A Canadian on Wall Street

I like how that title implies that risk has a positive or negative connotation. I’ve seen people talk about “positive” risk, which is a corruption of the original meaning, but I can’t think of a better word that indicates the improbability of being one of the high-flyer Buffets or Tudor Jones’s of the world. This is all by way of saying that after Sacha’s positive review of Jeff Rosenthal’s book on probability, I’ve been thinking about how the profit and success of the totality of people invested in the market, from the extremely short term to the extremely long term, probably fits the good ol’ Gaussian distribution, meaning that on average there are a lot of people that have middling returns, some that are doing well and some poorly, and some people being taken to the cleaners (my friend, he of RIM shorting fame is a case in point) while others have more money than the GDPs of most medium-sized countries. Although I’m not a believer in efficient market theory and have my doubts about any form of mathematical modelling being signficantly better at outperforming, I’m pretty sure this distribution holds, which means that for all the scrabbling and statistical analysis and financial document reading we all do, on the whole most of us aren’t going to do all that well, optimistic though we may be. Or am I wrong to assume such a distribution? I don’t know, and I think I might do some more research into this, but it seems that if somehow enough investors were savvy enough to shift the Gaussian’s middle to the right (this is apparently called negative skew), that this would not be an equilibrium condition, that the underlying set of investors would modify their strategies accordingly and the effectiveness of the investing that allowed the skew to exist would stop and the distribution would become symmetric again. This is all just hunch and I don’t know if it’s supported by any research in finance, but it does make me wonder if an individual investor can actively “displace” someone else who is also attempting to succeed. That is, if I go about my day thinking I will do very well in the market, and I am able to develop “skills” (arguable that this is a skilled game, still) to do well, to balance that out, due to the zero-sum nature of investing, the other side of all my trades will have negative effects. Is that the mechanism that ensures such a distribution? Without people blowing up, would it be possible for Buffett to exist? Or put another way, does Bill Gates have a fortune because a million other companies went out of business?

I probably sound pretty naive with respect to the underlying math, but it’s something I wanted to get down so I could explore it more later. I don’t think it is incompatible with the concept of skill in investing, but if it were true, it would imply that it’s not really possible to actively work towards being Buffett — Buffett’s success is in good part the winning of a lottery ticket, as he’s been quick to say (although he meant in terms of a genetic lottery, where he gained the propensity for “investment skill” through birth). In his essay The Super-Investors of Graham and Dodd-ville, he puts forth the idea that the sheer number of successes among the top investors is due to their common value philosophy, but is it also not possible that at the time when all these people were building their fortunes, that value philosophy worked? If Buffett and co did not exist, and we looked at a different timeframe, would there be a growth investor out there writing an essay about how the top investors in the world all seemed to search for growth? How does the success of a small subset of investors in a relatively short span of time (less than a century) indicate the worth of their philosophy? Were there value investors throughout the ages, Buffetts of their time? In the longer scheme of things, say over a thousand years or ten thousand, will his methodology stand up? I suspect that the mid-century success of Buffett may be more anomalous than he thinks, and less attributable to his modification of Graham’s philosophy. In my opinion, it was likely a lucky confluence of that strategy and the environment that have made the majority of his fortune. One factor that comes to mind is the rush of money that has come into the stock markets since the time he started, making the earliest investors the most successful, but can we honestly use the past character of the market to predict the future movement of the market? “The market always goes up in the long run?” Says who? Not to implicitly doomsay, but I can think of a number of markets that no longer exist, or exist in a decrepit form. Why is this homey aphorism considered to be a truism now? It’s something to think about. As William Goldman once wrote, “Nobody knows anything.”

I’m reading The Predictors, after wolfing down The Eudaemonic Pie, Thomas Bass’s earlier work on Doyne Farmer and Norman Packard’s excursions into money-making schemes. The latter is his earlier book about the pair’s scheme at winning roulette, which entailed using physical models and shoe computers to improve the odds of winning, while the former is about the apparently successful use of their chaos theory work to make money in the financial markets. Both books are pretty breezy reading, although if you know a little about either field Bass does a pretty good layman’s job of touching all the bases. He even makes mention of the Mandelbrotian usage of fractals and the fat tail stuff that folks like NN Taleb love, which I wasn’t expecting. There are some choice disses of technical analysis, likening chartists to astrologists and entrail-readers, and a quote from Farmer referring to that time as like the Middle Ages, with said “astrologists” co-existing with the patrician, institutionalized view, akin to the old establishment viewing the world as flat, who hold strong to efficient market theory. I’ll have to quote some of it when I get the time.

Not that long ago, I investigated getting a degree in financial mathematics, even though as a Vancouver-based investor, I’m nowhere near the major equity and option markets of New York, London and Chicago. Browsing the list of hedge fund jobs, I had daydreams of joining one of these firms, living some fast-paced life with long hours and big money. However, with my computer science and physics background coupled with my abhorrence of the MBA and wealth management programs offered (which seemed more about salesmanship than skillful investment), it seemed like financial mathematics would be more up my alley. After auditing a few courses at SFU in Risk Management, I realized ultimately that the MFin and MA in Risk Management programs, as Emanuel Derman points out in his book My Life as a Quant, are chockful of new immigrants and foreign-born students with educations emphasizing mathematics. In fact, the more glamorous jobs of portfolio manager were often plucked not from the ranks of the risk managers (the actuaries of finance) but from those same MBAs and wealth management programs I didn’t find appealing, the ability to gladhand and socialize often paramount — like most things in life. The few exceptions to this hierarchy include the “quant hedge fund” epitomized by Renaissance Technologies, whose founder, the ex-SUNY Stony Brook professor Jim Simons, has quite vocally derided the poor math skills of North American students. He tends to hire foreigners, instead.

In the end, I decided I didn’t really like any of those options, and so, in my haphazard way, continue to work towards some vaguely stated goal of being an independent investor, like the folks at Contra the Heard. One of the founders of Contra is a software designer, which I find unsurprising, somehow. Why are so many people in the software industry drawn to the markets? Is it a belief in trading systems and algorithmic methodologies that is most easily tested against the markets, with the various APIs and tracked statistics available making it probably one of the most comprehensive and consistently updated data sets available? The ex-physics majors often prefer the options and bond markets, with more quantitative factors that can be used to create mathematical models; physicists are much more numerate than the average computer science person and they take solace from that fact, thinking that it gives them an edge. (They may be right.)

In my earlier investigations, I had looked around to see if there were hedge funds in Vancouver; the majority of Canadian hedge funds are obviously situated near Bay Street. There are a few here, like Asset Logics, KCS Funds and BluMont Capital (not strictly based here, but likely their resource arm is). That first fund lists Ian St. Martin as a manager, one of the successful investors at Marketocracy, his Optimal Risk Reward fund increasing its NAV about 7 times since May 2001 (convenient, no? It’s an excellent return, but top-performing funds that were started after September 11th haven’t been around long enough to determine long term performance, in my opinion). His bio reads: “After a successful career in software consulting, research, and development, Mr. St. Martin has turned his analytical eye to the US equity markets, spending the last five years developing a system-based approach to trading.” Is it the analysis aspect of software design that crosses over with market analysis? The hodge-podge of business requirements and more technically-minded introspection required when creating software probably maps quite nicely to investing in equities. I come from a software background, career-wise, and I know that my own personality is well-suited to design and analysis; many of the other people I’ve worked with have taken an inordinate interest in investing, too. Just something to think about, I guess.

Funny, telling quote from Derman’s book My Life as a Quant:

Although options theory originated in the world of stocks, it is exploited more widely in the fixed-income universe. Stocks (at least at first glance) lack mathematical detail–if you own a share of stock you are guaranteed nothing; all you really know is that its price may go up or down. In contrast, fixed-income securities such as bonds are ornate mechanisms that promise to spin off future periodic payments of interest and a final return of principal. This specification of detail makes fixed income a much more numerate business than equities, and one much more amenable to mathematical analysis. Every fixed-income security–bonds, mortgages, convertible bonds, and swaps, to name only a few–has a value that it depends on, and is therefore conveniently viewed as a derivative of the market’s underlying interest rates. Interest-rate derivatives are naturally attractive products for corporations who, as part of their normal business, must borrow money by issuing bonds whose value changes when interest or exchange rates fluctuate. It is much more challenging to create realistic models of the movement of interest rates, which change in more complex ways than stock prices; interest-rate modeling has thus been the mother of invention in the theory of derivatives for the past twenty years. It is an area in which quants are ubiquitous.

In contrast, quants have been a rarer presence in the equity world. There, most investors are concerned with which stock to buy, a problem on which the advanced mathematics of derivatives can shed little light. Fixed income and equities have fundamentally different foci. When you walk around a frenetic fixed-income trading floor, you hear people shouting out numbers–yields and spreads–over the hoot-and-holler; on a busy equities floor, you mostly hear people shouting company names. Fixed-income trading requires a better grasp of technology and quantitative methods than equities trading. A trader friend of mine summed it up succinctly when, after I commented to him that the fixed-income traders I knew seemed smarter than the equity traders, he replied that “that’s because there’s no competitive edge to being smart in the equities business.” (ed: emphasis mine)

Or as Woody Allen recalled in his script for Match Point, “it’s better to be lucky than to be good.”

Here’s a succinct statement, attribute it to E. Derman:

If you can diversify over a large
enough M-neutral portfolio of stocks so
that their accumulated unavoidable risk
cancels, then this M-neutral portfolio of
zero volatility must earn the risk-free rate
r. The same must therefore be true of each
M-neutral element of the portfolio. This
leads to the result that:

(u - r) = β(uM - r)

This is the result of the capital asset
pricing model or arbitrage pricing theory:
in a world of rational investors, the excess
return you can expect from buying
a stock is its β times the expected return
of its hedgeable factor. Put differently, you
can only expect to be rewarded for the
unavoidable factor risk of each stock,
since all other risk can be eliminated by
diversification.

Notice that assumption: “if you can diversify over a large enough…” Not only is the rationalist methodology employed to derive this a little shaky, there’s still that additional caveat that you have to diversify over a “large enough…portfolio”. I’m sure there’s some bit I don’t know, where at a certain level of diversification you decrease the “risk” to a certain livable amount, so you don’t have to be perfectly diversified, but yeah, still seems like a lot of conditionals.

It’s a tough thing, trying to make money this way. It’s even tougher with the overlay of being conscious of the possibility of pure randomness, and the possibility that skill doesn’t exist. The hedge fund rebuttal guy described here doesn’t seem to really know that, though, he’ll tell you that the top hedge fund guys are just goddamn masters of their game. Modern celebrity kind of hews to the weird logic of hedge funds, too, with certain specific people taking off — would hedge fund guy claim that Britney Spears was a skillful singer that didn’t somehow get swept along in the fickle interest of the public? How would we know? The idea that luck (in the form of randomness) outruns skill every day of the week is something that more people have to be aware of.

“Liquid” is essentially synonymous with “popular” — possibly why I’m sure there exist secretive, quant-run hedge funds that focus on using their models for liquid securities on the markets for illiquid versions (cf. Emanuel Derman). They can get a “fair value” and determine what kind of arbitrage exists in markets that are unpopular, where there are not enough people to guarantee that every instrument is fairly priced in an un-tradable time frame.

Starting to curry to Nassim Nicholas Taleb’s writing again. I had skimmed his book something like six or eight months back but failed to appreciate how closely aligned his world view is with mine. Or the fact that so many other historical figures have come to the same conclusion: you can’t predict the future using the past. It just occurred to me wonder what NNT thinks about Santayana: “Those who cannot remember the past are condemned to repeat it.” Of course, history is never perfectly repeated, but we can develop lore and instinct from these past interactions, which is something I think NNT does agree with — empirical (experiential) observations are where we should be looking. So I guess instead of simply “you can’t predict the future using the past,” we should add to that “but we can keep an eye on it.” Predictability implies future knowledge and that is something we don’t have, but certainly there are particular arrangements of preceding factors that may (BUT NOT DEFINITIVELY) give rise to similar future results.

I like quantitative finance for the admission that probability is a huge factor in markets, which is something completely missing from the “campfire story” tenets of “technical” trading. I do have to heed NNT’s view that the Gaussian probability distribution probably is not the best way to understand a market that has numerous blow-ups (and if the Mandelbrotian fractal power law distribution or whatever is more applicable, what does that say about the size of some possible future blow-up? We ain’t seen nothing yet…?). Is there any way to realistically account for these kinds of things? Taleb would buy huge numbers of OTM options (calls I think? Maybe both sides) with the idea that the view rare events that put him in the money were less rare than people thought, although it’s not clear to me how that strategy worked out — talk of that is conspicuously hard to find.