SELLING OPTIONS: Naked or Hedged? (06:02)

By Lawrence G. McMillan

This article was originally published in The Option Strategist Newsletter Volume 6, No. 2 on January 22, 1997. 

In this article, we're going to take a look at the strategy of selling options. Just how profitable it is, and some of the considerations for naked selling or for using credit spreads. With option premiums inflated in many markets because of increased volatility, this seems like a timely topic. I'm not specifically including covered writing in this discussion, but since a covered call write is equivalent to selling a naked put, you can apply any of the commentary that pertains to naked put selling.

Some traders think that selling options naked is the road to easy profits and that it's what the pros do. I have noticed from comments in user groups on the Internet that it is often the rather less experienced option traders who feel this way. They have probably been burned by buying options with too little time remaining and too far out of the money, so they figure that if they were to just sell those same options, they could make money as time wears away the option's value. For those of us who have been around longer, we all know that it only takes one blow-up to erase many profits, if you're not careful.

The "conventional" wisdom is that naked option selling is just too dangerous for most people, and that credit spreads are the better way to go. This is evidenced by the fact that some brokerage firms won't even allow naked index or equity option writing, and others require ridiculous amounts of equity in the account. Futures traders don't normally have these problems, since in that market, if you have the margin, you can make the trade. So, many traders have turned to credit spreads, which have limited risk and normally require much lower margin than a naked write. However, you give away a lot of profit potential with a credit spread, so is it worthwhile or have you merely hedged yourself to death — and increased your commission costs considerably — with the spread strategy instead of the naked strategy? We'll attempt to shed some light on the subject by using the Russell 2000 Index options as a means of comparison.

First and foremost, as a strategy, option writing should be conducted in a neutral manner and only in situations where implied volatility is high. It would be considered "high" if it is well above it's three-year average of daily implied volatility readings. If you have an opinion about a stock (as we did with Zitel in Position E65), then a non-neutral, one-sided position can be established. But, more often as option strategists, we are looking to capitalize on high implied volatility by using neutral strategies — selling both puts and calls (as spreads or as outright naked positions).
Here are the pertinent option quotes for the Russell 2000 on Tuesday afternoon, January 21st, with $RUT at 370:

Option        Bid     Ask
Feb 380 call   4      4-3/8
Feb 385 call   2-1/2  2-7/8
Feb 390 call   1-5/8  1-7/8
Feb 355 put    3      3-3/8
Feb 350 put    2-1/2  2-7/8
Feb 345 put    2      2-1/4
Feb 340 put    1-5/8  1-7/8
Feb 335 put    1-1/8  1-3/8
Feb 330 put    3/4    1

There are no Feb calls with higher strikes than 390. In order to compare the naked write and the spread, we'll select approximately-spaced strikes. The naked sell combo is the following:
Sell the Feb 385 call
and sell the Feb 355 put
for a credit of 5 1/2 points

The credit spread will consist of selling the 385-390 call credit spread and the 350-355 put credit spread. We will make the rather liberal assumption that this spread can be sold for 1½ credit. Thus, the same options are being sold in both cases (the Feb 385 call and the Feb 355 put), but they are unhedged in the naked write whereas they are spread in the double credit spread position.

The first thing we do is decide how we'll operate the strategy. We cannot possibly calculate an expected return for a strategy without defining how we'll operate. For example, it does no good to say we'll calculate the expected profit for holding until expiration, if we fully intend to take follow-up action at some point prior to expiration if the index makes an adverse move. Rather, these are the strategies that I would recommend for each strategy:

                    Follow-Up Strategies
Naked Write                                   Credit Spreads
Cover the calls if                        Close out the call
the upside breakeven is                    spread at 385 and
hit at 390½, and cover the                 close out the put
puts if the downside                          spread at 355.
breakeven is hit at 349½.

These are consistent with the follow-up strategies that we normally use for positions of this type, and — while some traders may be more liberal with their mental stops for a credit spread — they are typical of the follow-up strategies that most traders use.

Given these parameters, we can now calculate the probabilities of ever hitting a break-even point (not just being above or below it at February expiration). Using our empirical model, those probabilities are:

Prob of upside       Prob of downside
   action                 action
Naked combo 4.5%           3.4%
Credit spread 13.3%       12.3%

It may seem like there is too much probability of having to take action on the credit spreads, but remember that this is the probability of $RUT ever trading at 385 or 355 up until expiration. The naked combo probabilities are those of RUT ever trading at 390½ or 349½ until expiration.

The only way to accurately calculate the expected profit is once again to use an empirical model, but a more intuitive approach will give us a good estimate and will perhaps be more enlightening and instructive. So far, we know the probabilities of taking follow-up action (and by inference, the probabilities of not taking follow-up action). So, if we were to calculate the actual dollar profit or loss that we would take in each case, we could then calculate the expected profit of each strategy.

Assume that we would be taking follow-up action in two weeks (we have to pick a fixed point in order to make comparisons; in reality, an empirical model that goes through a large number of trials would take into account lots of different times when follow-up action might have to be taken). Using a simple option model, we can determine the following profits and losses:

                    Gain or loss...
        At Upside      At Downside     If No Follow-Up
                                           Needed
Nakeds   –2              –1                 +5.20
Spread  –0.94          –0.95                +1.04

The losses on the credit spread make the assumption that you would be buying the spread back at the bids and offers typical of the RUT 2000 markets (which are normally wider than an eighth of a point). All trades assume an equal commission of $6 per option.

Now, we can calculate the expected profit: the probability of each event occurring (see table, page 2) times the profit or loss of that event (above table). The resulting figures:
Expected Profit
Naked combo +$467
Credit spread +$53

Finally, we must include the investment in order to calculate a complete expected return. If we are selling the naked combo, we must allow for the $RUT index to move to 390 — our upside breakeven point. That would require margin equal to 15% of 390 (times $100), or a total of $5850. The credit spreads must both be margined, less the initial credit received, a total of $876. Dividing the above expected profits by these investments, we find:
Expected Return
Naked combo +$8.0%
Credit spread +$6.1%

Thus, the naked write is slightly better than the credit spread. I think this is fairly typical — the naked write generally has a better expected return than the credit spread. The unknown is what would happen if market volatility increased dramatically (as in a crash, perhaps). The credit spread has a maximum loss whereas the naked combo does not. Moreover, your broker may not even allow naked option writing (in which case, I would recommend switching brokers). Thus, it's not easy to say that one should always choose the naked write over the credit spreads, but most of the time the naked write is slightly better theoretically. That's why we generally use the naked write, as in Position I113, the naked RUT sell combo, which is still an attractive position to establish.

This article was originally published in The Option Strategist Newsletter Volume 6, No. 2 on January 22, 1997.