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The BMW Method
Taking Advantage of the Option Price Disconnect

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By mklein9
December 3, 2007

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As described in various previous posts, I have been running a real-money experiment with LEAPS in my portfolio that I think takes advantage of what I see as a disconnect between option price modeling and reality, at least over the longer term. As many discussions here and on other boards have noted, option prices are modeled using the base assumption that their price movements are random and log-normally distributed, or some close relative to that. Any intrinsic value of the underlying stock is probably not usually taken into account. So according to random walk math, the probability "envelope" of the option prices expands over time as the square root of time.

Maybe really short term option prices follow some random or random-ish behavior (although I have my doubts on that as well) but over the long term I am entirely convinced they don't, and there is plenty of empirical evidence to support that. The reason is that the underlying stock of a well-chosen growing company, over the long term, roughly follows an exponential curve (compounded growth). Given long enough, an exponential curve *always* beats a square root curve - always, always. Given enough time. That was the observation I made and then I tried to figure out a way to take advantage of it.

My approach was simple, thanks to the availability of LEAPS. I selected big, stable companies with long histories and good future prospects, and currently undervalued. I would then look for the longest possible LEAPS calls available, and looked for a relatively low implied volatility on those (15% more or less). I felt that that was an undervalued option. After two years the option envelope is at 15% * sqrt(2) = 21% but the stock, if compounding at 15%, is at a gain of 1.15 * 1.15 = 32% (ignoring the effects of the risk-free rate and dividends which "tilt" the option pricing envelope up and down respectively). Now if I could select stocks that had a good chance of increasing by more than 32% in two years, I could take advantage of the silliness of the square-root shape of the option pricing model. I'd be buying options based on the assumption of a square-root increase in underlying stock price, but counting on the stock to show an exponential increase. Over a 2-3 year period I figured this race should mostly come out with the exponentials winning.

Because of high expected volatility of the options and the likely outcome that some of the options would increase a lot in price and some fall to almost worthless, the underlying approach is one of constructing a basket of options and only caring about the average return of the basket. The basket would get added to slowly over time as options become attractive to buy or sold off as they near expiration.

I started this experiment in September 2005 and have been slowly buying LEAPS as the stocks became pretty easy to identify. These are pretty much all selected with a simple BMW Method application but IV stocks are excellent candidates as well.

Since it is only 2 months before the expiration of the Jan08 LEAPS, this update will be the last to track their prices and all Jan08 positions will be considered closed as of 11/30/2007.

Here is a summary of each of the LEAPS positions (basis includes my transaction fees):

 Stock LEAPS Strike@Exp Buy Date Basis Price Return � � � � � � � ABT ABTAI 45@Jan08 11/15/2005 4.02 13 223% AVP AVPAF 30@Jan08 9/23/2005 3.81 12.2 220% BMY BMYAE 25@Jan08 9/25/2005 2.51 4.75 89% BUD BUDAI 45@Jan08 3/13/2006 4.11 8 95% KO KOAI 45@Jan08 12/20/2005 3.11 18.33 489% PFE PFEAE 25@Jan08 10/20/2005 3.02 0.4 -87% PFE PFEAF 30@Jan08 10/7/2005 1.89 0.05 -97% WMT WMTAX 52.50@Jan08 3/2/2006 3.5 0.25 -93% JNJ VJNAN 70@Jan09 3/2/2007 3.21 4.5 40% MMM VMUAN 70@Jan09 7/25/2006 10.08 18.2 81% WMT VWTAK 55@Jan09 4/26/2007 3.26 2.75 -16%

The average return is 94% right now, or 36% annualized given 26 months since the beginning of the experiment.

The returns are highly volatile. Back in April 2007 the average return was 88% then fell precipitously to 36% at the end of August, recovering steadily to its current level of 94%. The first 6 months of the experiment had the portfolio showing a loss. A chart of the portfolio's performance since the beginning in Sept. 2005 is here: http://invest.kleinnet.com/bmw1/LEAPS.gif.

The option prices greatly magnify the movement of the underlying stock. The volatility of each individual LEAPS is immense. I think it only makes sense to build a basket over time, buying when the LEAPS themselves are cheap in addition to the underlying stocks being cheap. Those days, possibly, may be over for a while as volatility measures are again relatively normal against historical standards.

It is again interesting to note, I think, the bifurcation of returns. By now all the Jan2008 LEAPS have either gone into major positive return territory or major negative return territory. There is no Jan08 LEAPS that has wallowed anywhere near break even. Not even close. All are either below -87%, or 89% and up.

Half the overall return of the portfolio comes from one LEAPS: KOAI. If I assume a 0% return (break even) for KOAI, the overall portfolio return drops from 94% to 48%. But KOAI was selected fair and square like all the others, and took over a year to move above break even. We'll see how the Jan09 LEAPS perform over the next year. And hopefully find some Jan10 LEAPS that are dirt cheap too -).

My groundrules for buying LEAPS are:

1) First, identify a good stock -- large, solid company, selling for a low price due to a probable short-term problem that is likely to resolve within the option's life (2 years).

2) Consider buying a LEAPS option only if the implied volatility is low; roughly 15% has been my guideline but around 20% has also worked out well. I believe this gives me a double level of discount: cheap stock, and a cheap way to buy it.

3) Buy the longest expiration LEAPS call possible to give the hoped-for stock price correction to occur and overwhelm the square-root-of-time shape of the volatility envelope that the option pricing model is based on

4) Buy a slightly out-of-the-money strike price. My simple rule of thumb has been to buy about 2x the number of shares I would have bought for the stock itself, but pay a total of only about 1/4 as much, i.e. the option price is selling at around 1/10 or 1/8 of the current stock price. That has tended to translate to a strike price about 10% above the current stock price. More or less.

5) Hold the option until near expiration, maybe 3-6 months before, and then sell it, to avoid the majority of the time decay.

Another result of the learning work I did to figure this out is that I refuse to sell options, especially when I think the market is good for buying them. For the same reason that I think the option pricing model is silly but lets me buy underpriced options, I think selling options would put me at too high a risk of being on the wrong side of an outlier event -- you know, those "25 sigma" events that happen every couple of years. There are likely going to be occasional individual exceptions to this rule, but I'm not going out of my way to find them, as I think the likelihood of safe option selling is lower than safe option buying, all other things held constant.

-Mike