Feb

9

It seems that to be a trader these days you must have a PhD in Math. Actually how much math does a trader need?

I've been struggling with math since childhood, and I'm taking statistics personal classes right now. Recently Victor told me that I would only have had to count Galton's way and that would be enough. It seems to be easy to immerse yourself in deep math and forget about what the markets really are.

I know this lecture is from last year, but Soros has a good point when saying that the statistic models available fail to consider the role of uncertainty. When you are too much leveraged and the event goes too many standard deviations, you know you’re in trouble. Take a look at:

George Soros at MIT and

Quantitative Trading, an excellent blog on quants by Ernest Chan. His latest post:

This Quebec pension fund lost some $25 billion due to non-bank asset-backed commercial paper (ABCP). Their Value-at-Risk (VaR) model did not take into account liquidity risk. As usual, the quants got the blame. But can someone tell me a better way to value risk than to run historical simulations? Can we really build risk models on disasters we have not seen before and cannot imagine will happen?

The replies to the post were most illuminating:

quarterback said…

"Nassim Taleb's ”Fooled by Randomness” is a must read. Simply we don't live in a Gaussian world.”

Paul Teetor said…

"The NY Times recently quoted Taleb as saying, “VaR is like an airbag that works all the time, except when you have an accident.” I think that’s a perfect characterization.Can we prepare for what we have not seen? The folks in the insurance business have faced this problem for centuries. Some actuaries use Extreme Value Theory, and I’ve often wondered if the finance world needs to look more closely at that. Are the quants to blame for VaR’s short-comings? Sort of. I ran the VaR reports for previous employer — who got wiped out. In retrospect, I should have been telling everyone, “These numbers do not mean what you think they mean.” That was my error.”

Bill Rafter replies:

Dr RafterYou do not need an advanced degree in mathematics to be a successful trader. What you need firstly is the ability to think for yourself and secondly the ability to do research in a scientific manner. Regarding statistics, what you need to know is that one event is not significant, and that your highest return will not be your average return. Those are common mistakes of novices.

Most “quants” are employed in “risk” work. That is, they are given tasks such as, “assuming you have a certain profit, how do you protect it?” Or, “given a certain alpha, how do you make it portable?” Perhaps the best-known quant made his money by finding an anomaly in the contract specs of a certain futures market and then exploiting that. Those points suggest that your efforts at profitable trading should not be concentrated in the risk area. Instead they should be directed towards generating that profit or alpha that the supervisors assume is inherently there.

Let me pose a scenario: Suppose you had perfect knowledge that the broad market was going to rise, what stocks would you buy? The standard philosophy is that you would buy the ones with the highest beta, because they should go up the most. For the most part you would be disappointed, because those with the highest beta (i.e. past beta) would be the most volatile, as past volatility is equated with subsequent bearish performance. Don’t take my word for it; there are lots of academic articles saying the same thing.

Also — and this is important — would you rather trade an efficient market or an inefficient one? Obviously the latter, so do not waste your time with the efficient ones. Oh, but the risk guys love the efficient markets. Yeah, but the risk guys do not make money.

Let me give you our experience. We screen for risk early in our selection process, and never look at it again. We never use stops, which we feel simply provide certainty in losses. Except in the odd times when we are in bills, we never buy one asset because we cannot predict one asset well. On the contrary, our success rate in predicting baskets of assets is better, so we stick to that. Of course they are baskets where the early screening was on a risk-adjusted basis, but with no other attention being paid to risk. I am not suggesting that ours is the only way or the best way; only that it is a profitable method that does not hold the risk mavens up as gods.

Dr. Rafter is President of Mathematical Investment Decisions, a quantitative research consultancy


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5 Comments so far

  1. david higgs on February 9, 2009 2:54 am

    here's some math: market down 40% will it take 4.4 years just to break even?!? could be a question, could be an answer?

  2. Nightly (Value) Investment Links#77 | Simoleon Sense on February 9, 2009 5:11 pm

    […] 4. Quant Models From Newton Lichen - Via Daily Speculations […]

  3. Chris Monoki on February 9, 2009 8:02 pm

    The previous post from Mr. Rafter is excellent, and I thank him for putting things into perspective.

    I’ve been in the buisness for twenty year (40 years old now), and I’m still learning. At GWU, I was troubled by statistics, so much so I was required to repeat the course, and again. Furtunately, and with several revolutions of the sun, I finally have decent grasp. Statistics certainly has it place.

    But I’m also reminded by Benoit Mandelbrot, Nassim Taleb and others that Gaussian and Bachelier statistics, while useful, are inherrently flawed. To quote from “The (Mis)Behavior of Market” (Mandelbrot, 2004): …”the whole ediface hung together — provided you assume Bachelier and his latter-day disciples are correct. Variance and standard deviation are good proxies for risk, as Markowitz posited — provided the bell curve correctly describes how prices move. Sharpe’s beta and cost-of-capital estimates make sense — provided Markowitz is right and, in turn, Bachelier is right. And Black-Scholes is right — again, provided you assume the bull curve is relevant and that prices move continuously. Taken together, this intellectual edifice is an extraordinary testament to human ingenuity. But the whole is no stronger than its weakest member”.

    Since David Li’s 2002 paper on Gaussian Copula application to value default correlation in securitized products, particularly CDOs, there’s been an explosion of such assets as their pricing became supposedly easy and thus making a market of what once was discrete transactions. Copula stats follw in line, much like Bachelier et. al. as Mandelbrot points out.

    But then houses started to use ‘proprietary’ models, each coming up with a non-standard value of such assets. So be it; that is the nature of the competitiveness of our industry — the edge. But each had different assumptions of default probability and default correlation, and as Mandelbrot pointed out later in the same book (and followed up with Taleb’s “Fooled by Randomness” and “The Black Swan”), events of an event, catastrophic risks, i.e. fat-tail risk, are not correctly valued in such models.

    This, among other things, has lead to a freeze in the markets that use such statistics to value such risks. The fact is that no one no longer deems these valuations credible. And without that, they are not tradeable (Gentlemen, correct me or add to this posit if I’m off path).

    So, for me, back to square one. The question is: where did the markets go wrong? Is it in application or is it in theory? Markets are inherrently inefficient (tell FASB that, please with FAS 133), but add to that an inefficient tabulation of asset values and you get an explosion, in my view.

    To me, in the world’s end, correlation is 1.0. And no model today can value that.

    Keep pressing,
    Chris Monoki

  4. douglas roberts dimick on February 10, 2009 1:25 am

    Reflexivity and Quantitative Relativity

    At least during my views of this site, perhaps no article may be found as subtly provoking as Mr. Newton’s query of math and the markets. Thank you.

    Here in China, I only now viewed Soros at MIT. His “take you down the abstractions” is reflective of Plato’s cave allegory of the Theory of Knowledge. Moreover, I find that his evolution of thought parallels the Theory of Quantitative Relativity (or QR): see http://seekingalpha.com/article/48689-a-paradigm-shift-for-hedge-funds.

    The Theory of Reflexivity, relative to cognitive and participating components of electronic exchange markets, invites one to align both with the potentially comparative function(s) of math – relative to natural law, such as rules-based programmatics. Nevertheless, Soros emphatically affirms, at the onset, that the idea of predicting the markets is “nonsense” because of that participatory phenomenon (what he says is) “endemic” within the market exchange process.

    His overview of Market Fundamentalism also amplifies the need for rules-based engineering, citing political (e.g., a la Thatcher and Reagan) and macro (e.g., Paulson and Greenspan) aspects, wherefrom markets are sanctioned and regulated. With this indication, we may come to understand how current modeling may fail to transpose rules-based structural accountancies when designing program trading and portfolio management systems. There is programmatic detachment – what the mathematic contingent labels as “anomalies” post de facto – at all phases (from education to hedge fund modeling); this failure to apportion and then integrate both (natural and human) elements is then replicated during the process of analyzing and distinguishing market situation, strategy, and execution.

    I too have found that the current paradigm is flawed in its reliance on math via correlation of that human (or participating) factor a la modeling of market quantifications. Causes for reoccurring anomalies – systemic or otherwise, which are epitomized by (and recounted by Soros as) “the bubbles” – are attributed to (closed-loop constituted) deviations. In contrast, with what we may term to be a new paradigm, those supposed anomalies are considered to be nominal attributions of the natural (or cognitive, rules-based) dynamics of a market exchange system.

    Accordingly, be it with Reflexivity or Quantitative Relativity, we may conclude that those reoccurring anomalies are statistically memorialized dynamics of market exchanges. For purposes of objectification, these occurrences are nominal functions, so attributed to rules-based parametrics – yes, that can be reduced (at least in theory) to varying approaches of systematic processing, such as with sequence and combination logic formulations.

    In this context, we may conclude that the existing (or old) paradigm is systemically flawed – as these few months tell us so. To date, since its youthful, nearly thirty-year existence (such as originating with VN’s programs), quantitative perceptions as a commercial endeavor in program trading and portfolio management have operated with either incomplete or inversed schematics of the core-circuitry operatives of market exchange systems involving financial instruments.

    Thus, my October 2007 offering as to “how much math”:

    ”… a paradigm shift in program emphasis from determinative statistical and mathematical analyses to their integration [is] based on prescribed (or rule-based) energy convergence and equivocation formulations. Consider a reported finding by two MIT theorists; their research concluded that optimized programs had not failed during recently publicized (quant fund) losses but simply did not factor in non-programmed corresponding market (sell-off) anomalies. Is that deduction actually evidencing that quantitative frameworks require inductive integration?

    … [Although] quantitative programs model prospective strategies, market exchanges represent behavioral transference and, consequently, are objectified by indicators and functions localizing the status of neural (i.e., psychological) profiles and networks. In summary, quantified particulars of any market exchange – as a human endeavor – are, by definition, correlative to the generalities of relative mass and velocity of position, trending, and environment; whereby, practical application then becomes strategic modeling of symbiotic placement and concordance.

    dr

  5. Newton Linchen on February 10, 2009 8:12 pm

    Thank you for all your thoughts. I surely learned a lot from them (some of them still makes me wonder, gazing, about how much more I have to learn (or learn again) to achieve profits in the markets).

    These Math/Trading issue goes deeper than we are prone to think. It lies in the heart of the trading experience: models give some tangibility, a haven, even though we know markets (and life) are not fully rational and predictable.

    As Chair says, quoting Wiswell, “a bad system is better than no system”.

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