The Econophysics Blog

This blog is dedicated to exploring the application of quantiative tools from mathematics, physics, and other natural sciences to issues in finance, economics, and the social sciences. The focus of this blog will be on tools, methodology, and logic. This blog will also occasionally delve into philosophical issues surrounding quantitative finance and quantitative social science.

Sunday, October 29, 2006

Daylight Savings Time and Network Effects

is coming to an end in the US. (Other parts of the world follow similar time conventions; e.g., 'British Summer Time' (BST) in the UK.) Appropriately enough, Tim Hartford, aka 'the Undercover Economist,' in his weekend column in the Financial Times (UK) wrote about the economics of Daylight Savings Time: Undercover Economist: Think inside the box (Oct. 27, 2006).

Specifically, he wrote about what economists call (or network externalities) and what affects, if any, the twice-a-year change to our clocks has on the coordination of both economic and social behavior. One possible network externality of the DST is that one type of profession needing to wake up one hour later (or earlier) will have a feedback effect that causes people in seemingly unrelated jobs to have to coordinate their work schedules even though they have no direct reason for doing so. An example that Tim Hartford used was a financial trader or analyst on the West Coast of the US having to adjust to -- not only the East Coast time at which the NYSE operates on -- the switch caused by the start or ending of DST.

There is an additional complication caused by the fact that some parts of the US (and other countries) don't recognize DST (or its equivalent); e.g., Arizona. Also factoring in regions at the borders of time zones and large time gaps between regions in large countries (e.g., 3 hour time difference between the coasts of the continental US).

Economic research seems to indicate that there are network effects to socio-economic coordination caused by timing conventions within and between regions. The somewhat surprising finding is that -- rather than the timing conventions themselves -- it is often television schedules (which both follow and have their own peculiar timing conventions) that set our social and economic clocks.
Three economists, Daniel Hamermesh, Caitlin Knowles Myers, and Mark Pocock, have devised a way to find out how important these co-ordination effects really are. One of their tools is based on a historical relic: the fact that television schedules in the US vary by time zone. This practice originated in the 1920s, when the Eastern and Central time zones received simultaneous live radio broadcasts, the Central time zone broadcast being an hour earlier on the clock. The sparsely populated Mountain and Pacific time zones had to listen to repeats instead. For no other reason than pure tradition, prime time evening shows screen at 10pm Eastern and Pacific, 9pm Central and Mountain.


Rather depressingly, late-night talkshow host David Letterman outshines the sun in his effect on what people are doing. Push the television schedules an hour later and 5 per cent of people will be watching television later - nearly a third of those actually watching the television. But if sunset is an hour later (because the individual is at the western end of a time zone) only half of 1 per cent of people will watch later television.

That itself might not be surprising, but the effect spills over on to sleeping patterns: the television, more than the sunrise, determines when people get up in the morning. It even governs the behaviour of people who don’t watch much television, since they need to be co-ordinated with everyone else. It seems that co-ordination with other human beings is more important than official time, or even than sunlight itself.

Tuesday, October 24, 2006

China's Inefficient Securities Markets

Over the last few years, there has been a great deal of excitement and interest about China. Not surprisingly, this also extends to the world of finance and business. For good or for ill (more often than not, the later), people have dreamed about the economic prospects of investing in China.

Despite the hoopla and the enthusiasm, however, it's clear that China's financial markets have to develop further before they are can live up to lofty expectations. The Economist magazine recently had two articles that highlights the perils of expecting too much out of China's securities markets and financial system.

The first article, Imperfect markets: China's different share classes damage its own prospects, points out the fact that share prices for the same publicly traded Chinese companies are different depending on the market in which those shares (again, for the very same company) are traded. Larger or more recognizable companies tend to have higher prices outside of mainland China (in Hong Kong, etc.) than they do on domestic stock exchanges (in Shanghai and Shenzhen). Smaller companies reverse this trend: they tend to trade at a premium on domestic exchanges relative to their valuations outside of the mainland.

These distorted prices -- where what is theoretically the same thing are priced higher in one place and lower in another -- violates the Efficient Market Hypothesis (EMH). According to EMH, arbitrage should eliminate these price discrepencies in short order. The distorted pricing of Chinese stocks violate the central tenet of economic price theory: Prices should be the ideal mechanism for conveying economic information about the good, service, or asset in question. When prices don't conform to the 'one price' principle, it makes the information revelation and exchange process -- via prices -- less efficient and less useful.

So why haven't these prices been arbitraged back towards some equilibrium price? The answer, as the article suggests, is that it is difficult to arbitrage Chinese securities because of institutional limitations. (To be fair, even with the limitations, there has been a narrowing of the gap between prices for companies traded in both Hong Kong and on mainland exchanges in Shanghai or Shenzhen.)

Chinese companies tend to issue shares using separate share classes with differing rights and restrictions. That, along with the reluctance of the government to cede authority over corporate governance matters in certain key industries, create legal risks that contribute to the pricing disparities. Furthermore, until recently, very few derivatives products have been allowed; derivatives that take into account share class differences and cross-border issues would allow traders to arbitrage away many of the distortions that now exist.

Despite its title, the second Economist article that caught my interest, Profits and prophecies: Chinese companies earn higher returns than is commonly claimed, also deals with the still developing nature of investing in China. This article highlights the debate between those optimistic about China's business prospects -- a couple of World Bank economists and Ms. Hong Liang of Goldman Sachs -- versus those who are more skeptical -- Mr. Weijian Shan, an economist and private equity investor for Newbridge, and others.

The optimists point out that both returns on capital and returns on equity have risen at a more than respectable rate for Chinese companies. They also cite reasons for optimism regarding how Chinese companies are financing their business investments. One of the fears that people have for China's economy is that there exists a pile of bad or dodgy debts that may collapse one day -- bringing down with it much of China's recent economic advancements. The optimists suggest that Chinese firms are increasingly relying on internal financing (investing out of their own cashflows and retained earnings) rather than bank loans.

Skeptics, like Weijian Shan (who I have a great deal of respect for; you can read a profile of him by clicking here), point out that costs -- commodity prices, labor costs, etc. -- are rising and China doesn't have the pricing power (i.e., goods are manufactured and bought from Chinese companies because of low prices) to offset those rising costs, profit margins are falling and may continue to fall. Furthermore, the skeptics point out that the optimists are naive in thinking that whatever move away from bank financing that may exist would solve the debt/insolvency crisis that could happen at any time in the near future.

[I ignore the issue of the rather sketchy nature of economic statistics and accounting in China. The optimists are well aware of the issue and do the best they can to deal with that (e.g., they look at return on equity of companies whose shares are traded outside of China).]

Without taking sides on this debate (since both sides make meritorious arguments), I think it's safe to say that a big part of the problem is that China doesn't have fully developed securities markets. Besides lacking full-featured derivatives markets (which is not necessarily a bad thing considering the stage of economic, regulatory, and legal development China is currently in), China doesn't really even have a mature bond market -- something so basic that we in the 'West' often take it for granted: As the article points out, corporate bonds are only 4% of China's GDP while they are over a 100% of U.S. GDP.

Having fully developed securities markets (debt markets, stock markets without byzantine multiple class divisions, etc.) would make the debates about China's economy and financial system much more fruitful. Although I doubt that what I'm proposing would fully solve all the thorny problems that exist, at the very least we would able to better measure -- through more efficient pricing -- the true condition of China's economy and that would, hopefully, allow policymakers, investors, and managers to better tackle the problems that exist.

PS: A brief sidenote on some econometric issues related to the second Economist article. The article points out that the optimists believe that improvements in what economists call 'total factor productivity' (or TFP) will offset high commodity costs, rising wages, and (although the Economist article doesn't mention this) demographic risks, that affect the inputs into China's manufacturing sector. The otherwise excellent Economist article neglected to mention the skeptics' potential objections to the increasing productivity argument. Namely, productivity gains (and losses) are difficult to measure and their affects, even if they could be properly gauged, is highly uncertain. So it's not clear to me that, as the article seems to suggest, TFP gains (even if they are real) would fully offset the risks.

Saturday, October 21, 2006

Randomness & the 'Ludic Fallacy' on Numb3rs

I'm a big fan of the CBS TV show, Numb3rs, where the FBI recruits a mathematics professor (and his colleagues) to help solve crimes. Every week (it's usually shown on Friday evenings), there are some interesting bits of concepts and trivial that I find to be educational and informative.

Yesterday's episode (Oct. 21, 2006) had the following storyline: There are a series of freeway attacks in Los Angeles -- some involving rifle shots, others involving bricks or other objects thrown onto windshields. Are they random attacks or is there a particular individual (or individuals) who are deliberately carrying out the attacks?

'Charlie Epps' -- the math professor who consults with the FBI -- initially concludes that the attacks are random (a reasonable conclusion factoring in the fact that it involves Los Angeles roads) and dismisses any concern that there might be a pattern to these attacks as the hopelessly untrained musings of the mathematically challenged. 'Megan Reeves' -- one of the seemingly mathematically challenged FBI agents -- comes to a rather different conclusion. She begins to wonder out loud whether or not the attacks are "too random" to be actually random.

To his credit, Prof. Epps eventually comes to agree with Agent Reeves. The process by which Prof. Epps initially dismisses challenges to his expert opinion and then comes to a more humbler change of heart says a lot about how mathematicians, statisticians, and similar quantitative professionals have notions about randomness that are even more flawed than the common sense ideas of the mathematically challenged laymen that the pros regularly (to be fair, usually correctly) deride. I also think the storyline of the show is a great object lesson on the intellectually challenging nature of .

Prof. Epps explains his initial conclusion of random attacks by drawing an analogy to the shuffle mode on IPods. According to the Epps character on the show, the shuffle mode has an algorithm that randomizes the selection of songs that your IPod will deliver to your ears. Thus, Prof. Epps asserts, any 'pattern' you discern from what songs your IPod selects is illusory. (Both the show and this blog post will ignore the fact that such algorithms are psuedo-random, at best, and not truly random since, by definition, algorithms are deterministic.)

Agent Reeves objects by wondering whether or not the supposed non-pattern of attacks seems too random. She points out that, compared to each other, none of the attacks follow a similar m.o. (modus operandi); i.e., in terms of methodology, the attacks are never repeated and/or clustered. While that may sound like it bolsters the case for random attacks, it is actually suspicious because -- as the very beginning of the show (where Prof. Epps makes this point to a class on probability theory) points out -- truly random series of events should have some clustering and/or repeats. In fact, one way people try to counterfeit randomness is by making events seem too evenly spread out from one another.

Prof. Epps realizes this error and corrects his IPod shuffle analogy: It turns out the IPod shuffle algorithm is not an ideal (psuedo-) randomizing algorithm because it does not repeat songs already played until all the songs on the playlist have been played (so, at best, it's like a well-shuffled deck in a hand of poker). So he winds up conceding that Megan Reeves was right to think that attacks were indeed "too random" to be random.

One of the fallacies that the Prof. Epps character committed was what Nassim Nicholas Taleb has called the "Ludic Fallacy" (to my knowledge, he first coined and defined this term in his forward to Aaron Brown's The Poker Face of Wall Street). As I understand it, the Ludic Fallacy refers to the unfortunate habit of many quantitative professionals (statistics and economics professors, Wall Street traders, management consultants, government technocrats, etc.) to over-simplify the nature of randomness and chance by making mistaken analogies to games ('ludic' -- of or relating to games or play -- comes from the Latin ludus -- game or play) of chance.

One of the several reasons why the Ludic Fallacy is a fallacy is because most games of chance (with the notable exception of poker, which -- as Nassim Taleb hints at -- is more reflective of real-life "wild" randomness because that game has major strategic and tactical components to it that is mashed up with the quasi-stochastic element of a shuffled deck) have probability distributions that are too neatly defined and managed to accurately reflect the real-life 'wildness' of randomness as we experience it in the real world. For example, the predicted results of those games of chance have nice, well-defined statistical 'moments' -- like mean (or average) and variance (or standard deviation) -- that are useful in classrooms or on hedge fund prospectuses but may not be as meaningful in our day-to-day lives (as this blog, NNT, and others have pointed out in the past).

Prof. Epps' analogy to the IPod shuffle mode was a ludic fallacy since the shuffle mode is essentially the same problem as shuffling a deck of cards (an ideal shuffled playlist of music on an IPod is analogous to the 'well-shuffled deck' problem in blackjack, poker, and combinatorics). The well-meaning TV character drew a bad analogy to a game of chance -- shuffled music on an IPod -- to explain something much more complicated to be shoe-horned into the IPod shuffle story. Sadly, it's not just TV characters that fall for this fallacy; statistics classes and investment sales pitches are filled with this sort of fallacy.

I don't want to be misunderstood. I can't speak for Mr. Taleb, but I want to make it clear that drawing analogies to even the simplest of games of chance (like flipping coins or throwing dice) can be -- and, in fact, are -- good ways of explaining and exploring the nature of randomness and probability. What I object to is the indiscriminate use of these stories where the storyteller is not thoughtful or informed enough to understand the benefits and limits of using such games in 'philosophical experiments.'

My bottom-line is: It's okay to draw analogies to games of chance when dealing with randomness. Just be sure to think through the true nature -- both the potential and the limits -- of those games of chance and chance itself.

One final note ... there is another side to the coin of how even math pros make mistakes about randomness. I've spent (and the TV show spent) most of the time talking about the nature of the underlying (and, usually, unknown) probability function. The other side of the coin of randomness fallacies is the idea of magnitude or impact of making the wrong predictions. As Charlie Epps' father (ably played by Judd Hirsch) pointed out to his son -- as the math 'genius' was telling story after story about card games, lotteries, and how all that makes it unlikely that dear old dad wouldn't get shot up on the freeways -- card games, lotteries, and dice games normally don't kill you.

That's the kind of lesson -- that the real-life consequences (financially, legally, reputationally, etc.) of guessing wrong is often devastating -- that traders and investors should take to heart as well.

Sunday, October 08, 2006

Belated Post-Mortems on Amaranth

Not to beat a dead horse, but here are some interesting post-mortems on Amaranth (a hedge fund that recently 'blew up') that I ran across recently. (Note: I had little to say on the matter up to this point because: (a) I was too busy to post anything to the blog while all that was happening, and (b) as I've said before, I don't like to chase after some transient news event.)

There were a couple of stories by Heather Timmons -- one for the New York Times and the other for the International Herald Tribune -- that did a good job of disecting the whole affair. The Times article focused on the foibles of one of Amaranth's young traders who made a bad bet on natural gas prices that people ascribe as the proximate cause of the blow up.

On Nassim Nicholas Taleb's non-blog section of his website titled "Notebook," he makes some interesting comments about the Amaranth situation (including brief comments on the Zelig-like coincidence of having once been in the same office complex with them in Connecticut).

Saturday, October 07, 2006

Nickels, Steamrollers, & Hedge Funds

I just got through reading a couple of extremely interesting articles -- one from The Economist and the other from The New York Times -- on .

The Economist article (from the Buttonwood column), Instant Returns: Why investors have become addicted to the carry trade (Oct. 5, 2006), dissects a strategy -- the carry trade -- that is widely deployed, in one form or another, by hedge funds. (The article focuses on one variant involving foreign exchange, but the following analysis can be applied to other variants.)

Basically, the carry trade is a bet that volatility will be low. As the article aptly points out, it is the functional equivalent of writing (or selling) an option. Ceteris paribus, option writers benefit from low volatility while option holders (buyers) benefit from high volatility. The benefit from the carry trade is that traders can make a small but relatively steady stream of gains (analogous to the premium from selling options). Usually, these small series of positive returns add up to a sizable amount of profit for the hedge fund.

So what's the catch? (And there is always a catch.) This steady stream of returns come at the cost of exposing traders to the risk that there will be a punctuated jump of prices against their positions (i.e., catastrophic risk). So traders are gaining a steady paycheck at the expense that one day they might be completely ruined. As Buttonwood points out, the carry trade is like "picking up nickels in front of steamrollers."

Fortunately (or unfortunately, depending on your frame of mind) for hedge funds, investors in hedge funds create incentives for hedge fund traders/managers to use this type of strategy. For marketing, logistical, and financial reasons (and, I suppose, psychological reasons as well), hedge funds have an incentive "to produce nice, smooth returns that can be plugged into the models" of pension funds, funds of hedge funds, endowments, and investment advisors to wealthy individuals.

Unfortunately for hedge funds, according to the New York Times article, Weak Results Dim Hedge Funds’ Luster (Oct. 5, 2006), strategies, like the carry trade, employed by hedge funds are losing their edge in a complex and adaptive financial marketplace. Nonetheless, as the Times article points out, there doesn't seem to be a let up in the amount of investment (especially institutional) money chasing after hedge fund opportunities. This is despite the fact that the trend appears to be for as many hedge funds to be liquidated (or 'blow up' as has recently happened to Amaranth Advisors) as they are started. The S&P 500, up 8.5% as of September vs. hedge funds' collective 7.23%, seems to have been the better bet (especially after factoring in the high costs associated with investing in hedge funds).

The response to all of this by hedge fund supporters would be that their investment returns are somehow uncorrelated with more traditional asset classes (like vanilla investments in stocks and bonds). Even if that was true (which I doubt as a general matter), return correlations change over time (they are non-stationary in mathematical statistics-speak). So I find these claims, which attempt to overplay the notion of diversification, to be as dubious as the justifications for the carry trade.