Structuring Synthetics!

# Structuring Synthetics!

There are no limits to the things you can do with options. Many people are already familiar with the use of options for hedging risk and increasing leverage. Today, I want to talk about the use of options for simulating trades that usually require equity ownership and therefore demand a large use of capital. A thorough understanding of options and their characteristics can allow you to design trade structures that yield most of the benefits of stock ownership without having to own the underlying stock. For the purpose of this article, I am going to ignore the effects of the bid-ask spread, interest rates and dividends, in order to simplify the explanation. In reality, these things do matter, but if you apply these concepts to a highly liquid equity that does not pay a large dividend, they should not matter much.

A synthetic position recreates the risk/reward profile of one trade structure using different instruments. An example that may be familiar to many readers is that of a covered call and a naked put with the options placed at the same strikes. Micron Technology (MU) is currently trading at \$33.73. I can buy the stock and sell the December strike 35 call for \$1.13. My cost basis and my risk, is now \$32.60 and my maximum profit is the difference between the cost basis and the strike of the call, or, \$2.40. Alternately, I could sell a naked short put on MU at strike 35 for \$2.38. My maximum profit is the credit of \$2.38, and my risk is the strike minus the credit – in this case, \$32.62. Theoretically, this is true for any strike in any month. The risk and reward of the covered call is the same as the risk and reward of the naked put at the same strike. In reality, the numbers may differ somewhat as you can from the example, based on the bid-ask spread, the interest rate or the existence of dividends.

In order to create synthetics for other trade structures, you can use a simple equation derived from the example we just discussed. Don’t worry, you won’t need too much math. For these equations, we will use the following symbols:
Long Stock = S
Long Put = P
Long Call = C

For a short call, short put or short stock, we will just add the (-) symbol so:
Short stock = -S
Short Put = -P
Short Call = -C

We have already shown that a covered call = a short put. We can use the symbols to write it as:
S + (-C) = -P, or, S – C = -P.

We can simplify this further with a little basic algebra by adding C to both sides, giving us:
S= -P + C.

In English, this means that a long stock is equivalent to a short put plus a long call. This makes sense if you think about the risk/reward profile of long stock. The risk is its cost basis, and the potential reward is unlimited. In the synthetic version, the long call provides the unlimited upside, and the short put provides the risk from the strike price of the put (minus the credit if any) down to zero. By using that one simple equation (S = -P +C), and a little algebra, you can derive the synthetic for just about any trade you wish.

Ok, so what is all this esoteric theory good for? You can use it to replace trades that usually require the significant capital requirement of owning the underlying equity with trades consisting entirely of options. The married put provides a simple example. A married put is a strategy consisting of long equity protected by a long put. The long put increases the cost basis, but dramatically lowers the risk and leaves the unlimited potential upside intact. We can achieve the same risk/reward ratio by replacing the married put with its synthetic equivalent.

We can rearrange the basic equation,
S = -P + C to read S + P = C.

In other words, a married put is the synthetic equivalent of a long call at the same strike as the protective put. At the time I write this; Facebook (FB) is trading at \$75. A married put using a December strike 75 long put would increase the cost basis of the trade to 78.09 and reduce the risk in the trade to \$3.09. A December strike 75 call is selling for \$3.15, providing a similar upside potential reward and a similar risk. There is a slight difference which is probably attributable to differences in the bid-ask spread.

Let’s look at another options trading staple, the standard collar trade. A standard collar involves owning an equity, selling a covered call and buying a protective put where both options expire in the same month. The put reduces the risk in equity ownership. The covered call helps offset the cost of the put, but caps the upside potential of the trade. Using FB again, you can buy the equity for \$75. To limit the risk of this position, you can buy a December long put at strike 72.50 for \$1.98. You can sell a call at strike 77.50 for \$2.02. Your cost basis is now 74.96. For simplicity, let’s just call it unchanged, at \$75. The risk is now only \$2.50 – the difference between the strike of the put and the cost basis. The upside is capped at a potential profit of \$2.50 – the difference between the cost basis and the strike of the short call. However, despite the fact that the risk is far less than the risk of owning unprotected equity, the margin requirement is still the full cost of the equity in a cash account and 50% in a margin account. In other words, the risk is small but the necessary allocated capital is large. This is capital you cannot use for other trades or investments. Moreover, if you have to borrow the equity on margin, you have to pay margin interest, which is often quite high.

Instead, we can structure a synthetic equivalent that uses only options and has no underlying equity requirement. The collar is a married put (P + S) and a short call (-C). We already know that the married put is equivalent to a long call at the same strike. If we replace the married put segment of the collar with its equivalent long call, we end up with a long call at a lower strike and a short call at a higher strike. In other words, a vertical bull call spread. Specifically, we could replace the collar in the previous paragraph with a bull call with a long call at strike 72.5 and a short call at strike 77.50 for the same potential risk and reward but with a far lower capital requirement.

Alternatively, we could replace the covered call portion of the collar (S – C). In fact, we already discovered that a covered call is a synthetic of the naked short put. Replacing S – C with –P turns our collar into a bull put spread. We have a long put at strike 72.50 and a short put at strike 77.50, giving the same risk/reward profile as the collar and the bull call. In short the standard collar, the bull put, and the bull call spreads are all synthetics of one another. Because of different bid-ask spreads on either side of the chain and the possible existence of dividends, these trades may not provide identical risk/reward profiles. You can do the math to determine which structure best suits your needs.

This is not to say that there is no reason to own equities, or that is always better to use a synthetic equivalent. If the underlying equity pays a dividend, you will lose the benefit of it by substituting an options only structure. The standard collar may make more sense if you are adding it to an equity that you have owned for a while and want to protect. Further, equities do not expire, making many potential adjustments more straightforward. However, knowledge of the synthetics can expend your repertoire and make some types of trades more accessible with less capital required.

Jodie Lane
OptionsANIMAL Instructor

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