CHAPTER
12

Synthetic Securities

In This Chapter

• Making custom combinations
• Different ways to earn the same pay
• The costs and risks of working with synthetics
• Strategies with synthetics

Options are contracts based on prices. They aren’t securities on an underlying item itself. They are based on the value of the underlying asset. If you have access to the value of the asset, do you need to own the underlying asset, too? This is the question behind options and other derivatives.

If we reduce assets to their payouts, then we can approach them in a different way. We can find ways to replicate the value, possibly at a lower cost.

A synthetic security is a package of investments created to have the same payoff as an actual security or asset. They are used to simplify trading and to manage risk. In many cases, they come with a lower cost than the underlying asset they are replicating. On occasion, the market presents an arbitrage opportunity where a synthetic can be used to help generate a profit.

The advantage of synthetics is they can help you find more ways to make money for the same amount of risk. There are two disadvantages. The first is that the commissions on the trades can reduce or even eliminate profits. The second is if they are not set up correctly, you can take on more risk than you realize and blow up your account. Think of these as advanced strategies.

Setting Up Synthetics

A synthetic security is a combination of two or more financial instruments that have the same risk and the same payoff as a third instrument. It is a way to copy the financial characteristics of a security.

Synthetics can be created to mimic the underlying or the derivatives on it.

When thinking about synthetic securities, think about the payoffs. The handy payoff diagrams shown later in this chapter can be used to show what you’re trying to replicate, and then give you clues about what the replication would look like.

A Synthetic Stock

If you own a common stock, then you have a financial asset that makes money if the business increases in value and one that loses money if the business decreases in value. The increased value will come from an increase in the stock price and the payment of a dividend.

The call and put should have the same strike price and expiration. If you have the call and the put, then you have one asset that makes money if the underlying increases in value and one that loses money if the underlying decreases. If both are at-the-money, then the premium should be the same, at least in a perfect world. At any other point, one option will be in the money and one will be out.

Of course, with a long synthetic, you lose the return from any dividend the company might pay.

Here’s an example: you buy a 30 January call for $2.97 and sell a 30 January put for $4.15. This is close to, but not precisely, the same as the underlying’s price of $29.39, and it generates a net credit position of $1.18.

If you are the shareholder and the underlying asset is at $35 at expiration, then you’d have a profit of $35 – $29.39 = $5.61. If you owned the synthetic, you’d be able to exercise the call for a profit of $35.00 – $30.00 = $5.00, plus the net credit from the premium, for a profit of $6.18. The put holder will let it expire, as it’s worthless.

Now, if expiration rolls around and the underlying asset is at $25, the shareholder would lose $29.39 – $25.00 = $4.39. If you were short the put, it would be assigned and you’d have to buy the stock at $30.00, for a loss of $30.00 – $25.00 = $5.00. The call would be worthless. But the premium received would reduce the loss to $5.00 – $1.18 = $3.82.

This example, which uses real numbers for General Motors Company (NYSE: GM) stock and options on the day I wrote this, shows that the synthetic stock gives a return that’s mighty similar to the return on the stock. The returns on the long call and short put position are slightly higher, which you would expect because the options position has slightly higher transactions costs. The following graph shows what’s going on:

The payoff of a put and a call.

As long as the premiums offset each other, then the money involved in establishing the position goes to 0 and there’s a nice, straight line. In theory, a dollar of increase in underlying price leads to a dollar of increase in the position value; in practice, that will be affected by changes in time value and volatility.

That’s the same payoff as owning the long stock.

Let’s look at being short a stock. In this situation, you have a contract that decreases in value if the stock increases in price. The contract also increases in value if the stock decreases.

Short Synthetic Stock

To have a synthetic short stock, you need to:

• Be short a call option
• Be long a put option

The call and put should have the same strike price and expiration.

What happens if you are short a share of the stock? You make money if the price falls and lose it if the price increases. And what if you have a short call and a long put? You have the same risk (which is substantial, by the way, because there is no theoretical limit on how high a stock can go) and the same return as the short position.

Here’s how that looks, using numbers for Facebook (NYSE: FB). You sell a 97.50 September call for $10.15 and buy a 97.50 September put for $12.20. This is close to, but not precisely, the same as the company’s price of $97.17, and it costs a net credit position of $10.15 – $12.20 = –$2.05.

If the stock is at $80 at expiration, then you’d have a profit of $97.17 – $80.00 = $17.17 if you had shorted the stock. If you owned the synthetic, you’d exercise the put, buy the stock at $80, then sell it to the put writer at $97.50, for a profit of $797.50 – $80.00 = $17.50. Subtract the $2.05 paid in premium, and your total is $15.45. The call would expire because it is worthless.

Now, if expiration rolls around and the stock is at $125, the short position would lose $125.00 – $97.17 = $27.83. The call holder would exercise, so you would have to buy stock at $125.00 and sell it at $97.50, for a loss of $27.50, less the $2.05 net premium, or $25.45. You’d let the long put expire, as it is way out-of-the-money.

The payoff diagram looks like this:

The payoff of the synthetic short stock position.

As with the long position, the premiums should offset each other. A dollar of decrease in underlying price leads to a dollar of increase in the position value.

The payoff of the actual looks the same. For every dollar the underlying price falls, the payoff increases by a dollar.

Synthetic Options

Synthetic options are designed using put-call parity. That’s the equation that says:

Stock price = strike price + call premium – put premium

The put-call parity equation can be rearranged like so:

Call premium = put premium + stock price – strike price

Or:

Put premium = strike price – call price + put premium

There are two refinements we need to throw in. The first is the dividend. If the stock pays a dividend, that has to be subtracted from the option holder’s return, as the option holder won’t receive it. The person who is long the stock will; if it’s you, that can reduce your cost of holding.

The second is interest. There is interest lost on cash while the position is being carried, and it costs money to carry positions. If it looks like the synthetic option returns a teensy bit more or less than the authentic position, make adjustments for interest and dividends to see if that’s still the case.

But there’s another way to think about it. A call is a contract that pays off if the asset increases in price. It does pays nothing if the asset goes down.

Long Synthetic Call

A long synthetic call position involves:

• Purchasing the underlying asset
• Purchasing an at-the-money put option on the underlying

This trade is a version of a married put, and it’s a common strategy used to protect a stock position on the downside. Here, I’ll discuss it in comparison to a long call so you can understand the payoff structure a little better.

With the long put, you’re insuring against the risk of loss on the stock while still retaining the upside potential, as you would with a call. The synthetic long call position pays off if the asset increases in price but pays nothing if the asset goes down. Nifty, huh?

Now, if you want some profit from the asset falling, you’d buy a put that was out-of-the-money. Here, we’re looking only at upside.

The following graph shows what’s going on:

The payoff of the long call.

The purchase of the asset means it will go up a dollar for every dollar increase in price, and the purchase of an at-the-money put means your loss is really limited if the underlying asset goes down in price.

If you remember from Chapter 7, that’s the same payoff from being long a call: pure upside, really limited downside.

Short Synthetic Call

A short synthetic call position involves:

• Shorting the underlying asset
• Selling a put on the underlying

With a short call, you collect the premium and then profit if the underlying asset goes down in price. That’s exactly what happens here. This is a bearish position.

You can see how it works here:

The payoff of the short call.

If the underlying asset falls in price, then the profit will increase accordingly. And if the asset increases, you’ll lose money—the same as you would with a short call.

The writer of a call receives the premium; in exchange, she loses money if the asset increases in price, dollar for dollar. That’s the same payoff from being short a call: the benefit is all from a decline in underlying price.

A Synthetic Put

A put gives you the right, but not the obligation, to sell an underlying asset at a particular price on or before a particular date. The synthetic has the same benefits.

Long Synthetic Put

A long synthetic put consists of:

• A long-call option
• A short-stock position

A put is a position that benefits from a decline in the stock price but does not benefit from price appreciation. A short stock position is one that’s really costly if the stock price increases in value. The synthetic put protects against the upside risk while retaining the benefit of a price decline.

The payoff of the long synthetic put.

If the underlying asset falls in price, then the profit will increase accordingly. Meanwhile, the ownership of the call reduces the potential loss from the asset increasing in price.

With an actual long put, of course, the buyer of the put receives makes money if the asset decreases in price. In theory, this is dollar for dollar. That’s why the two charts match. In practice, though, you’ll see variations in the rate of price change.

Short Synthetic Put

A short synthetic put looks like this:

• A long stock position
• A short call position

A short put generates income for the writer, and it loses money if the asset falls in price. The upside is limited to the amount of the premium paid.

With the synthetic short put, the same thing happens. The writer receives the premium for the short call. It loses money if the asset falls in price. The upside is limited to the amount of the premium paid because if the asset increases in price, the option will be exercised and the underlying asset will be called away.

The payoff of the short call and long stock.

If the underlying asset falls in price, the profit will fall accordingly. Meanwhile, the sale of the call means the position’s gain will be limited if the asset increases in price.

The short put is profitable at the strike price plus the premium received.

As with the long call or regular short put position, the short synthetic put pays off if the underlying asset increases in price.

The Role of Interest

When comparing the costs of a synthetic versus the costs of the standard position, you have to consider the costs of interest. This comes in three forms:

• The opportunity cost on money committed to the position
• The cost of margin in the options market
• The cost of margin in the underlying market

In many cases, the cost of carrying the underlying asset will be less than the cost of carrying options because options are considered to have more risk than the underlying. The difference in rates will vary at different times, but it might be substantial enough to make the synthetic the better alternative.

A Reminder About Volatility

The discussions in this chapter have looked at the effects of price changes on the synthetic positions. The options prices might not move as expected in the real world because the more volatile the underlying asset, the more opportunities there might be for an option to be exercised. That makes the option on a volatile asset more valuable, and it might affect the decision to go with a synthetic or with the straight option. As a result, the premium received from writing the one type of option might be more valuable than the premium paid to purchase a different option.

Synthetics and Moneyness

For a synthetic stock, the strike and the expiration date of the two options should be the same. As long as that’s in place, the position will perform as the stock would—at least in a perfect world. In the real world, options prices will often vary from perfection.

For synthetic options, though, you get to choose the strike price. What should it be? An option that’s at-the-money will give the most protection on the underlying, but it will also cost the most. And, the closer an option is to being in the money, the more likely it is to be exercised, thus affecting the position.

Hence, a synthetic should be placed only if you have a good sense of the volatility and other risks of the underlying asset.

What’s the Downside?

There are two problems with synthetics. The first is they might not be available because of market conditions. The second is they can be expensive.

In addition to the payoff, you need to consider the costs of carrying the trade, the commissions involved in placing it, and the tax structure that will apply. (See Chapter 18 for more information on taxes.) There are plenty of strategies that look good on paper but don’t work in real life, at least not for all traders.

Why and How to Use Synthetics

After making it to this point in the chapter, you might have one big question: why? Why do all this rearranging to create synthetics when the financial markets have done a perfectly good job of creating actual options and other financial instruments? What’s the point?

And, in fact, most traders never use synthetics because they have no need to. Others use them only when interest rates make them favorable.

Synthetics come in handy for a few different situations, such as for arbitrage or to manage risks at a lower cost.

Can’t Borrow Shares to Short

To sell a stock short, you have to borrow the shares. Brokers do this regularly, but sometimes, there is no stock to borrow—especially if it’s the kind of overheated stock that everyone is trying to short. This may be because so much has already been sold short or because many of the shareholders do not allow the shares in their accounts to be loaned.

With a synthetic short stock, a trader can mimic the payoff of a short position without having to borrow the shares. This might have a lower cost and be easier to establish than a traditional short position for a trader who is able to large and manage complex margin requirements. The broker will need to see a large capital position in the account before approving this trade.

No Exchange-Traded Product

The financial markets are a wonder of creativity and disruption. The different participants have the amazing ability to develop new products traders want and need. In almost every situation, the option you want already exists, no synthetic needed.

Every now and again, though, you might want to trade an option on an underlying asset even though the precise option you want has not yet been created. Or maybe the underlying asset doesn’t exist in physical form because you’re looking at options on a metric rather than an asset. This doesn’t happen often, but sometimes it crops up. In that situation, you can use a synthetic to create the payoff pattern you want. (For an interesting example of this, check out the movie The Big Short, or the book of the same title by Michael Lewis, about the 2008 financial crisis. Many traders had reason to believe housing and mortgage markets were overheated, but they had to put a lot of effort into figuring out how to trade on that information.)

Greater Efficiency on Some Hedges

The standard academic valuation discussion of options assumes there are no taxes or transactions costs, and options are infinitely divisible. If you need 15.2 options to hedge a position, then you will be able to buy 15.2 options in this perfect world.

In the real world, options trade in lots of 100. There are commissions, carrying costs, and taxes to consider. When these factors are thrown into the mix, it might turn out that a synthetic is a cheaper, more efficient way to carry out a desired trade. In most cases, however, it will be far more expensive.