddle, you collect dividends.  Dividends account for the slightly higher position of the synthetic in the graph above.  Another advantage is that you only risk the entire premium of one leg, rather buying two wasting assets as you do in a standard straddle.  To see the importance of this, let's look at another picture of the same Graphic Analysis, but this time with the vertical axis representing the Yield of each position rather than Profit/Loss in dollars.

Look what happens if the stock price finishes at exactly $95 on the September expiration day, the worst possible outcome for both trades. The standard straddle loses 100%. With the synthetic straddle you have just a 22% loss since you still have your position in the stock.

The Greeks: Delta, Vega and Theta

A long synthetic straddle takes advantage of the discrepancy between deltas of the long puts and the security itself, and would generally be used if you felt the stock price is going to break out in one direction or the other but you don't know which way. With a position in a stock you then buy some puts to protect the stock. You should look at the overall position deltas to determine how many puts to purchase.

A stock has a fixed delta of +1 or -1 (depending if you are long or short). So if you are long 100 shares of stock, you have +100 deltas. No matter what happens to the price of the underlying stock, its delta will remain +100. Options have variable deltas and they change in relation to movement in the underlying stock. Synthetic straddles are typically placed using at-the-money options. An ATM put options will have a delta near -50, so when you buy 2 puts for each 100 shares of stock the resulting position should be very close to delta neutral.

How changes in the underlying price affect synthetic straddles is fairly straightforward. When the stock price drops, delta increases, giving you a small profit in the puts.  When the stock price goes up delta decreases and the puts lose money, but you get a small profit on the underlying stock to offset this.  Buying puts near-the-money means a sharp move down in the underlying has a better chance of helping the overall position, driving the puts deep in-the-money.

Volatility (measured by vega) is very important when looking for trading opportunities in standard straddles, with the best candidates having the lowest implied volatility (IV) relative to its past history. But a synthetic straddle benefits more from movement in the underlying and is not as sensitive to changes in IV.  The best candidate for a synthetic straddle is a stock that has been volatile in the past, or is likely to be in the future.  But since we are buying options with one side of the trade, you cannot ignore the IV situation completely.  You would still prefer to avoid buying IV that is extremely high relative to its past history. Since the ATM options have the highest vega, that is yet another reason to buy the puts near-the-money with a synthetic straddle.

Time decay (measured by theta) is a concern with any kind of straddle, including synthetic straddles, although time decay is less in the synthetic. You may wonder why it theta is smaller in the synthetic, when both positions require you to purchase two options.  It is not because one leg of the synthetic is stock (which has a theta of zero).

Without going into detail, the difference in theta between calls and puts depends on the cost of carry for the underlying stock. When the cost of carry for the stock is positive (the dividend yield is less than the interest rate) theta for a call is higher than a put with the same strike and expiration date. So the theta of the second put you but for the synthetic is less than theta from the call you buy in a standard straddle (for most optionable stocks today, and certainly for all the stocks that move enough to consider placing a straddle).

You are still buying options, however, so just as in a standard straddle it is still best to look at puts that do not expire for at least 60 days, preferably for 90 days or more.

Synthetic straddles are optimally placed when the trader believes a major move is going to occur.  Putting it all together, you should buy longer-term ATM put options with long synthetic straddles.  Buying at-the-money puts will give you the best result if the stock price drops.  Since this price movement might not happen right away, you want to use longer term options to give yourself plenty of time.  The longer term options also have a higher vega and smaller theta, maximizing your gain when IV increases and minimizing any loss due to time.

Making Adjustments

The biggest advantage of the synthetic long straddle is that it provides the trader with many opportunities to make adjustments as the market moves up or down, giving you the ability to profit regardless of market direction.  Once you enter a synthetic straddle, you can only lose the amount paid for the options side of the trade.  Even if the stock drops all the way down to zero, the long puts more than offset the loss in the stock.

If the stock makes a big move in a short time, it may be worthwhile to close out part of your position.  If the stock makes a quick move up, you can capture the remaining time value in the puts.  If the stock price moves down quickly, close out your put position at a profit. You can always buy more puts closer to the new underlying price and start again.

The key to making adjustments with the synthetic straddle is that the long stock always has a delta of 1 so you can adjust the trade back to delta neutral to lock in profits.  As the stock moves higher, the overall delta position will become positive.  As the stock moves lower, the overall delta position will become negative.  When this occurs, you can buy or sell stock to bring the trade back to delta neutral.  You can also buy or sell options. They do not have to be the same put options you opened the trade with.  You can make adjustments with a different strike or expiration month in both calls and puts.

While the synthetic straddle gives a trader the ability to make adjustments along the way, it is usually best not to do this until the trade is at least 30 deltas over or under zero.  How and when to make adjustments is always the biggest question and I would like to give you a simple rule.  This is not very scientific, but a good rule of thumb is that you should look to make adjustments when the overall delta is plus or minus more than 100 for each 100 share x 2 puts straddle.

However, just because the delta gets out of place by more than 100 doesn't always mean you should adjust.  For example, if a stock has a big price drop on negative news, causing delta to become extremely negative, you would only want to get rid of the negative delta if you expected the stock to turn around.  If you expect a continued decline, you are better off leaving the delta negative.  When making adjustments, you may want to incorporate the view you have for the stock and the market overall.

While the long synthetic straddle is normally a good strategy to use when you want to make adjustments, there is always the possibility that the stock price just may bounce around the original price without really going anywhere.  Even a synthetic straddle loses a little each day due to time decay on the puts, and only after the underlying makes a solid move in one direction can you make adjustments.  If the stock price remains in the same range for a long period of time, you can always roll the puts out to a farther month. 

As with any trade, one adjustment that you should always look at is simply closing the entire position. You can also leg out of the losing side and let the good side run, leaving you with either a long stock or long put position.  If the trend begins to falter, you can then close the remaining side for a profit, or look to readjust to the current market. 

One important thing to remember is that you don't want to hold the puts all the way until expiration.  If you still want to be in a synthetic straddle with a month left until expiration, close the long puts and roll them into a farther-out month with more time left.  The biggest advantage to using synthetic straddles is that even if things when things aren't working out, you still do not lose much capital.

One final thing to keep in mind is that when you adjust to delta neutral, all, else being equal, it is better to sell (either stock or options) rather than buy, if possible.  The more you buy the more capital the trade is going to require.  Making adjustments can let you create a profitable trade with little risk, and can enable you to get consistent profits.  This style of trading is rarely going to give you a home run, but the risk-to-reward ratio is very good.

Conclusion

Stockholders and short sellers alike can use synthetic straddles to completely change the risk/reward of a directional stock position.  If you are no longer happy with the view your stock position implies, or fear a sharp move in the opposite direction may be possible, the synthetic straddle allows you to change to a delta neutral position and gives you the ability to make money if the stock price moves in either direction.

Whatever your market assumptions are, you can create a position that will profit if you are right; and protect you in the event you are wrong.  You can build a bullish or bearish bias into the synthetic straddle just by adjusting the number of puts you are using. 

The adjustments that can be made to synthetic straddles make this type of trading fun, and having fun when you are trading can be nearly as important as making money.  As with all combination strategies, the option trader must analyze the risk graph closely to determine if the trade is feasible or not.  This type of position should be studied and practiced before actually placing it, but you will find it is well worth the effort to learn. As you become more proficient, you will find the profitable adjustments that can be done make this a very flexible and attractive strategy.