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What was your career goal in college?
My plan was to be a research physicist.
What area of physics were you interested in?
I majored in biophysics. One of the projects I spent a lot of time on was trying to develop a method for displaying three-dimensional information using a light microscope. When you look at very small structures inside of a cell, you essentially have two choices: you can look at them with an electron microscope or you can look at them with a light microscope. If you use an electron microscope, you have the advantage that it magnifies objects very well. The problem is that you don’t have any idea whether the cell you see bears any resemblance to what it looked like when it was alive because in order for the image to show up, you first have to infuse the cell with heavy metals. I don’t know about you, but I’m sure that if someone shot me and placed me in a vat of molten lead, I wouldn’t come out looking anything like what I look like. The method of observation changed the object being observed. People would write papers saying that they had found a new structure in a cell, but then it would turn out to be merely an artifact of metal crystals precipitating inside the cell.
Everyone recognized the problem with using electron microscopes. Therefore the preferable approach was to try to use light microscopes. The main problem with light microscopes, however, is that when you use the extremely high magnification needed to look at very small objects, the depth of field approaches zero. You can see one flat slice in focus and everything else is out of focus, which makes it very difficult to view three-dimensional objects. If you try to view more than one layer, all you get is mud because the out-of-focus information wins out. To circumvent this obstacle, we had to come up with programs that would filter out the out-of-focus information. It’s a very interesting mathematical problem.
Why did you gravitate away from physics?
Physics was a lot of fun as a student. Everyone wants you to provide research help. You get a chance to work on stuff you find interesting, write research papers, and show everyone how smart you are. When you are no longer a student, however, you have to support yourself in the eyes of the institution, which means writing endless grant proposals and churning out papers for the main reason of getting tenure. You end up spending 90 percent of your time not doing physics. I would be busy working on physics all day while the other people in the lab would be tearing their hair out writing grant proposals. I realized that wasn’t for me.
When did you first get interested in the market?
When I was growing up, I spent all my time thinking about math and physics. I was a bit of a twisted kid. I started looking at the options market as early as high school because I thought it was a fun way to apply the mathematics I was learning.
When did you start trading?
In my senior year of college. The thing that I liked about trading was that the only limitation you had was yourself.
What did you trade?
Stocks and stock options on the Philadelphia Stock Exchange.
How did you end up trading on the floor?
I had a friend who was a market maker. I went down to the floor with him a few times and decided it was a perfect job for me. I had always been interested in the markets and mathematics, and option trading combined the two perfectly.
How did you get the money to trade when you first started out on the floor of the exchange?
I was able to raise $80,000 from a few backers who were professional gamblers. Because I was a serious Go and backgammon player, I had met some of the world’s best backgammon and poker players. One of my investors had just won the World Series of poker and another investor was one of the most successful backgammon players in world.
What did they get for backing you?
Initially, 50 percent of my profits. I eventually bought them out. There are a lot of similarities between gambling and trading, although gambling is a bad term.
Because?
Because it implies that your results depend on luck. The people that I’m talking about look at poker or backgammon as a business, not a game of chance. There are a few things that are essential to success in both trading as well as playing gambling games as a business. First, you have to understand edge and maximize your edge. Second, you have to be able to deal with losing. For example, a world-ranked backgammon player could lose $100,000 to a total pigeon because of bad luck. If that happens, he can’t lose his head. He has to stay calm and continue to do what he is supposed to be doing. Third, you have to understand gambler’s ruin—not playing too big for your bankroll.
It might seem that if you have an edge, the way to maximize the edge is to trade as big as you can. But that’s not the case, because of risk. As a professional gambler or as a trader, you are constantly walking the line between maximizing edge and minimizing your risk of tapping out.
How do you decide what is the right balance?
There is no single right answer to that question. It depends on the individual person’s risk tolerance. Let’s say you saved up enough money to live out your life in relative comfort but without the ability to make extravagant expenditures. I come along and offer to give you ten-to-one odds on the flip of a coin. The only catch is that you have to bet your entire net worth. That bet has a tremendous edge, but it is probably a bet that you wouldn’t want to make, because the value of what you can gain, even though it is a much larger sum of money, is much less than the value of what you could lose. If, however, you are just out of college with $10,000 in savings and your whole earnings career ahead of you, you would probably want to take the same bet. As a fund manager, the correct answer as to how to maximize your edge will depend not only on your own risk characteristics, but also on your perception of the risk profiles of your investors.
How long did you trade on the floor of the Philadelphia stock exchange?
Just over five years.
How did you do?
By the time I left, I had turned my initial $80,000 stake into over $7 million after paying back my investors.
If you were doing so well, why did you leave the floor?
As I made more money, it became increasingly difficult to invest it trading only two or three stocks; it made sense to go off the floor in order to be able to diversify.
How have you been able to make such consistent gains trading options?
To make money in options, you don’t need to know what the price of the stock is going to be; all you need to know is the probability distribution [the probabilities of a stock being at different price levels at the time of the option expiration].*
[The Black-Scholes formula (or one of its variations) is the widely used equation for deriving an option’s theoretical value. An implicit assump tion in the formula is that the probabilities of prices being at different levels at the time of the option expiration can be described by a normal curve*—the highest probabilities being for prices that are close to the current level and the probabilities for any price decreasing the further above or below the market it is.]
If the Almighty came to me and said, “I won’t tell you where IBM is going to be one month from now, but you’ve been a pretty good boy, so I will give you the probability distribution,” I could do the math—and it’s not very complicated math—and tell you exactly what every option that expires on that date is worth. The problem is that the Almighty is not giving me or anyone else the probability distribution for the price of IBM a month from now.
A normal distribution would be appropriate if stock price movements were analogous to what is commonly called “the drunkard’s walk.” If you have a drunkard in a narrow corridor, and all he can do is lurch forward or backward, in order for his movements to be considered a random walk, the following criteria would have to be met:
1. He has to be equally likely to lurch forward as backward.
2. He has to lurch forward by exactly the same distance he lurches backward.
3. He has to lurch once every constant time in
terval.
Those are pretty strict requirements. Not many variables meet these conditions. Stock prices, I would argue, don’t even come close [substituting daily price changes for the drunkard’s steps].
I don’t mean to suggest that Black and Scholes made stupid assumptions; they made the only legitimate assumptions possible, not being traders themselves. In fact, they won the Nobel Prize for it. Although, to be honest, that always seemed a bit strange to me because all they used was high school mathematics. All my trading operates on the premise that the most important part is the part that Black-Scholes left out—the assumption of the probability distribution.
Why do you say with such assurance that stock prices don’t even come close to a random walk?
As one example, whether you believe in it or not, there is such a thing as technical analysis, which tries to define support and resistance levels and trends. Regardless of whether technical analysis has any validity, enough people believe in it to impact the market. For example, if people expect a stock to find support at 65, lo and behold, they’re willing to buy it at 66. That is not a random walk statement.
I’ll give you another example. Assume people get excited about tech stocks for whatever reason and start buying them. Which funds are going to have the best performance next quarter when mom-and-pop public decide where to invest their money?—the tech funds. Which funds are going to have the best inflows during the next quarter?—the tech funds. What stocks are they going to buy?—not airlines, they’re tech funds. So the tech funds will go up even more. Therefore they’re going to have better performance and get the next allocation, and so on. You have all the ingredients for a trend. Again, this is not price behavior that is consistent with a random walk assumption.
You’ve seen this pattern increasingly in the recent run-up in the U.S. stock market. The rampant uptrend has been fueled by constant inflows into the same funds that are buying the same stocks, driving these stocks to values that are ridiculous by any historical valuation. You have stocks that have reproduction values of $20 million—someone’s Web page system—trading at $1 billion or more. Are they really worth that? I don’t want to be the one to say no—after all, they are trading there—but I think ultimately you’re going to see the same thing you saw with RCA during the TV boom: a run-up to stratospheric levels and then a crash.
If these companies do their job right and the Internet is what it’s supposed to be, with every company having access to every customer, they’re going to be cutting one another’s margins to the point where very few companies will make much money. If you pick up an issue of The New Yorker, you can find twenty ads for booksellers on the Internet. It’s a classic example of an industry with perfect competition. There will be some exceptions because there are brand names and some people will do their job better than others, but can the structure support the valuations that are currently out there for the industry? I doubt it.
Why are we seeing valuations for stocks that are so far above their historical levels? Has something changed fundamentally?
Because of the repetitive cycle of price strength bringing in new buying, which causes more price strength. An important factor that has amplified the rally in the Internet stocks is the limited supply of shares in these companies. Most Internet stocks float only about 20 percent or less of their shares.
Another major development during the past five to ten years has been a substantial upward shift in the amount of money insurance companies and pension funds allocate to stock investments. As hedge fund managers, we think we are huge if we are trading one billion dollars. That is nothing compared with insurance companies and pension funds that have assets of trillions of dollars.
If I understand you correctly, your basic premise is that stock price movements are not random and therefore the assumption that prices are normally distributed, which everyone uses to determine option values, cannot be the accurate mathematical representation of the true market. Does that imply that you’ve come up with an alternative mathematical option pricing model?
Not in the sense that you are probably thinking. It’s not a matter of coming up with a one-size-fits-all model that is better than the standard Black-Scholes model. The key point is that the correct probability distribution is different for every market and every time period.
The probability distribution has to be estimated on a case-by-case basis.
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If your response to Bender’s last comment, which challenges the core premises assumed by option market participants, could best be summarized as “Huh?,” and assuming that you really care, then you should probably reread the explanation of probability distribution (footnote, page 228). In essence, Bender is saying that not only are conventional option pricing models wrong because they make the unwarranted assumption that prices are normally distributed, but the very idea that any single model could be used to estimate option prices for different markets (or stocks) is inherently wrong. Instead, it is necessary to use a different model for every market (or stock).
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How do you estimate the probability distribution?
By looking at everything from the fundamentals to technical factors to who is doing what in the market. Each stock has its own probability distribution that depends on a host of factors: Who has what position? Where did the major buyers accumulate their positions? Where are their stop-loss points? What price levels are likely to be technically significant?
Can you get that type of information reliably?
I get that information off the floors in the case of stocks and stock options and from the banks in the case of currencies.
How do you turn information like who is doing what into an alternative option pricing model?
The best example I can think of involves the gold market rather than stocks. Back in 1993, after a thirteen-year slide, gold rebounded above the psychologically critical $400 level. A lot of the commodity trading advisors [money managers in the futures markets, called CTAs for short], who are mostly trend followers, jumped in on long side of gold, assuming that the long-term downtrend had been reversed. Most of these people use models that will stop out or reverse their long positions if prices go down by a certain amount. Because of the large number of CTAs in this trade and their stop-loss style of trading, I felt that a price decline could trigger a domino-effect selling wave. I knew from following these traders in the past that their stops were largely a function of market volatility. My perception was that if the market went back down to about the $390 level, their stops would start to get triggered, beginning a chain reaction.
I didn’t want to sell the market at $405, which is where it was at the time, because there was still support at $400. I did, however, feel reasonably sure that there was almost no chance the market would trade down to $385 without setting off a huge calamity. Why? Because if the market traded to $385, you could be sure that the stops would have started to be triggered. And once the process was under way, it wasn’t going to stop at $385. Therefore, you could afford to put on an option position that lost money if gold slowly traded down to $385–$390 and just sat there because it wasn’t going to happen. Based on these expectations, I implemented a strategy that would lose if gold declined moderately and stayed there, but would make a lot of money if gold went down huge, and a little bit of money if gold prices held steady or went higher. As it turned out, Russia announced they were going to sell gold, and the market traded down gradually to $390 and then went almost immediately to $350 as each stop order kicked off the next stop order.
The Black-Scholes model doesn’t make these types of distinctions. If gold is trading at $405, it assumes that the probability that it will be trading at $360 a month from now is tremendously smaller than the probability that it will be trading at $385. What I’m saying is that under the right circumstances, it might actually be more likely that gold will be trading at $360 than at $385. If my expectations, which assume nonrandom price behavior, are correct, it will imply pr
ofit opportunities because the market is pricing options on the assumption that price movements will be random.
Could you give me a stock market example?
I’ll give you a stock index example. Last year [1998], it was my belief that stocks were trading on money inflows rather than their own intrinsic fundamentals. IBM wasn’t going up because the analysts were looking at IBM and saying, “Here’s the future earning stream and we predict the price should rise to this level.” IBM was going up because people were dumping money into the market, and managers were buying IBM and other stocks because they had to invest the money somewhere.
A market that is driven by inflows can have small corrections, but it has to then immediately recover to new highs to keep generating new money inflows. Otherwise, money inflows are likely to dry up, and the market will fall apart. Therefore, this type of market is likely to either trend higher or break sharply. There is a much smaller-than-normal chance that the market will go down 5 or 6 percent and stay there. Based on this assumption, last year I implemented an option strategy that would make a lot of money if the market went down big, make a little bit if the market went up small, and lose a small amount if the market went down small and stayed there. The market kept up its relentless move upward for the first half the year, and I made a small amount of money. Then the market had a correction and didn’t recover right away; the next stop was down 20 percent. I made an enormous amount of money on that move.
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Each of your examples has been very market specific. If I said to you that you could come up with any alternative model you wished instead of Black-Scholes, but you had to apply it to all markets, could you do any better than Black-Scholes?
Stock Market Wizards Page 26
