## 17 August 2009

### Synthetic Equivalence - What It Ain't.

I've posted a bit on synthetic equivalence a few time in recent months, both here on the blog and on some message boards. Some people have a few trouble with this concept even when proven mathematically, so thought I would talk a bit on what it is and what it isn't.

For what it is, I'll leave the explaining to Charles Cottle, from The Hidden Reality:

There is the raw (actual)position consisting of the exact options that contribute to an overall strategy. For every raw position there are a number of alternative positions called synthetic positions (synthetics). A synthetic position has the same risk profile as its raw position and achieves the same objectives.

What that means is that the risk profile of an option strategy can be duplicated via different combinations of options and/or stocks. A few examples:

A covered call is a synthetic naked short put
A married put is a synthetic long call
A collar is a synthetic vertical spread

There are dozens of combinations that can duplicate the risk profile of different combinations.

The problem seems to be that some people feel that the positions must me identical in every respect to be synthetically equivalent. The most common objection is that of different capital/margin requirements. - that if one position needed more money to trade than the other, they can't be synthetically equivalent.

One fellow didn't feel that a long call/short corresponding put wasn't synthetically equivalent to long stock, because he could get the option combo on margin, whereas the stock required the full investment of the value of the stock. That *may* be true for some traders. But it is certainly not true for others due to different margin rules, haircuts or whatever.

The logical extrapolation of that logic would be that stock bought on margin is not the same as stock bought for cash.

In any case, capital/margin requirements are not relevant to synthetic equivalence. What is relevant, it the risk profile... the payoff diagram adjusted for cost of carry and dividends if necessary.

Capital/Margin is not considered when looking at synthetic equivalence.

#### 4 comments:

ormuz said...

Another aspect that is usually left uncovered in concept of syntetical equivalence is profile of early expiration risk.

Most options traded are american ones, and we should not forget that about 10 percent of such options expire early.

Wayne said...

Possible early exercise is a consideration when implementing and managing a trade, for sure.

For example a deep ITM covered call with an imminent dividend has the risk of early exercise, whereas the corresponding WOTM short put does not.

But they are still synthetically equivalent.

ormuz said...

They aren't synthetically equivalent since you can't synchronize liquidation of other legs in case of early exercising one of leg in your position.

For example, short put has risk of early exercise, and if your put is exercises, you have to exercise your call in equivalent covered call position. And thing is,that you can't do it in a few seconds, period between these two events can be counted in days.

This is especially true, if you are trading options on stock, trading shares of which is temporarily suspended. In this case options still can be exercised, while, for example, one leg of covered call - long stock is not trading at all.

Wayne said...

ormuz,

These things, however valid, have nothing to do with synthetic equivalence.

Cheers