Models, random walks and the performance of fund managers
If you can look into the seeds of time
And say which grain will grow and which will not,
Speak then to me
Macbeth
A reader of charts
It was a reader of charts who accurately forecast the Great Market Crash of 1929[1]. Speaking at the Annual National Business Conference on September 5, 1929 Roger Babson observed: "Sooner or later a crash is coming, and it may be terrific". JK Gailbraith records:
"Babson was not a man who inspired confidence as a prophet in the manner of Irving Fisher or the Harvard Economic Society. As an educator, philosopher, theologian, statistician, forecaster and friend of the law of gravity he has sometimes been thought to have spread himself too thin. The methods by which he reached his conclusions were a problem. They involved a hocus pocus of lines and areas on a chart. Intuition and even mysticism played a part. Those who employed rational, objective and scientific methods failed to foretell the crash. In these matters, as so often in our culture, it is far, far better to be wrong in a respectable way than to be right for the wrong reasons. Wall St was not at a loss as what to do about Babson. It promptly and soundly denounced him."
The use of charts endures and they are widely used by technical traders to identify and confirm trends in prices. A state-of-the-art trading workstation can be expected to include tools to plot prices and volumes on a tick by tick basis and to overlay moving averages, Bollinger bands, candle stick charts and a host of other artifacts designed to divine signals from apparent noise.
Today's market players rely heavily, some would say too heavily, on forecasts based on models. Forecasters devise theoretical and empirical models and use them to price derivatives, to achieve optimal asset allocation, to quantify risk, and to derive trading signals.
The Black and Scholes model developed by Fisher, Myron Scholes and Robert Merton is used widely for options pricing, and for the discovery of implied volatility in underlying assets from a knowledge of options market prices. Simple and weighted moving average models along with more sophisticated autoregressive conditional heteroscedasticity (ARCH and GARCH) models are used to estimate volatility from an analysis of price histories. The capital asset pricing model (CAPM) finds application in portfolio management to indicate the expected or required rates of return on risky assets. Value at risk (VaR) models are used to measure market risk, to estimate capital requirements and for risk management within firms. ARMA (autoregressive moving average) models are used to find serial correlations in stationary (differenced) time series. The analysis of raw prices is employed in the search for co-integration between time series and arbitrage opportunities.
The business of model building and forecasting is big, and occupies the best scientific minds. Mathematics and statistical analysis play a key role, as does an ever broadening church of sciences, notably physics, biology, psychology, games theory and computer science.
Babson may have been on the right track after all.
Tales of the unexpected
Lest we forget that models are just models, abstractions and statistical artifacts that stand to be tested by real world experience and rare events, let us remind ourselves of some spectacular model failures.
On October 19, 1987 -- 'Black Monday' -- the Dow Jones Industrial Average plunged 508 points, to that date the largest one-day drop in history.
The Brady Commission identified the use of portfolio insurance models as a significant factor in the sharp decline in stock prices.
The brainchild of Leland and Rubenstein, Portfolio Insurance draws inspiration from the Black and Scholes model to create the idea of a synthetic option.
Jacobs[2] builds the case for how portfolio insurance and dynamic hedging exacerbated the 1987 crash and points out that dynamic hedging has played a similar role in recent periods of market volatility. The strategy, known as option replication, requires mechanistic selling as stock prices decline and buying as stock prices rise. When a large enough number of investors engage in this type of trend-following 'dynamic hedging', their trading demands can sweep markets along with them, elevating stock prices at some times and causing dramatic price drops at others. Jacobs maintains that dynamic hedging associated with some USD100bn in option-replication strategies caused the US stock market crash in 1987.
An often cited and dramatic example of model failure concerns the hedge fund, Long Term Capital Management Company (LTCM).
John Meriwether, erstwhile head of bond trading at Salomon Brothers, founded LTCM in 1993. The LTCM partners included the Nobel laureates, Robert Merton and Myron Scholes, and former regulator David Mullins.The standing of the partners allowed it to trade with the big names on equal terms. It was able to put on interest rate swaps at the market rate for no initial margin. It could borrow 100% of the value of any top-grade collateral, and with the proceeds buy more securities. These could be posted as collateral for further borrowing. In theory it could leverage itself without limit.
In LTCM's first two years of operation it produced 43% and 41% return on equity and had amassed an investment capital of USD7bn.
Meriwether is a relative-value trader. Relative value means (in theory) taking little outright market risk, since a long position in one instrument is offset by a short position in a similar instrument or its derivative. It involves betting on small price differences that are expected to converge over time. LTCM, for example, bought Italian government bonds and sold German Bund futures. It played the same arbitrage in the interest-rate swap market, betting that the spread between swap rates and the most liquid treasury bonds would narrow. It became one of the biggest players on the world's futures exchanges.
To make 40% return on capital, however, requires big bets. In theory, market risk isn't increased by increasing the stake, provided you stick to liquid instruments and don't get so big that you become the market.
Some of the big macro hedge funds had encountered the latter problem and reduced their size by giving money back to their investors. When, in the last quarter of 1997, LTCM returned USD2.7bn to investors, it was assumed to be for the same reason: a prudent reduction in its positions relative to the market. But it seems the positions weren't reduced and the leverage increased. Fatefully, LTCM got into emerging markets, including Russia. One report said Russia was 8% of its book, some USD10bn exposure.
On August 17, 1998 Russia declared a moratorium on its ruble and domestic dollar debt. Hot money, already jittery because of the Asian crisis, fled into high quality instruments. Top preference was for the most liquid US and G-10 government bonds. Spreads widened even between on and off-the-run US treasuries.
Most of LTCM's bets had been variations on the same theme, convergence between liquid treasuries and more complex instruments that commanded a credit or liquidity premium. Unfortunately convergence turned into dramatic divergence.
LTCM's counterparties began to call for more collateral to cover the divergence. On one single day, August 21, 1998, the LTCM portfolio lost USD55m. The New York Fed, on hearing concerns from its constituent banks, decided to take a look at the LTCM portfolio. They were surprised by what they saw. LTCM's total off balance sheet business ran to around one trillion dollars. The off-balance sheet contracts were mostly collateralised. Unfortunately the value of the collateral had taken a dive since the Russian default.
LTCM was too big to be allowed to go down. In the event it was bailed out to the tune of some USD3.6bn by a consortium of banks who stood to lose heavily if the edifice collapsed.
Despite the presence of Nobel laureates closely identified with option theory, it seems LTCM relied too much on theoretical market-risk models and not enough on stress-testing, gap risk and liquidity risk. There was an assumption that the portfolio was sufficiently diversified across world markets to produce low correlation. But in most markets LTCM was replicating essentially the same credit spread trade. In August and September 1998 credit spreads widened in practically every market at the same time.
Markets -- a tough nut to crack
Perhaps the most controversial model in financial markets is that formalised by Eugene F Fama. Building on work by Samuelson and others, Fama's Efficient Markets Hypothesis[3] (EMH) implies that market prices fully reflect all the information that is available to the players in the market. Future changes in prices can only be the result of 'news', which by definition is unpredictable, so the best forecast of the price on any future date is simply the price today. Put another way the price today is simply yesterday's price plus a random element. Fama's model is built on a body of research that has its roots in the work of the French mathematician, Louis Bachelier.[4]
In Théorie de la Speculation published in 1900 Bachelier observes:
"Past, present and even discounted future events are reflected in market price, but often show no apparent relation to price changescontradictory opinions concerning changes diverge so much that buyers believe in a price increase and sellers believe in a price decreaseit seems that the market, the aggregate of speculators, at a given instant can believe in neither a market rise nor a market fall since, for each quoted price, there are as many buyers as sellersclearly the price considered most likely is the true current price; if the market judged otherwise, it would quote not this price, but another price higher or lower."
Bachelier set himself the ambitious goal of postulating a formula which expresses the likelihood of a market fluctuation in a given instant. This led him into deep investigations into probability theory and the dynamics of the random movement of particles in a free space (Brownian motion).
The young mathematician came to some surprising conclusions. The probability of a rise in price at a given time is equal to the probability of a fall; the mathematical expectation of the speculator is zero. The market is 'a fair game' akin to throwing a coin.
Bachelier's work lay buried until discovered by accident in the 1950s when it sparked further research.
In terms of the modern theory of stochastics used by Fama and his colleagues, the process implied by Bachelier's fundamental principle is called a martingale. A more restricted form of the theory is called the random walk.
The efficient market hypothesis paints a picture where many rational, like minded, profit-maximising agents consume all available information to deduce current prices. These prices clear to produce equilibrium. In the absence of news, future prices fluctuate randomly.
That the model is controversial should be no surprise. What the theory implies is that the endeavours of the armies of analysts, proprietary traders and fund managers who attempt to beat the market consensus are futile.
Tests for market efficiency
The conditions sufficient for market efficiency are zero transaction costs, all information is available at no cost to all participants, and at any given time all agree on a fair value price that clears the market in a given security. In such a market the current price of a security obviously fully reflects all available information. But the above conditions are not descriptive of real markets. Fortunately these conditions are sufficient for market efficiency but not necessary. Empirical tests of EMH must therefore measure to what extent price formation is efficient, given real-world conditions.
EMH tests can be divided into three categories; weak, semi-strong and strong according to which category of information is under the spotlight. The corresponding information categories are historic prices or returns, publicly available information such as company announcements, stock splits and so forth, and finally non-public or proprietary information of a kind that might be held, for instance, by a fund manager.
Weak form tests look for serial correlations in stock market returns. If successive price movements are random and there is little or no serial correlation in price histories, this will indicate market efficiency. A substantial body of work has indicated this to be the case, so supporting EMH. For example see Fama[5], Kendall[6], Granger and Morgenstern[7], and Godfrey, Granger and Morgenstern[8].
A weak form experiment carried out by Alexander[9] is instructive. It involves testing a simple mechanical trading system characterised as follows:
If the price of a security moves up at least y%, buy and hold the security until its price moves down at least y% from the subsequent high, at which time sell and simultaneously go short. The short position is maintained until the price rises at least y% above a subsequent low, at which time one covers the short position and buys. Moves less than y% in either direction are ignored. Such a system is called a y% filter.
After extensive tests using daily data on price indices from 1897 to 1959 and filter parameters from 1 to 50%, in his final paper Alexander concludes:
"In fact, at this point I should advise any reader who is interested only in practical results, and who is not a floor trader and so must pay commissions, to turn to other sources on how to beat buy and hold."
The results indicate very small filter parameters (1%) do yield very small possible returns with high frequency data but in the Alexander experiment these are eclipsed by trading costs.
Trading costs are the bane of the active trader and set performance hurdles for technical trading systems.
Bernstein[10] points out that if stock prices are random and independent of each other their changes over time should look like a normal distribution or bell curve (the central limit theorem). He illustrates this by charting monthly, quarterly and annual percentage changes in S&P 500 prices from 1926 through to 1995. The resulting charts do approximate to normal distributions, allowing for the overall upward trend over this period.
Semi-strong tests also support EMH. For instance an experiment to measure the impact on prices of information implicit in stock splits by Fama, Fisher, Jensen and Roll[11] indicates that the market makes unbiased forecasts of the implication of stock splits, and these forecasts are fully reflected in prices by the end of the split month.
The most surprising confirmation of EMH comes in strong form tests involving fund management performance.
Institutional funds dominate investment activity. At the time of writing there is some USD7tr under management in US funds alone (Investment Company Institute).
Institutional fund managers spend vast sums on research and could be expected to have an information edge. Does this show up in performance that is above the norm?
A landmark experiment by Jensen[12] sets out to determine this on the basis of a norm which represents the results of an investment policy based on the assumption that prices fully reflect all available information. Using the Sharpe Lintner model of equilibrium expected returns, Jensen develops a norm represented by a 'market line' which relates returns to risk in a linear manner. Performance above the line is superior and below inferior. He uses this risk--return framework to evaluate the performance of 115 mutual funds over the ten year period of 1955-64. In terms of net returns to investors Jenson finds that in 89 out of the 115 cases the funds risk--return combination is below the market line and the average over all funds of the deviations on ten year returns from the market line is -14.6%. Jensen concludes:
"Although these results certainly do not imply that the strong form of the martingale hypothesis holds for all investors and for all time, they provide strong evidence in support of that hypothesis. One must realise that these analysts are extremely well endowed. Moreover they operate in securities markets everyday and have wide ranging contacts and associations in both business and financial communities. Thus, the fact that they are apparently unable to forecast returns accurately enough to recover their research and transaction costs is a striking piece of evidence in favour of the strong form of the martingale hypothesis."
A later comprehensive study by Carhart[13] (1997), which uses a database that includes all dead funds to compensate for survivor bias*, underpins Jensen's findings.
In comparing active vs. passive trading styles Shefrin[14] observes:
"Vanguard offers an index fund, the 500 Index Portfolio that tracks the S&P 500. Vanguard reports that in 20 years between1977-1997, the 500 Index Fund outperformed more than 83% of Mutual Funds. During 1997 the 500 Index Fund actually beat most, over 90% of the diversified US equity mutual funds. For the year, S&P returned 32.61% in comparison to the 24.36% return on the average equity mutual fund."
The evidence of mutual fund performance tends to support EMH and lends support to passive rather than active management styles.
A large body of evidence thus indicates that stock markets are efficient and hard to forecast. However the evidence is not all one-way.
Evidence of market inefficiencies
In the book A Non Random Walk Down Wall St, Lo and Mackinlay[15] report significant positive serial correlation in weekly and monthly samples of the Centre for Research in Securities Prices (CRSP) equal weighted returns index taken from September 1962 to December 1985. Interestingly they find tests on more recent data (1986-1995) reveal that the correlation has disappeared. They observe that several Wall Street firms have been known to have been engaged in 'statistical' arbitrage during the intervening period based on the patterns they had uncovered in their earlier research. They conclude that this provides a plausible explanation of the trend towards randomness in more recent data. Ironically, this is a nice argument in favour of EMH.
There is evidence of serial correlation in high frequency tick by tick data that could be the basis of successful trading systems. For example see Olsen[16] and Lequeux.[17] Intuitively this makes sense because at this resolution we are seeing the wheels and cogs of the market's microstructure at work.
Cochrane[18] (1999) observes:
"Whilst daily, weekly and monthly stock returns are still close to unpredictable, and technical systems for predicting such movements are still close to useless, variables including the dividend/price ratio and term premium can predict substantial stock return variation over business-cycle and longer horizon."
He points to an example where 'low' prices relative to dividends, book value, earnings, sales and other divisors predict higher subsequent returns. Whilst the effect is very small over the short term it can be forecast over a five-year period. This effect inspires a reversal trading strategy based on statistical evidence that winners become losers and losers become winners over the long term.
Schiller[19] finds it difficult to reconcile EMH with the dramatically increasing disparity between stock market prices and dividends in the run up to the turn of the millennium. Schiller's observations, published just before the March 2000 sell-off, were prescient. One graph reproduced here is quite striking. It illustrates the patterns of inflation-adjusted stock prices and dividend present value of stocks in the S&P composite index from 1871 through to 2000. Whilst dividends follow a smooth and modestly up-trending line, prices perform like a roller coaster. They repeatedly surge upwards, often over a sustained period of years, to a point where they seem to lose any rational relationship with fundamentals. Then they crash. Schiller asks how such behaviour can be reconciled with an efficient market and rational investors. He observes:
"Stock prices appear to be too volatile to be considered to be in accord with efficient markets. If stock prices are supposed to be an optimal predictor of dividend present value, then they should not jump around erratically when the true fundamental value is growing along a smooth trendexcess volatility due to speculative bubbles is probably just one of the factors that drive speculative markets, and the prominence of this factor varies across markets over time."
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Inflation adjusted stock prices and dividend present value of stocks in the S&P composite index from 1871 through to 2000. No prizes for guessing what happened next -- as of February 2002 the S&P 500 stands at 1089.
Bubbles, greed and fear
It is perhaps too much to expect a model that has its origins in equilibrium and rational agents to cope with the dynamics of market bubbles. Bubbles are certainly persistent and recurring phenomena. The great bubbles, Tulip Mania, the Mississippi and South Sea Bubbles, the Great Crash of 1929 and now the Great Millennium Bubble are all firmly imprinted on our minds. The works of Charles Mackay and Joseph de la Vega enjoy the status commanded by the best of novels. Uninhibited supply meets insatiable demand!
Bubble plots follow a familiar form. The seed is in a story of untold riches in prospect, a new era, a new paradigm. The word is put about. The smart money buys and prices rise. A clamour for stock is met by a ready supply on easy terms. Rising prices become the news that drives demand higher. What can have greater utility than an asset that grows in value by leaps and knows no bounds? Demand increases. More paper is manufactured. The dynamics of chain letters, pyramid selling and Ponzi schemes now click in. The great and the good affirm all is well. Discordant voices are shouted down. Prices lose all touch with reality, the smart money sells. Disbelief is no longer in suspension. Panic selling takes hold. The last in lose everything. The guilty are sought out and pilloried. The memory fades.
One could surmise that such a predictable run of events could give rise to trading opportunities, and we will return to this later.
People are fallible, often irrational, follow intuition and rules of thumb, make biased decisions and, in short, are human. This needs to be factored into any understanding of how markets work.
This realisation has spawned much literature classified as behavioural finance. One theme is that investors tend to make irrational investment decisions because of over-reliance on imperfect rules of thumb and intuition. An example is 'past performance is the best predictor of future performance'. This heuristic bias we are told can lead to over-confident trading and nasty accidents. Another theme is that we tend to be influenced by how decision problems are framed. For instance we feel losses much more acutely than gains of equal magnitude. Loss aversion may cause us to hang on to a losing position for too long. The behaviourists maintain that these effects can lead to price distortions and market inefficiency.
EMH describes markets as rationale, mechanistic and efficient. Traders by contrast see markets as offering speculative opportunities. Many believe that technical trading is profitable, that a 'market psychology' exists and that herd effects unrelated to news can cause bubbles and crashes. We often hear of the market being 'nervous' or 'sluggish' or 'jittery' as if possessing its own moods and personality. From this viewpoint markets are psychological, organic and imperfectly efficient. From the traders' viewpoint the standard academic theory is unrealistic and at odds with their experience.
The opinions of two eminently successful traders are illustrative.
Soros[20] has this to say about EMH:
"Existing theories about the behaviour of stock prices are remarkably inadequate. They are of so little value to the practitioner that I am not even fully familiar with them. The fact that I could get by without them speaks for itself. Generally theories fall into two categories: fundamentalist and technical. More recently the random walk theory has come into vogue; this theory holds that the market fully discounts all future developments so that the individual participant's chances of over or underperforming the market is as a whole even. This line of argument has served as a theoretical justification for the increasing number of institutions that invest in index funds. The theory is manifestly false -- I have disproved it by consistently outperforming the averages over a period of twelve years. Institutions may be well advised to invest in index funds rather than making specific investment decisions, but the reason is to be found in their substandard performance, not in the impossibility of outperforming the averages."
Soros appears to make money by exploiting disequilibrium in markets and he has devised a mental model to identify and read the dynamics of such situations. He contends that whilst markets might appear to be in equilibrium, this is an unstable state. There are always forces which tend to tilt towards disequilibrium. Soros thinks that markets are always biased in one direction or another and crucially markets can influence the events they anticipate. The latter factor he calls reflexivity. For instance a company with particularly favoured management might happen to operate in a currently favoured sector. This could lead to an above the norm valuation in the market. The company can capitalise on this to go on an acquisition spree thus growing more quickly than its competitors. This in turn can increase its valuation and so on in a positive feedback loop. As well as the fundamentals affecting the stock price the stock price can influence the fundamentals. When the latter effect is strong Soros contends that this can lead to disequilibrium such as the boom/bust cycle that can be exploited for profit.
As an example Soros cites the conglomerate boom of the late 1960s where he made money on the way up and on the way down. He maintains the key to this boom was a prevailing misconception amongst investors. Whilst valuing on the basis of per-share earnings, investors had failed to discriminate how the earnings growth was accomplished. A few companies learned to produce and hone earnings growth through acquisitions. Once this was reflected in stock prices they could use their premium-priced paper to acquire other companies, the seed of a boom/bust cycle.
Buffet[21] has this opinion on EMH:
"Proponents of the theory have never seemed interested in discordant evidence. Apparently a reluctance to recant, and thereby demystify the priesthood, is not limited to theologiansObserving correctly that the market was frequently efficient they went on to conclude incorrectly that it was always efficient. The difference between these propositions is night and day."
A student of Benjamin Graham, the doyen of value investing, Buffet's focus style of management involves picking a few stocks that from fundamental analysis appear to have good long term prospects, taking large positions in the chosen few and holding them for the long term. Whilst flying in the face of efficient markets and modern portfolio theory, Warren Buffet's style has certainly worked well for him and his followers.
Getting a life
In an attempt to breathe life into models, and to imitate more closely real-world dynamics, some model builders have turned to adaptive agent-based simulation. For an example see Axelrod.[22]
Such simulations typically run in discrete steps, the inputs for each step being the outputs from the previous step. At each step conditions evolve according to the model parameters and algorithms. This open form approach can be used to investigate and explain the dynamics of complex and emergent processes. Game theory often provides inspiration for agent interaction and evolutionary theory for agent development.
A good example of an adaptive agent based model is the Santa Fe Institute's Artificial Stock Market* (ASM). In the following I draw from the experiment performed by Arthur, Holland, LeBaron, Palmer and Tayler.[23]
ASM models markets as a changing world of less than rational agents who embark on a voyage of discovery. Agents continually explore and develop forecasting models, and buy and sell assets based on the predictions of the models that perform best. Each agent acts independently, following its currently best forecast, but the returns to each agent depend on the decisions made simultaneously by all the other agents in the market. ASM uses a genetic algorithm# to evolve winning strategies.
In contrast to the EMH picture of homogeneous agents with perfectly rational expectations who deduce prices from available information, the thinking behind the ASM model is that asset prices are determined by heterogeneous agents whose expectations continually adapt to the market these expectations aggregately create.
Agents continually form individual, hypothetical expectational models or 'theories of the market', test these and trade on the ones that predict best. From time to time they drop hypotheses that perform badly, and introduce new ones to test. Prices are driven endogenously by these inductive expectations. Individual expectations therefore evolve and compete in a market formed by others' expectations. In other words agents' expectations co-evolve in a world they co-create to endow the market with a psychology, of the sort a trader like Soros could identify with.
The natural question is whether these heterogeneous expectations co-evolve into homogeneous rational expectations, beliefs and equilibrium, upholding the efficient markets theory; or whether richer individual and collective behaviour emerges, upholding the trader's viewpoint.
The simulated market is based on a simple neoclassical two asset market. Where it breaks with tradition is that agents form their own expectations individually and inductively. The market contains two assets: a risky stock which pays a stochastic dividend, in finite supply; and a risk-free bond, available in infinite supply. Agents, initially endowed with a certain sum of money, must decide in each time period of the simulation how to allocate their capital between the two assets. They do this by forecasting the price of the stock, and assessing its riskiness measured by the variance of the prices.
Agents may recognise two different kinds of market states (possibly simultaneously): technical and fundamental. A market state detected by an agent is 'technical' if it identifies a pattern in the past price history, and is fundamental if it identifies an immediate over- or under-valuation of the stock. An example of a technical state would be 'the price is greater than the 50 period moving average', and an example of a fundamental state would be 'the price is over-valued by 10%.'
If the market state in a given period matches the descriptor of a forecasting rule, the rule is said to be activated. A number of an agent's forecasting rules may be activated at a given time, thus giving the agent many possible forecasts from which to choose. An agent decides which of the active forecasts to use by choosing at random among the active forecasts with a probability proportional to its accuracy, a measure that indicates how well the rule has performed in the past. Once the agent has chosen a specific rule to use, the rule is employed to make an investment decision. Agents determine how much stock to buy, sell or hold, using a standard risk-aversion calculation. They submit their decisions to the market specialist, an extra agent in the market whose role in life is to clear the market.
The evolution of the population of forecasting rules over time is determined by a genetic algorithm. Whenever the GA is invoked, it substitutes new forecasting rules for a fraction of the least-fit forecasting rules in each agent's pool of rules. The GA may be compared to a real-world consultant. It replaces current poorly performing rules with rules that are likely to perform better.
It is important to note that agents in this model learn in two ways. First, as each rule's accuracy varies from time period to time period, each agent preferentially uses the more accurate of the rules available to it. Second, on an evolutionary time scale, the pool of rules as a whole improves through the action of the genetic algorithm.
What the model reveals
In one experiment, only one aspect of the model was varied: the agent's rate of exploration of alternative expectations (the evolutionary learning rate).
At a low exploration rate the market price converges rapidly to equilibrium where there are no winners and losers, trading volume is low and bubbles, crashes and technical trading do not emerge.
As the exploration rate of agents is increased, however, the market springs to life. Interestingly, experimentation has indicated that, if given the choice, agents will select this rate as it maximises their wealth. Temporary prices, bubbles and crashes appear in prices and agents' holdings diverge. Variance of the price--time series is relatively high and GARCH volatility signatures, typical of real markets, appear. The evolved rules are complex; technical trading strategies emerge and persist, and trading volumes are higher.
Technical analysis can emerge if trend following (or mean reversion) beliefs are by chance generated in the population, and if random perturbation in the dividend sequence activates and subsequently validates them. From then on they may take their place in the population of patterns recognised by agents, and become self reinforcing.
Another interesting experiment by Joshi, Parker and Bedau[24] shows that widespread technical trading can arise due to a multi-person Prisoners' Dilemma* in which inclusion of technical trading rules in single agent's repertoire is a dominant strategy. The use of this dominant strategy by all traders in the market creates a symmetrical Nash# equilibrium in which wealth earned is lower and volatility is higher than in a case where agents rely only on fundamental rules.
Does ASM experience 'moods'? Agents can entertain more than one market hypothesis. Thus one can imagine circumstances of a prolonged 'bull market' up-trending to well above fundamental value in which the market state activates predictors that indicate the uptrend will continue, and simultaneously other predictors that point to a rapid downward correction. Such combinations could well be described as 'nervous'.
What about motivations to trade in the ASM model? In the rational expectations model the deductively rational agents have no motivation to trade, even where they differ in beliefs. In contrast, ASM agents do not necessarily converge in beliefs. Thus they retain a motivation to trade betting ultimately on their powers as market statisticians. Although their abilities are the same, their luck in finding good predictors diverges over time. At each period the accuracy of their predictors is fully accounted for in their allocations between the risk-free and the risky asset. Given that traders only act as market statisticians, their behaviour can be fairly described as rational.
The conclusion to all this is that agents' forecasts create the world that agents are trying to forecast. Thus, to borrow a term used frequently by Soros to explain market behaviour, asset markets have a 'reflexive' nature in which prices are generated by traders' expectations, but their expectations are formed on the basis of others' expectations.
The ASM experiment shows that both the rational expectations model and the trader's views can be accommodated.
A fair game?
At the time of writing (February 2002) the game appears to be on a losing streak; the gold price stands at a 2-year high. AIB has just announced a surprise loss of USD750m on foreign exchange trading, approaching the amount that brought down Barings. The story of the Enron collapse, the biggest corporate bankruptcy in US history, is unfolding and revealing huge bad debts at several major US banks. For instance JP Morgan Chase recently wrote down USD451m and is reported to have a further USD2bn potential loss on its books. Needless to say, the bank's stock has taken a tumble. Tech stocks continue to be hammered across the board two years after the pricking of the dot com bubble. For instance the price of Worldcom -- one of the highest telecoms fliers -- currently stands at USD6, down from a high of over USD60 two years ago. Global Crossing, another high flier at one stage valued at USD50bn, has just filed for protection under Chapter 11. Computer Associates the world's fourth largest software company, has been forced to delay a KSD1bn stock issue and is facing a credit downgrade. The NASDAQ composite index took some 25 years to rise surely and steadily up to the 1000 mark. In 1996 it took off sharply, to reach over 5000 by March 2000, leaving its more staid S&P 500 and DJIA brethren languishing. It currently stands at 1800. What statisticians would call a good example of reversion to the mean. One might conjecture from all this that the financial markets are only for the foolish or the brave.
Investors' appetite for risk nevertheless seems to be undiminished: witness the explosion in hedge funds, some of which appear to deviate from the philosophy first articulated by Alfred Winslow Jones, and appear to be anything but hedged. In spite of the spectacular implosion of Long Term Capital Management, money continues to pour into hedge funds and is estimated to have risen from USD20bn in 1990 to some USD400bn at present. The number of funds has risen from 200 to 3000 over the same period (Temple, 2001[25]).
If you don't qualify as a hedge fund investor, and still have a strong taste for risk, you could join the 20 million or so online account holders and churn and burn using your home PC. Once signed up you can download a state-of-the-art desktop trading system, check the state of the market using 'heat maps', and ride intra-day charts taking long or short positions, on margin of course. If you don't fancy individual stocks you can buy and sell exchange traded funds, or you can second guess the big boys at Vanguard by trading their wonderfully named 'Vipers'.
Alternatively you could peruse the Morningstar.com Investment Radar to select a fund management style that suits your tastes and appetite for risk.
On the other hand you might decide to forego such niceties and go directly to Fidelity.com or Vanguard.com to do the business.
It you are a gentleman or woman of means you could always avail yourself of the tailored services of Babson Investment Advisors Inc at www.babson.com. Oh yes, the spirit of Babson lives! Please do not apply unless you have more than GBP500,000 to play with though.
In fact you can obtain price charts in printed form or Internet-delivered from the Securities Research Company, a subsidiary of the venerable Babson-United Investment Advisors Inc. I know that Soros uses them.
Peter Bennett advises stock exchanges and practitioners on trading systems development. Amongst many achievements, he is the architect of TOPIC, the system that allowed the London Stock Exchange to move trading from the traditional floor to a system of screen trading. TOPIC endures and is now owned by Thompson Financial Networks. He is co-founder of the Tradepoint Investment Exchange, now called virt-x and owned jointly by the Swiss Stock Exchange and a consortium of the leading Investment Banks and ECNs. Peter can be contacted at peter.m.bennett@btinternet.com.
References
[1] The Great Crash 1929, J K Galbraith, Pelican, 1954.
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