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Friday, 13 November 2009

A Sideways Look At ... Economic Models

Economic Models on the Psy-Fi Blog

Almost inevitably economic models keep on appearing on this blog, an annoying but inevitable occurrence. These models underpin so much of what happens in finance that it’s impossible to ignore them. In fact they’re now so important that the models themselves can change markets, although usually only because they've screwed everything up again.

All models are simplifications of the real-world – a model that described everything would have to be bigger than the universe, so until we can figure out how to start consuming other dimensions we’ll have to make do with approximations. Of course, when we do break out of this cosmos we’ll end up with a bunch of do-gooders complaining about the effects of dimensional change as vast chunks of the space-time continuum break off and strand the pan-dimensional equivalent of the polar bear.

Anyway, here’s a brief summary of the Psy-Fi Blog’s thoughts on economic models ...

Newton’s Financial Crisis: The Limits of Quantification

It all started nearly three centuries ago when a bewigged philosopher-scholar named Issac Newton went and invented calculus in order to model planetary motion. Soon if you weren’t using maths to do your modelling other physicists were calling you a sissy. It wasn’t long before generating mathematical models became the gold standard for everyone and that’s where the trouble started. The next thing you know we have the Efficient Markets Hypothesis:
“The Efficient Market Hypothesis is one of the great blights of modern investment analysis. What it says is that markets price efficiently, all the time. So all known information is already in the price of stocks or bonds or whatever which means that unless you know something that’s not in the public domain you can’t, on average, profit by trading. The corollary of this is that you can develop mathematical models to describe – and predict – market movements.

Charlie Munger, the octogenarian billionaire Vice-Chair of Berkshire Hathaway has a name for the Efficient Market Hypothesis. He calls it “bonkers”.” >> Read More
Markowitz’s Portfolio Theory and the Efficient Frontier

In investment circles math was, for a very long time, something done by rocket scientists. In the wake of the Second World War the climb and climb of the stockmarket led many to think that there was something inevitable about the perpetual rise of stocks. Then the seventies hit, the Arabs decided that the oil in their countries was, well, theirs and the markets went into a dizzying tailspin.

Belatedly recognising the existence of risk, and casting about for some way of managing it, fund managers happened upon some twenty year old research which equated risk with volatility and meant that everything could be boiled down to a few simple numbers. The Efficient Market Hypothesis and models that go with it were born.
“What Markowitz did was put a number on risk to allow it to be managed. The first danger for investors is in not understanding the importance of Portfolio Theory for risk management of stockmarket investments. The second is in believing that it can explain everything. People don’t get programmed linearly – we come with randomness built in, not as an optional extra. Thank goodness.” >> Read More
Of course, no one understood the downside of what rapidly turned into a quest for spurious precision.

Alpha and Beta – Beware Gift Bearing Greeks

Markowitz’s ideas led eventually to something called the Capital Asset Pricing Model (CAPM). CAPM assumes that returns from a market lie on a Bell Curve or, in the jargon, are distributed normally. Sometimes you get very bad returns, sometimes you get very good returns but mainly you get something in the middle. Only this turns out to be dead wrong.
“The markets can behave normally for long periods of time but when they go wrong it can be spectacular. Long Term Capital Management (LTCM) a hedge fund run by Nobel laureates found this out to their cost in 1998 when their normally distributed model collapsed when they were unable to sell assets at any price due to the collapse in the Russian bond market. Only concerted government intervention prevented a massive financial crisis.” >> Read More
The search for spurious mathematical precision was to lead to all sorts of problems.

Holes in Black Scholes

The LTCM Noble Laureates had made the basic assumption that the world they knew was the only world that there was to know and constructed their models accordingly. Unfortunately a human lifetime isn’t time enough to get to know even a fraction of the possibilities. What’s odd, not to say worrying, is that the inefficient Black-Scholes option pricing model that underpinned LTCM (which itself depends on the distribution of returns on a Bell Curve, aka the Gaussian distribution) is still in use today.
“Peer under the covers of Black-Scholes and you find our old friend, the Gaussian distribution, assuming that extreme events are impossible instead of just rather unlikely. The unlikely happens all the time in markets, usually because of human behavioural biases which kick in at extreme moments and lead to sustained overshoots in valuations and liquidity.” >> Read More
Of course, any hope that the lessons of the past would be learned by the financiers of the future was forlorn.

Risky Bankers Need Swiss Cheese Not VaR

Underpinning many of the risk models being used by financial institutions is something called Value at Risk (VaR) which attempts to measure the likelihood of an unlikely event under everyday conditions. Unfortunately, like many models, it’s open to abuse if the people overseeing it don’t know what they’re doing or are too distracted by large bonuses to bother. Guess what?
“To summarise a vast range of problems in simple terms, the people running the banks, the credit rating agencies and the regulatory bodies didn’t have a clue about the limitations of the risk management models they were all using. They were all looking at the same data and using the same models. And all drawing the same conclusions. Which were wrong. >> Read More
Which eventually led to the almost inevitable problems the world started reluctantly facing up to in late 2007.

Quibbles with Quants

The rise of all of these quantitative models, based on the spurious precision accompanying analogies with Isaac Newton’s models of gravitation, have resulted in continual market failures culminating in the crash of 2007-2008, which was by far the most spectacular implosion of math based financial models yet.
“The sheer nuttiness of the credit rating agencies changing their risk models purely because a quantitative model existed that indicated that the risk of these securities collapsing like dominoes in the event of isolated defaults was remote is still hard to believe. It’s not that the models didn’t indicate exactly that. ... You’ve got to ask – did none of the overpaid executives running the world’s financial corporations and regulators actually stop to wonder whether someone might have, just possibly, failed to predict everything that might happen in the real world? Did none of them look at the collapse of LTCM and wonder?” >> Read More
The Death of Homo economicus

Dig hard enough into these models and you’ll uncover the idea of the perfectly rational human being, weighing up decisions in the light of perfect information. Yet the brain is, at best, an imperfect rationalising machine making all sorts of shortcuts in an increasingly desperate attempt to make sense of our information saturated world. In 1979 Kahneman and Tversky came up with a different model, behavioural finance, based on human psychology which suggest that ...
“...investors – were more risk adverse when it came to protecting a profit than they were in trying to recover a loss.

So, in effect, if something went wrong with a stock they were holding the theory stated that they would be more likely to sell it if they were in profit than if they were making a loss. This is, indeed, illogical since it’s the same company with the same prospects. If investors were truly rational they would decide whether to sell or not based on the current information – stock history is irrelevant to whether a stock is currently a good investment or not. Yet the evidence suggests that this decision is, in fact, heavily biased by their personal history and, therefore, that the decision is not really a rational one.” >> Read More
Exit homo economicus, leaving a mathematical vacuum just dying to be filled.

The Special Theory of Behavioural Economics


The death of Homo economicus is required by behavioural finance, which looks at how intelligent human beings behave irrationally for the most rational of reasons. Increasingly it looks like the Efficient Markets Hypothesis is just what happens when we don’t all have some particular bee in our collective bonnets.
“A hypothesis, then, is that behavioural biases effect investors all of the time but while there’s a reasonable balance between different types of investors in the market any deviation in valuation is corrected, leading to a market that exhibits the hallmarks of a standard efficient model. However, this is only correct at the gross level – look under the covers and you’ll find a whole bunch of behavioural biases twitching away but doing so fairly randomly, cancelling each other out.” >> Read More
To Infinity and Beyond

If rational man is dead and the rational models they go with him are similarly extinct you’d hope that these adventures in stupidity are over. Unfortunately the quest for spurious precision through mathematical models that can be programmed to make institutions easy money isn’t likely to end any time soon. Whether any of these models can successfully integrate human behaviour is questionable but, on the other hand, perhaps we should hope that they don’t.

At least we can be reasonably sure that people will continue to do exactly what these models expect until they don't. That's the thing about people, we're unpredictable. Which, fortunately, is still about the only predictable thing about us.

7 comments:

  1. It is so easy to be critical and cynical when a blogger doesn't allow facts to get in the way of a good rant. It's tiring to to read blather of this sort. Thank you, anyway, for not saying risk managers' models assume returns are normally distributed - a great fiction. Still, permit me to point out that the statement, "Value at Risk (VaR) which attempts to measure the likelihood of an extreme event, like an unexpected market crash" is not true. Value at Risk does not attempt to measure a market crash. I hope that language is clear. Value at risk attempts to measure the level of loss corresponding to an infrequent event in an ordinary market environment (say something that could be expected to occur a couple of times a year). I hope the distinction between "infrequent event in an ordinary market environment" and "an extreme event, like an unexpected market crash" is not too subtle. You may still curse an umbrella for failing to protect you from the damage caused by a falling piano, of course.

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  2. It's a fair point, loose language to be sure, and I shall adjust accordingly. However, it's just an intro to the underlying article which states:

    "Its aim is to predict the probability that a portfolio of investments will rise or fall by more than a certain amount. So a one-day 5% VaR of $1 million means that you’d expect the portfolio to rise or fall by $1 million once in twenty days (i.e. 5% of the time), all things being equal (which they never are, of course). Such an event is called a VaR break."

    I love the piano/umbrella analogy, just perfect.

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  3. good argument, it is true every coin has two sides, let alont these financial models, although some model, for example, black scholes model, has its shortcomings, it does help lots of investors to understand the financial world in a simple way.

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  4. Hi abiao

    I certainly don’t mean to imply that these models have no value – on the contrary they’re very valuable if they’re used properly. By and large the underlying flaw is that the models don’t account for the possibility of a catastrophe. And usually the problem isn’t really the limitations of the models, it’s the way people interact with them (and ignore the limitations).

    See also: http://www.nytimes.com/2009/01/04/magazine/04risk-t.html?pagewanted=1&_r=1

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  5. Increasingly it looks like the Efficient Markets Hypothesis is just what happens when we don’t all have some particular bee in our collective bonnets.

    This is a beautiful sentence. This gets it exactly right (in my view, to be sure).

    I think you're wrong though (and that you miss the power of your own insight) with the subsequent line that concedes that the market is efficient "in a gross sense." It's not that there are micro inefficiencies in a market that in a macro sense is efficient. It's the overall market price that is often wildly wrong.

    The beauty of the quoted language is that it shows us the path back to efficiency. The market really does want to be efficient. There is a pull toward efficiency. The problem is with the darn humans (isn't it always the case?).

    The rational way to invest is to always engage in long-term timing. After all, if you stay at the same stock allocation despite big price changes, you are letting your risk level swing around like crazy. For what purpose?

    If we all invested rationally, each upward move in valuations would bring sales of stocks (because the long-term value proposition had worsened). Those sales would bring the price back down to where it belonged. The market is naturally efficient. The market price is naturally self-regulating.

    So why do I say that the market price is often nutso?

    There are often heavy pressures causing investors not to invest rationally. For the past 30 years, the Stock Sellling Industry (which would be happy if no one ever invested in anything other than stocks) has been pushing Buy-and-Hold down our throats 24/7. Buy-and-Hold is the opposite of Rational Investing. Buy-and-Hold is ignoring price rather than always being sure to take it into account when setting one's allocation.

    With the popularity of Buy-and-Hold, all price discipline goes out the window. That means a huge bull market. And that means a price crash to pull things back to fair value (the market collapses if we don't eventually get back to reasonable price levels). The heavy promotion of Buy-and-Hold is the true cause of today's economic crisis.

    The models we use to understand stock investing matter. Big time. We should all want the market to be efficient. To achieve that goal, we all need to be willing to abandon Buy-and-Hold. There can never be an efficient market so long as many believe in Buy-and-Hold. Market timing is required for the market to remain efficient for long.

    Rob

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