Regardless of whether you’ve ever traded an option in your life, if you’ve traded in any market for any length of time, you almost certainly have run across the claims of some number of promoters, usually titled something like “Fantastic Profits in Options,” or something equally flatulent. These types of claims and promotions too frequently employ, as their “secret strategy” or “lesson of a lifetime” or some such bilge, the tactic of buying call options whose striking price is way the heck away from the underlying asset’s current price.
If some month’s crude oil futures are at $25.00/bbl, a way-out-of-themoney option, or WOOM as I always call it, might be the 31.00- or 32.00-strike call. The types of promoters I’m talking about don’t deal in WOOMs,though. No, no, they rave about WTBOOMs, options that are way-the-BLEEP-out-of-the-money, the 39.00- or 40.00-strike calls, or even higherstrikeones. Typically, they’ll “recommend” that the suck-, uh, trader buy such options with a term of six months or nine months or a year.
All right, let’s play these sleazeballs’ little game—on paper only, of course, since we really don’t want to contribute to their upkeep. Let’s crunch the numbers on a trade this type of lowlife might advocate and keep a sharp eye on the expectation of the trade throughout.Fair question. For a very good reason:it’s not enough to look at a prospective trade and say, “That’s a loser” or “That should be profitable.”More than this, we want to know how to recognize the difference between a profit opportunity and an accidental purchase of the Brooklyn Bridge, and the way to do so is to watch expectation in action.
As a side benefit of this little analysis, we will also permanently vaccinate ourselves against these types of hyped promotional viruses. Here we go. So rave the headlines in the promotional mailer or on the Internet site,both of which doubtless prattle on for quite a while, with lots and lots of exclamation points (I’m actually skimping here on the number you’re apt to see in such a promotion).
The hype hints strongly at astonishing profits to be made in anticipating political developments by buying six-month call options in crude oil with a striking price of 40.00. Well, well, WTBOOM,boomity, boom. As I write this on May 17, 2002, the market in NYMEX December 2002 crude oil, ticker symbol CLZ, settled at 26.15 and December crude oil’s 6-month SV is 32.4%. Table 3.3 shows the pertinent data for the expectation of this trade, evaluated according to the lognormal model.
One fact, not included in the table, about the CLZ call options tonight is that they’re right near their theoretical fair value until we get into WTBOOM-land. The other way to say this is that the calls’ IVs are about equal to the SV of CLZ itself. Evidently, option traders in crude oil don’t seem to share our hypester’s optimism right now. The WOOM and WTBOOM calls are a tad pricier than they should theoretically be, so if we purchase these,we’ll be paying up a notch—not necessarily a sin, but hardly advantageous either.
We’ll assume that we can buy the CLZ 40 calls with just 1 point of slippage, so we’ll be paying 0.11, or 11 points, $110.00 plus a $15.00 commission,thus $125.00 including our unavoidable contest risk.The main portion of our expectation in this trade is easy to compute. If CLZ is not above $40.00 when the December options expire, we’ll lose our entire purchase price and contest risk, so this portion of the expectation in this trade is perfectly clear. As Table 3.3 shows, the delta of the CLZ 40 call is 0.042 tonight.
Hmmm. Only about 42 times out of 1,000 will the market theoretically be above 40.00 when our options expire? We’ll lose all our capital and costs in this trade roughly 95.8% of the time? Geez, that’s terrible. I don’t know about you, but I want a second opinion on this deal! We can easily get one, too, but to do so we must digress for a moment.
The Bad News Only Gets Worse:In fact, the situation is actually worse than this for the option buyer in this
or any purchase of WTBOOM call options. The delta figures of WTBOOM call options are over-optimistic, proportionally too high. Why so? The unmodified normal distribution curve is perfectly symmetric, but we aren’t
using that curve, are we? We aren’t, and the lognormal curve we are using is not symmetric; it has a measurable bias to the right-hand side, the “upside” in terms of markets.