## Honest: Equivalent Positions are Equivalent

Hi Mark,

I've been thinking about the equivalence of some option strategies, and how to determine which position would be better.

Take for instance a put debit spread:
Sell XYZ Jan 50 Put

Sell XYZ Jan 50 Call

If both the above have the same profit & loss potential, how do you evaluate which is the better position? With the debit spread, time decay would chip away at it, while the credit spread would increase in value.

NK

***

You are trying to turn something very simple into something that is more complex.

1)If the positions are equivalent, neither one is better. Time decay is the same for each spread.

They provide, by definition, equal profit/loss pictures. That 'equal profits' takes into considerations dividends, if any, and interest costs – which make a different when interest rates are high. What is not included are trading costs.

2) One is better than the other – when it is priced out of line. That does happen on occasion, but not frequently.

One is better than the other if trading costs are reduced (think naked put vs. covered call).

One is better than the other if it is easier to exit the spread – if you elect not to hold to expiration (again naked put much better than covered call).

Look at your example. If you buy the put spread, your best result (XYZ < 50) makes the put spread worth 10. If you sell the call spread, your best result occurs when XYZ < 50, and the spread is zero. Thus, each makes the maximum profit in the same price range.

Similarly, XYZ > 60 gives you the maximum loss. The put spread is zero and the call spread is 10.

3) At every possible price, the sum of the two positions is 10. Thus, if you pay 10-x for the put spread, it's the same trade as selling the call spread for x.

If you pay \$7.10 for the put spread, then selling the call spread and collecting \$2.90 provides the same payoff.

Which is better? Neither. But there are reasons why selling is better than buying. If you buy the put spread, you pay interest on that cash. Today that may be essentially zero, but that's not always the case.

If you sell the call spread, you collect interest on \$290. To the extent that interest is above zero, you always want to collect the cash rather than pay. Unless the spread prices account for that difference in interest costs.

But if you can buy the put spread @ \$700 instead of \$710, then that's the better deal (assuming that the call spread can still be sold @ \$2.90. It's not a better deal if the call spread can be sold @ \$3.00).

For traders with very small accounts, selling may result in a problem if assigned prior to expiration.  Buying eliminates that risk (if assigned, just exercise) – and to prevent a margin call, buying may be preferred.

One final consideration. You buy the put spread because you are bearish. If you are correct and both options are ITM at expiration, most brokers charge two exercise/assignment fees. If you sell the call spread, both options expire worthless and the broker is paid nothing. So once again, selling is better than buying.

593