Stock Markets and Catastrophic Tendencies
“Even apart from the instability due to speculation, there is the instability due to the characteristic of human nature that a large proportion of our positive activities depend on spontaneous optimism rather than mathematical expectations.”
- John Maynard Keynes.
Gyrating Markets
Writing in the shadow of the Great Crash of 1929 Keynes tacitly assumed that markets were unstable. He also warned that attempts to build bigger and better organised markets could make things worse.
Unfortunately instability, measured in terms of asset price volatility, appears to be persistent and on the rise.
CBOE Volatility Index
Volatility measures the intensity of price fluctuations. A century ago Louis Bachelier coined the term coefficient of nervousness or instability to describe the phenomenon. Now we speak of historical price volatility. Also with the marvelous invention of the Black and Scholes options pricing model and the associated development of liquid forward markets, we can deduce implied price volatility of the underlying from quoted option prices.
Recently Ms Tumpel-Gugerell of the European Central Bank observed that:
“The pattern of development of stock market volatility is quite simple to summarise. We can distinguish two sub-periods over the past decade. Before 1997, the volatility on the leading stock indexes hovered around 15% in France and Germany and in the United Statesm both in terms of historical volatility and of implied volatility. From 1997 onwards, the typical value of those volatilities doubled. This doubling was the result of a slow but steady rising trend, lasting more than six years. A doubling period as short as six or seven years is certainly quite remarkable.”
She went on to observe the effect on equity market volatility of another invention of our age, credit derivatives:
“We can relate the increase in stock market volatility to a similar increase that can be observed in credit spread volatilities, which have been growing more or less since 1998. In addition, the credit spread markets and the stock market are linked to a certain extent, in particular because the stock of a given issuer offers a natural hedging tool to the financial engineers that create credit derivatives on that issuer.[1]”
| Tulip Mania | 1637 |
| South Sea Bubble | 1720 |
| US Rail Road Mania | 1857 |
| The Great Crash | 1929 |
| The Crash of 87 | 1987 |
| Sterling Falls out of ERM | 1992 |
| The Mexican Peso Crisis | 1994 |
| The Asian Crisis | 1997 |
| The Russian Crisis | 1998 |
| The Dot Com Bubble | 2000 |
| Argentine Peso Crisis | 2001 |
Some notable periods of volatility
Pristine academic models hold that markets for financial assets are constantly and rapidly driven to equilibrium as rational profit maximisers compete to establish prices of securities, consuming all relevant information in the process. The Efficient Markets Hypothesis (EMH) asserts that market prices fully reflect the effects of events past and anticipated. In other words, in an efficient market today’s price will be a good estimate of its intrinsic value. In the absence of news, the future price will be anyone’s guess.
Although in many ways convincingly argued, the efficient market model fails to explain why markets periodically exhibit irrational pricing and unstable bubble-like behaviour. It seems that the efficient market model could be a special case that holds for some, but not all of the time. An altogether more comprehensive explanation is required to characterise the price dynamics of real markets as they unfold over time.
Recent research goes beyond the somewhat utilitarian econometric models that are central to modern financial theory. Some researches have returned to Keynesian insights that market prices can be influenced more by game playing than considerations of the fundamental value of investments.
New theories draw on a diversity of sciences to breathe life into abstract and soulless financial models. The new thinking embraces a broad church of disciplines including complex systems dynamics, game theory, behavioural sciences, physics, geophysics, ecology and biology. The general approach is to delve inside the markets black box, and to identify the machinations that may lead to the excess volatility and the bubble-like behaviour which is all too evident in real markets. Much of the work has centred on the human element.
A picture that emerges is of markets where irrational and herd-like behaviour play a part in price distortion, where self reinforcing and destabilising feedback loops are pervasive, where cooperative and self organising behaviours lead to complex and non-linear outcomes, and where markets stand in a sort of continuous dynamic disequilibrium which at times can be very sensitive to changes in sentiment.
In this piece I review and discuss the quest find a satisfactory explanation of market behaviour, and propose a model for asset price behaviour based on Catastrophe Theory. This appears to provide a context in which the efficient market model can coexist as a special case amongst other theories of price formation.
The Great Game
Keynes was by all accounts an astute and successful investor, and of the school that regards investment as a game. His thoughts regarding The State of Long-Term Expectation[2], recorded in 1936, make stimulating reading. He describes the game thus:
“…the professional investor is forced to concern himself with the anticipation of impending changes, in the news or in the atmosphere, of the kind by which experience shows that the mass psychology of the market is most influenced. This is the inevitable result of investment markets organised with a view to so-called “liquidity”…
This battle of wits to anticipate the basis of conventional valuation a few months hence, rather than the prospective yield of an investment over a long term of years, does not even require gulls amongst the public to feed the maws of the professional; — it can be played by professionals amongst themselves. Nor is it necessary that anyone should keep his simple faith in the conventional basis of valuation having any genuine long-term validity. For it is, so to speak, a game of Snap, of Old Maid, of Musical Chairs — a pastime in which he is victor who says Snap neither too soon nor too late, who passes the Old Maid to his neighbour before the game is over, who secures a chair for himself when the music stops.”
Keynes asserts, with some irony, that the game is an inevitable outcome of our attempts to build bigger and better organised markets, and in particular the quest for the holy grail of liquidity.
Given that it is rare amongst mortals to posses the ability to deduce the long term expectations of our investments with any precision, he argues that we invest on the basis of short term expectations, banking on liquid markets to revise our positions if something is in the air. He asserts:
“In practice we have tacitly agreed, as a rule, to fall back on what is, in truth, a convention. The essence of this convention — though it does not, of course, work out quite so simply — lies in assuming that the existing state of affairs will continue indefinitely, except in so far as we have specific reasons to expect a change.
Thus investment becomes reasonably safe for the individual investor over short periods, and hence over a succession of short periods however many, if he can fairly rely on there being no breakdown in the convention and on his therefore having an opportunity to revise his judgment and change his investment, before there has been time for much to happen. Investments which are fixed for the community are thus made liquid for the individual.”
The truth, of course, is when things take a turn for the worse, markets can be anything but liquid. Keynes maintains that the illusion of liquidity can lead to instability.
A young Keynes
“With the separation between ownership and management which prevails to-day and with the development of organised investment markets, a new factor of great importance has entered in, which sometimes facilitates investment but sometimes adds greatly to the instability of the system. In the absence of security markets, there is no object in frequently attempting to revalue an investment to which we are committed. But the Stock Exchange revalues many investments every day, and the revaluations give a frequent opportunity to the individual (though not to the community as a whole) to revise his commitments.”
Keynes depicts organised markets as casinos and points, with some disdain, to the propensity of players on the New York Stock Exchange to invest for capital gain. He contrasts the New York Exchange to the then relatively exclusive club that was the London Stock Exchange, and the propensity of English gentlemen to invest for income. Alas no more. One is left with the impression that Keynes felt that exclusive nature of the old London Exchange was not altogether a bad thing.
Early days at the London Stock Exchange
Keynes also likens professional investment to a beauty contest:
“… professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors.”
This theme, of course, was to be developed famously by John Nash in his theory of games.
As an end-note Keynes contemplates the future with some pessimism:
“If I may be allowed to appropriate the term speculation for the activity of forecasting the psychology of the market, and the term enterprise for the activity of forecasting the prospective yield of assets over their whole life, it is by no means always the case that speculation predominates over enterprise. As theorganisation of investment markets improves, the risk of the predominance of speculation does, however, increase.”
Playing with the price of American Sugar
In April 1894 American Sugar was to join the elite band of twelve companies that constituted the nascent Dow Jones Industrial Average Index. The move portended the beginnings of our unhealthy addiction to sweetness. The following incident, recorded in the Boston Journal of March 17th 1899, depicts some of our other innate tendencies, namely fear and greed. The description of a foray onto the floor of the Boston Stock Exchange by a certain Thomas W Lawson is a nice description of these tendencies at work in the formation of stock market prices.
“Sugar was the big card of stock speculation yesterday. Indeed the stock had one of the wildest days in its history, and its high price - $170- reached amid great excitement – is the highest on record. From the opening it quickly advanced to 149, receded a point or more, and shortly after noon started sharply upward. The demand for it came so rapidly that the tape could not keep up with it, and excitement grew as demand increased...at one point the quotation in the Boston market was fully four points behind the New York list...the small army of shorts scrambled to get covered up…”
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Another contemporary account, this time in the Boston Herald of March 16th 1899 sheds light on what triggered this particular assault on Sugar.
“Mr Thomas W. Lawson was the mover in the deal, and his orders for 20,000 shares early in the day excited other buying, which encompassed the astonishing rise. What point Mr Thomas had to trade upon in his own asset, if it had any point, and it would not matter so far as the event was concerned if it had any point. The market was in a position to respond to orders of these dimensions and it did respond.”
A further account in the New York Journal of March 17 1899 describes the scenes on the New York Stock Exchange floor as the price action rattled off the ticker tape.
Frenzied Finance
“The frenzied brokers fought like madmen around the Sugar Post. The rest of the floor was practically abandoned. There was no warning. The sudden jump of stock almost threw the brokers into panic. Men become ferocious in their efforts to fill orders. So great was the din and so compact the yelling crowd that those on one side of the post did not know the bidding on the other. Members of firms who were not on the floor gathered around tickers in excited groups… the quotations came out at two and three points apart…”
Finally a piece from the Boston Post of March 22nd recounts, at first hand, Mr Lawson’s side of the story.
“Thinking things over of late I determined to make a final demand on astute and relentless Wall Street for my accumulated deposits – a kind of give me back my losses demand. I carefully loaded up two weeks ago to the extent of 20,000 Sugar in the thirties, and feeling the atmosphere was rendolent of opportunities, last Friday I bought 20,000 more, the last 5000 of which in a rather open and frank way that seemed fair to my scalping New York friends. Well you know the rest. It took fire. I cleaned up something over $700,000 and put out a short line of 30,000 shares, the last of which I have covered today at something over $350,000 profit. In doing what I did I depended on no fakes nor stories. I simply followed Charley Osbourne’s old admonition: If you want to bull stocks buy ‘em. If you want to bear ‘em sell ‘em.”
We can glean much from this story to explain the dynamics of financial markets, and the factors seem to be as relevant today as they were over 100 years ago.
First the trigger for the rapid rise in Sugar was not news about the prospects for sugar, rather it was Mr Thomas’s expedition into the market designed to regain past losses. His orders had nothing to do with expectations of a change for the better in the fundamentals, they were purely speculative. However others were not to know this, and may have construed that the strong buying contained new and positive information, and jumped on the band wagon accordingly.
The foray into the Boston market, which we can safely assume to have been less liquid than the New York market, was calculated to have the maximum impact at the early stage of the price rise.
As word of the price rises reached the New York Exchange the buying pattern took hold, and the sharply upward trending sugar prices became the news that brought waves of buyers into the market. The relatively larger latent liquidity of Wall Street now clicked in as New York became the epicentre for the feeding frenzy, with the quotation at the Boston exchange lagging the New York signal.
We see that liquidity can be key factor in relation the dynamics of asset price movements, although in not a clear cut way. For example in this story the relatively illiquid Boston market provided the tinder to kindle the buying flame. The liquid New York market provided the fuel to sustain a raging fire.
The buying frenzy was further fuelled by shorts running for cover. They stood aside the stampeding herd.
The tickers could not keep up with the rate of changes in prices which gapped up, adding to the speculative fervour. Even in 1899, it appears that communications technology played a key role in linking market centres and amplifying speculative activities.
The vicious upward spiral in prices continued until it became clear that the fundamentals of sugar had not changed. The whole process then rapidly reversed itself with Mr Thomas’s short position leading the way down.
Although Mr Thomas made a killing on this occasion this was offset, by his own account, of substantial losses on other occasions.
It is very difficult to beat the market over the long term.
Market Efficiency – A Subject for Great Debate
"I'd be a bum in the street with a tin cup if the markets were efficient."
- Warren Buffet.
At about the same time that Thomas W. Lawson was making a killing on the Boston Stock Exchange a young Louis Bachelier, was attempting to explain, in mathematical terms, the price dynamics of bonds traded speculatively on the Paris Bourse. The Exchange had become by 1850 the world market for perpetual government bonds guaranteed by the value of the gold franc, and was a veritable hive of speculative activity.
Bachelier set himself the ambitious goal of expressing mathematically 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, or Brownian Motion.
In defending his thesis, Théorie de la Speculation, to his professors, who included the pre-eminent mathematician Henri Poincaré, Bachelier asserted:-
“Past, present and even discounted future events are reflected in market price…it 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 sellers…clearly 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.”
The young mathematician came to the conclusion that 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. The trajectory of price changes is akin to a random walk.
Bachelier’s work lay dormant until rediscovered by researchers at MIT in the 1950’s, who were to put it to the test. If the random walk hypothesis holds, there should be little or no empirical evidence of serial correlation in histories of market price changes.
“I know of no study in which standard statistical tools have produced evidence of important dependence in series of successive price changes.”
-Eugene F. Farma
Numerous tests were to show this was indeed the case. For example see Fama[3], Kendall[4], Granger and Morgenstern[5], and Godfrey, Granger and Morgenstern[6]. An experiment by Alexander[7] 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% 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 success of empirical tests gave impetus to formalising Bachelier’s theory using modern quantitative techniques and stochastic mathematics.
In 1965 Paul Samuelson, published “Proof that Properly Anticipated Prices Fluctuate Randomly.[8]” This work was to be developed by Fama in a grand synthesis of theories of rational expectations, market equilibrium and the random walks to form the Efficient Markets Hypothesis[9].
The hypothesis implies that market prices fully reflect all the information that is available to market participants. Future changes in prices can only be the result of news, which by definition is unpredictable.
That the theory is controversial should be no surprise. In the same way that the laws of thermodynamics offer scant hope for those intent on earning their fortunes from perpetual motion, so the efficient market hypothesis offers little encouragement for those seeking to attain riches and fame by divining the future of the market. What it implies is that the endeavors of the armies of analysts, technical traders and fund managers who attempt to beat the market consensus are futile.
A perpetual motion machine
The absence of significant correlation of price changes in historic price streams is one thing, but a more impressive test of market efficiency lies in the performance of professional investors such as Mutual Fund Managers. If prices fully reflect available information then it is unlikely that particular fund managers will, on a consistent basis, perform better than their peers.
Professionally managed mutual funds dominate investment activity. At the end of 2002 there were some $6.4 trillion invested in US Mutual Funds alone, of which $2.7 trillion was invested in equities (down from $3.4 Trillion in 2001) [10]. About $1 trillion is invested in passively managed equity index funds in the US.
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?
In comparing active vs. passive trading styles Shefrin[11] 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.”
Given the volatile performance of the major indices in the wake of the dot com crash it is reasonable to assume that active fund managers may have had an edge on passive indexed funds. Surprisingly this also appears not to be the case.
The S&P Indices Versus Active Funds (SPIVA) Scorecard reports performance comparisons corrected for survivorship bias. The report ending 2003 indicates that over the last five years, the S&P 500 has outperformed 53.2% of large-cap funds, the S&P MidCap 400 has outperformed 81.7% of mid-cap funds, and the S&P SmallCap 600 has outperformed 69.8% of small-cap funds.
Similarly, over the last three years, the S&P 500 has outperformed 63.7% of large-cap funds, the S&P MidCap 400 has outperformed 73.3% of mid-cap funds, and the S&P SmallCap 600 has outperformed 68.6% of small-cap funds.
Additionally landmark academic studies performed by Jensen[12] and Carhart[13] add to the weight of evidence that beating the market consensus is the exception rather than the rule.
It is interesting to note that in attempts to beat the market, active fund managers have been increasingly churning their portfolios.
This propensity to trade was recently highlighted by John Bogle, Founder and Former Chairman of The Vanguard Group[14]. Referring to his Princeton thesis written at the start of his career in 1950 he remarks:
“Mutual fund managers today are not investors. We are speculators. When I say that this industry has moved from investment to speculation, I do not use the word "speculation" lightly. Indeed, in my thesis I used Lord Keynes' terminology, contrasting speculation ("forecasting the psychology of the market") with enterprise ("forecasting the prospective yield of an asset"). I concluded that as funds grew they would move away from speculation and toward enterprise (which I called "investment"), focusing, not on the price of the share, but on the value of the corporation. As a result, I concluded, fund managers would supply the stock market "with a demand for securities that is steady, sophisticated, enlightened, and analytic." I was dead wrong. We are no longer stock owners. We are stock traders, as far away as we can possibly be from investing for investment icon Warren Buffett's favorite holding period: Forever”.
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| Mutual Fund Churn |
The inability of a majority of professional fund managers to better the markets consensus appears to lend much weight to the argument that markets are efficient.
As one would expect, the minority of professional investors who have consistently outperformed the market, strongly refute EMH.
Warren Buffet has this to say:
“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 theologians...Observing 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[15].”
A student of Benjamin Graham, the doyen of value investing, Buffet’s 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. The investment style is also opportunistic and involves taking advantage of market inefficiencies as and when they arise. Followers of Graham’s strategy play the mood of “Mr Market”, and buy their preferred investments when negative sentiment has led to bargain basement prices, and sell when buying euphoria has inflated prices.
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| US securities market capitalisation expressed as a percentage of GDP, an artifact used by Warren Buffet as a valuation gauge. |
George Soros voiced similar opinions to Buffet:-
“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.” [16]
Soros describes his money making approach as exploiting disequilibrium in markets. He has devised a mental model to identify and read the dynamics of such situations. Rather than betting on fundamentals he bets on future crowd behaviour. 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. He calls this reflexivity.
As an example he cites the conglomerate boom of the late 1960’s 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 achieved. 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. Rather than go short at the beginning of the cycle Soros went long and only went short when he judged the boom was about to play itself out in 1970.
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| Inflation adjusted stock prices and dividend present value of stocks in the S&P composite index. No prizes for guessing what happened next. |
Coming from another angle Shiller [17] finds it difficult to reconcile EMH with the dramatically increasing disparity between stock market prices and dividends in the run up to turn of the millennium. Shiller’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. Shiller 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 trend.”
The losses since March 2000 have wiped out about $13 trillion in market capitalisation worldwide[18]. How’s that for efficiency?
“If Schiller’s rejection of market efficiency is sustained, then serious doubt is cast on the validity of this cornerstone of modern financial economic theory.”
– Robert C Merton, Nobel Laureate.
The tendency of markets to exhibit price volatility and bubble-like behaviour has stimulated a search for alternative models. The school of Behavioural Finance[19] investigates how our ingrained irrational tendencies may lead to price anomalies. We just don’t behave the way the mathematical models assume. The theory argues that investors are fallible, often irrational, follow intuition and rules of thumb, make biased decisions and, in short, are human. This needs to be factored into a theory of how markets work. An example of a frequently used rule of thumb 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 example 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[20]. The behaviourists maintain that these effects can lead to price distortions and market inefficiency.
Supporters of EMH respond to such realities by arguing that the theory still holds even if one accepts irrational noise traders into the scheme of things. The argument goes that noise trades are by definition random, and therefore cancel each other out. The behaviourists argue that irrational behaviour often manifests itself in herding and imitation, and far from the trades being random they can be highly correlated. EMH supporters retort that if such behaviour moves prices from fundamental prices, rational arbitragers will step in to bring prices back in line with rational expectations. Following this line of argument the case for efficient markets appears to rest on the effectiveness of such arbitrage.
In search of a free lunch
There can be no doubt that arbitrage plays a significant and growing role in the operation of securities markets. It is at the heart of proprietary trading operations of the big investment banks and the burgeoning hedge fund industry.
In essence arbitrage involves a search for market pricing inefficiencies, ideally between the same or essentially similar securities. Typically a trade involves buying what is regarded as a cheaper security and simultaneously shorting what may be regarded as an over-priced security in the expectation that the prices will converge as efficient market theory predicts. The intention is to lock in a profit which is immune to market risk. It is important that prices converge in the short term because arbitrage trades are typically highly leveraged to multiply what can be tiny pricing anomalies. If the spread widens, the so called basis risk, the beneficial effect of leverage reverses, and the cost of carrying the trade can be very damaging to the arbitrager’s capital. If the arbitrager is putting on trades with other people’s money, the so called agency effect may also limit an arbitrager’s time horizons and his appetite for risk. He needs to avoid big mistakes to maintain the confidence of his investors.
Today’s arbitrage business grew out of currency hedging in the wake of the collapse of the Bretton Woods system in 1971, and the advent of freely floating exchange rates. The development of pricing models, organised derivatives exchanges and standardised contracts on a host of underlying financial instruments and commodities opened the door for financial intermediaries with an appetite for risk to provide derivatives based insurance services. Corporate treasurers and fund managers were to be eager consumers. The use of standardised and OTC derivatives contracts for risk hedging and purely speculative purposes has grown enormously since the 1970’s. The scale of activity can be appreciated by looking at some statistics.
BIS figures for 2003 indicate some $37 trillion in notional outstanding, and $874 trillion in turnover in exchange traded derivatives. OTC derivatives account for some $170 trillion in notional outstanding, and gross market values stood at $7.9 trillion.
Intuitively arbitrage should act like negative feedback in systems dynamics and restore disturbed prices to equilibrium. So why do price bubbles occur in asset markets?
The simple answer is that you need a lot of capital and staying power to go against the crowd. Also technically to put on a “risk free” arbitrage you need to find classes of assets that have similar characteristics and are mispriced. If the whole market for an asset class is mispriced, this can be problematic.
Negative feedback leads to equilibrium in a system via adaptive or goal-seeking behaviour.
In this sort of situation the smart money may just elect to ride the irrational pricing planning to get off before sentiment turns. As is the case with the Soros macro and directional approach to investing, market timing signals may be derived from an innate understanding of the market psychology, and the particular situation that is developing. The trading style may involve large positions and can be expected to operate like positive feedback, boosting prices on the way up and accelerating the decline on the way down.
Another problem is that hedging strategies, far from restoring disturbed prices to equilibrium can have the opposite effect. Spectacular examples are the LTCM hedge fund blow-up[21] and the sudden and extreme market crash of October 1987.
Positive feedback, if left unchecked, will destroy a system through a blow up or the blocking of its functions.=
The LTCM story is good example of what happens when the market overreacts to a surprise event and causes a web of finely balanced and highly leveraged arbitrage positions to unwind.
Trading on the reputation of its partners, John Meriwether erstwhile star bond trader at Salomon Brothers, two Nobel Laureates, Robert Merton and Myron Scholes, and former Federal Reserve regulator David Mullins, the fund was able to borrow on the finest terms, and to operate with unprecedented leverage ratios.
One thing is clear about the partners. They had incredible faith in the theory of efficient markets and their models. In fact they bet the ranch on the assertion that markets are efficient and, if price anomalies do crop up, they soon correct themselves, particularly if given a nudge in the right direction by arbitrage trading. The recipe was simple. Find pricing anomalies in similar asset classes. Go long the underpriced and short the overpriced assets. Go large. Finance the bet with borrowed money. Wait for Mr Market Efficiency to do his stuff. LTCM’s trades were calculated to go with the flow of the theory. Just as water finds its own level and energy is conserved, the pricing anomalies that were the basis of their trades would converge.
A house speciality was relative value trading in bonds. LTCM, for example, bought Italian government bonds and sold German Bund futures. The fund 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.
In the first year of operation, 1994, LTCM returned 28% to its partners and investors. In 1995 this rose to 59% and 57% in’96[i]. By then the fund had amassed some $140 billion in assets with investment capital of $7 billion. The partners could do no wrong. Markets were indeed efficient. The supremely confident arbitragers were magnificently emboldened.
By 1997 the formula had worked so well that pricing anomalies in LTCM’s favourite hedges were drying up. Much to the dismay of their investors the fund was to return $2.7 billion to them. Crucially the partners did not reduce their trades. This had the benefit that their own equity had more participation in any upside performance. The disadvantage was that funds leverage ratio headed towards the sky. The behaviourists might say that the rational traders had perhaps become overconfident. Indeed the partners took on more risky bets. They amassed a host of directional trades on the equities of M&A targets. They put on short and highly illiquid OTC equity market volatility trades on the perception that market volatility was too high and the expectation that it would reduce in time.
In August of 1998 the fund is reported to have had 60,000 trades of all sorts on its books. It had exchange traded derivatives positions of $500 Billion, OTC positions of $150 Billion and swap contracts pf over $750 billion, a total of $1.4 trillion notional derivatives positions. It had long arbitrage positions of over $50 billion balanced by equivalent value short positions. It was heavily long Russian debt (about 8% of its book) balanced by short positions in US Government bonds. The total fund assets were $125 billion of which only $4.8 billion was equity and even less cash.
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 to safe havens.
As a classic flight to quality played out US Treasury bond prices soared whilst the prices of riskier bonds went into freefall.
“The question …is whether the LTCM disaster was merely a unique and isolated event, a bad drawing from natures urn; or whether such disasters are the inevitable consequence of the Black-Scholes formula itself and the illusion it may give that all market participants can hedge away all their risk at the same time.”
Merton H Miller, Noble Laureate.
Distressed sellers dumped positions. Credit spreads widened everywhere. Equity markets became more volatile. Even the most liquid instruments were becoming harder to trade. Fear was now driving the markets across the board in directions 180 degrees opposite to those predicted by LTCM’s theoretical models. And this was not just a blip. Fear was to feed on itself to sustain and exacerbate the market inefficiencies over the weeks and months ahead.
The embattled partners were now between a rock and a hard place. Their capital was decreasing on a daily basis. On August 21 alone they were down $550 million. If they attempted to liquidate their positions the market conditions would lead to fire sale prices which would dramatically devalue the entire portfolio. It would also signal to the market their distressed position and threaten a classic bear squeeze. All they could do was to ride the storm and hope rationality would return to the market before their capital ran out.
Unfortunately the storm was set to endure. John Meriwether was to make increasingly distressed calls for cash to the Street as well as to high fliers such as Soros and Buffet. In the process the fund was making its plight and trading positions known. The partners were laying themselves wide open to attack from the poker players on the Street.
“The result was a downward spiral which fed upon itself driving market positions to unanticipated extremes well beyond the levels incorporated in risk management and stress loss discipline”
– LTCM memorandum January 1999.
The partners had regarded markets as a black box which they observed and played with some detachment. But they were to discover that they were in reality enmeshed in the game, and in the end became the object of the game itself.
They were to realise that today’s huge and highly organised markets are not liquid when everyone heads for the exit at the same time. They learned, as Keynes had intoned, that the notion that investments which are fixed for the community are liquid for the individual can be a dangerously false illusion. They also came to learn in a very painful way that markets can at times become and remain stubbornly inefficient.
LTCM’s demise came to threaten gridlock in the global clearing and payments systems. The big investment banks also faced huge losses as a web of bilateral transactions with the ailing fund stood to default. It was enlightened self interest that was to save the day when the biggest banks that stood to lose the most organised a $3.7 billion bailout. In an attempt to avoid a moral hazard the Federal Reserve, whilst pulling strings, was not to participate directly.
In the final hour the wily Buffet was to make a bid for the fund’s assets at a rock bottom price, in the best tradition of a value investor. Another twist is that, following interest rate reductions by the Fed, the markets eventually moved towards efficiency and many of LTCM’s trades came through having burnt some $5 billion in capital on the way. Over half this was lost in swaps and equity volatility trades. Over the short life of the fund a dollar invested at the outset was to be reduced to 23 cents.
“Any virtue can become a vice if taken to the extreme, and just so the application of financial models in finance practice. At times the mathematics of the models become too interesting and we lose sight of the models’ ultimate purpose. The mathematics are precise but the models are not, being only approximations to the real world.”
– Robert C Merton, 1993.
If the incident was to blunt the appetite for such risk taking, this was short lived. The hedge industry continues to grow unabated. In 1990 assets under management were about $20 billion[22]. A recent SEC report[23] on the US notes 6,000 to 7,000 hedge funds operate in the United States, managing approximately $600 to $650 billion in assets. In the next five years, hedge fund assets are predicted to exceed $1 trillion in the US alone. Imagine the games that can be played with a leverage ratio of 25 or more. One concern of the regulators is the corresponding growth in lucrative prime broking services offered by the big investment banks to the multiplying hedge funds. The banks provide clearing and trading services in exchange for lucrative fees. Importantly they also provide access to funds on fine terms. A major worry is the potential conflicts of interest in this credit provision[24].
In the best traditions of Alfred Winslow Jones, hedge funds bets are meant to avoid market risks. But it stands to reason that if such funds are expected to yield above average returns, then the commensurate increase in risk must come from other quarters. Certainly basis risk cannot be ignored if one accepts that markets can move from being efficient to inefficient and back again unpredictably. In periods when markets are nearly efficient leverage ratios will be increased to multiply returns from shrinking spreads. Given that there are now thousands of hedge funds chasing the same or similar opportunities many may be driven to take on unhedged trades exposing themselves to market risks. Now add intensive sell side competition to lend on the finest terms. We have a recipe for multiple blow ups as and when, for whatever reason, things take a turn for the worse, markets go into an inefficient phase, spreads start to diverge and liquidity risk rears its ugly head.
In the case of the ‘87 crash it did not take a shock for markets to go into freefall.
When recalling the October 1987 Market Crash one is reminded of the notion favoured by complex systems theorists, of a storm occasioned by the flap of butterfly’s wing.
No bad news of any significance preceded the crash although the markets were jittery in the previous week. Things really took hold when on Monday 19th The London Stock Exchange suffered a fall of some 10% on the day, wiping out £50 billion in share values.
A parallel with our story of Sugar emerges. This time it was activity on London Exchange that was to spark an inferno on the New York Stock Exchange.
Remarkably in 100 years, the system of specialists and trading posts on the New York Exchange floor had changed little. The same sort of frenzy ensued this time across the board. A thin veneer of specialist’s capital was swept away, prices gapped down and the tickers ran slow. The Dow Jones Industrial was to fall a record 22% on the day.
What had changed at the New York Exchange was that orders poured onto the floor from a vast electronic order delivery network fed by computerised and mechanical trading systems. These were programmed to sell when prices fell, positive feedback in action! How could this be?
The villain of the piece was named portfolio insurance. The brainchild of Leland and Rubenstein, Portfolio Insurance draws inspiration from the Black and Scholes model to create the idea of a synthetic option[25]. The strategy, known as option replication, requires mechanistic selling as stock prices decline and buying as stock prices rise, a kind of dynamic hedging. Several mutual funds had bought the schemes enthusiastically.
So it came to pass that as the markets started to trend downwards after a steady bull run lasting several years, a group of fund managers mechanically liquidated their equity portfolios as prices fell through certain thresholds, selling huge amounts of stock and stock index futures into a falling market. As was the case with LTCM, each believed in the illusion that “what was fixed for the market was liquid for them.”
In the event, the market declined to serve as guarantor of insured portfolio values. Later the SEC was to find that some firms who had sold portfolio insurance schemes had actually placed sell orders at the market opening anticipating and effectively front running their customers mechanical selling as prices fell, thus exacerbating the decline.
Other actors were to add to the turbulence. The heavy selling of stock index futures in the market maker centred Chicago markets allied with a log-jam in executing orders on the relatively less liquid specialist based New York Exchange caused the S&P 500 future to trade at a substantial discount to the underlying index. Computerised arbitrage systems clicked in to correct the anomaly, buying the future and selling the underlying stocks, thus adding to the congestion in New York. This, combined with portfolio insurance selling, created a self-reinforcing cascade which caused the market to drop like a stone.
By mid-Tuesday 20th the New York Exchange was on the brink of meltdown. The only thing that saved the day was that prices had dropped so low that companies opportunistically bought back their stocks.
Portfolio insurance of the sort sold in the 1980’s needless to say has fallen from grace. However the desire to insure portfolios endures. The need is fulfilled by dealers who sell exchange traded and OTC derivatives to fund managers looking for comfort. Unfortunately the undesirable market dynamics persist. It is now the option writers who may sell down the market when things start to slide, as they cover their positions with dynamic hedging strategies.
In the same vein yet another source of instability and equity market volatility is on the rise, credit derivatives. The notional value of credit derivatives has grown from some $200 billion to over $2 trillion in 2002. The British Bankers Association estimates that, excluding asset swaps, the market could reach some $5 trillion by 2005. In particular the single name credit default swap is sold increasingly by insurance companies to banks. In this way banks buy protection against credit default by their corporate borrowers. Thus banks are transferring credit risk from their balance sheets to the insurance companies. The insurance companies in turn use the corporate bond and equities markets to measure and hedge their credit risk exposure. Daily movements in equity and bond prices feed directly into the insurer’s risk models. If a company’s securities prices fall the probability of default is deemed to rise. An insurance intermediary writing insurance on said company will hedge its credit default swap. It could do this by selling bonds if a liquid bond market exists or shorting equities. By selling bond and equity prices down it can increase the assessment of the probability of default - a vicious cycle.
This is the portfolio insurance problem again in another guise. Moving risks from their balance sheets using credit default swaps gives banks more scope to lend for a given capital base, but this has an unintended consequence. It makes public asset markets more volatile.
It seems that financial risk is conserved, it can be moved about but it cannot be eradicated.
It may also be the case that our public markets are like our oceans. They do not have unbounded capacity to take everything we throw into them, nor do they have limitless capacity to be fished.
Certainly modern luminaries are pointing to the dangers of using public markets to dissipate credit risks. They also advise that liquidity risks need to be given more emphasis in trading decisions[26].
Credit default chain
Bubbles and the reasons for them
So what have we established? The efficient markets theory appears to be supported by a strong weight of evidence. In particular, professional fund management performance indicates that it is very difficult to beat the markets as the theory predicts. However the inability of fund managers to beat the markets might be a case of right answer, wrong reason. It may just be that, as Soros implies, there are a lot of mediocre managers, out there. Certainly in the case of LTCM, an increasing emulated model, the poor overall outcome appears to be the result of nearly efficient markets turning resolutely inefficient beyond the partner’s planning horizon. It seems that more conventional active management styles have trouble beating the market whether it be in a near efficient or in an inefficient phase. Increasing churning of active portfolios does not seem to help, and may itself contribute to market inefficiency. It is plain that inefficiency does exist sometimes, and that a minority of professional traders successfully exploit this.
It also appears that arbitrage, although it is an increasing and dominant feature of modern markets, may not be effective in countering mispricing when this occurs on a grand scale in the build-up of a bubble or in a crash situation. In fact the rapid unwinding of arbitrage positions can exacerbate volatility if a shock precipitates market turbulence, or indeed if markets start to fall under their own weight, as was the case in 1987.
The activities of macro traders can also add to volatility.
The assertion that noise trading is countered by arbitrage does not hold up when a market bubble starts to form or when fear driven turbulence takes hold, and EMH does not provide a satisfactory explanation of how markets operate all the time.
Recent research, that has focussed on the conditions that may give rise to bubbles, is illuminating. Some researchers argue that bubbles are, statistically speaking, outliers that deserve their own explanatory models.
The dynamics of bubbles certainly appear to have more in common with human frailties than stark and cold financial models of rational expectations and market equilibrium. I can think of no better description of such phenomena than that offered by J K Galbraith[27], incidentally a fan of Keynes.
Writing about the Great Crash of 1929, a subject on which he is a famous, insightful and ironic observer he recounts:
“In March of 1929 Paul M. Warburg, a founding parent of the
Federal Reserve System and an immensely prestigious banker in his
time, called attention to the current orgy, as he said, of
"unrestrained speculation" in the stock market and added
that were it not brought to an end, there would be a disastrous
collapse. His warning was badly received. It was made clear that he
did not appreciate the new era in economic well- being that the market
was so admirably reflecting; he was said by one exceptionally
articulate critic to be "sandbagging American prosperity."
Less eloquent commentators voiced the thought that he was probably
short in the market.
There was a decidedly more sympathetic response somewhat later that
year to the still remembered observation of Professor Irving Fisher,
of Yale, one of the most diversely innovative scholars of his time.
Fisher said, "Stock prices have reached what looks like a
permanently high plateau." Fisher was, in fact, long in the
market and by some estimates lost between eight and ten million
dollars in the almost immediately ensuing crash.
There is a compelling vested interest in euphoria, even, or perhaps
especially, when it verges, as in 1929, on insanity.
Any long-continued increase in stock prices, such as preceded the 1929
crash, brings a change in the purposes of the participants in the
market. Initially the motivating force is from institutions and
individuals who buy securities (and bid up prices) because of some
underlying circumstance, actual or imagined, that is judged to affect
values…But as a stock-market boom continues, there is
increasing participation by institutions and people who are attracted
by the thought that they can take an upward ride with the prices and
get out before the eventual fall. This participation, needless to say,
drives up prices. And the prices so achieved no longer have any
relation to underlying circumstance. Justifying causes for the
increases will, also needless to say, be cited by the sadly vulnerable
financial analysts and commentators and, alas, the often vulnerable
business press. This will persuade yet other innocents to come in for
the loss that awaits all so persuaded.
For the loss will come. The market at this stage is inherently
unstable. At some point something -- no one can ever know when or
quite what -- will trigger a decision by some to get out. The initial
fall will persuade others that the time has come, and then yet others,
and then the greater fall will come. Once the purely speculative
component has been built into the structure, the eventual result is,
to repeat, inevitable.
There will previously have been moments of unease from which there was
recovery. These are symptoms of the eventual collapse. In 1928 and
through the winter, spring, and summer of 1929 the stock market
divorced itself from all underlying reality in the manner just cited.
Justification was, of course, asserted: the unique and enduring
quality of Coolidge and Hoover prosperity; the infinitely benign
effects of the supply-side tax reductions of Secretary of the Treasury
Andrew W. Mellon, who was held to be the greatest in that office since
Alexander Hamilton; the high-tech future of RCA, the speculative
favourite of the time, which so far had not paid a dividend.
But mostly speculators, amateur and otherwise, were getting on for the
ride. In the spring of 1929 came the initial indication of instability
-- a very sharp break in the market. Prices recovered, and in the
summer months they rocketed up. There was another bad break in
September and further uneasy movements. Then, at the end of October,
came the compelling rush to get out and therewith the crash. No one
knows what precipitated it. No one ever will. A few -- Bernard Baruch
and, it has long been said, Joseph P. Kennedy -- got out first. Most
went down with the mob; to an extraordinary degree, this is a game in
which there are mainly losers.”
Recent fascinating research supports Galbraith’s assertion that what triggers grand market reversals is of lesser importance than the root causes of the bubble formation in the first place. It also draws inspiration from Keynes idea that market price formation is the result of speculative game playing.
The research models markets as evolving communities of heterogeneous, self-organizing and game playing agents.
Rationality now involves second guessing the other players next moves as well as constant experimentation and refinement of winning moves. The cold deductive logic possessed of rational traders assumed by efficient market theories is replaced by inductive logic that more nearly matches our innate abilities.
We are only moderately good at deductive logic. We are, however, very good at seeing or recognising or matching patterns—behaviors that confer obvious evolutionary benefits[28]>. Supporters of this line of thought talk about bounded rationality. In reality we induce a variety of working hypotheses, act upon the most credible, and replace hypotheses with new ones if they cease to work.
Such reasoning can be modeled in a variety of ways. Usually this leads to a rich psychological world in which agents’ ideas or mental models compete for survival against other agents’ ideas or mental models—a world that is both evolutionary, complex and not that safe.
In contrast to efficient markets theories these models are more likely to be recognised by traders as approaching real life. What they demonstrate is that bubble behaviour can emerge spontaneously from the dynamics of the game. No external influences or “news” are required once the game is set in motion. Furthermore the models tend not to settle to equilibrium. If they do, this is a fleeting phenomenon. For the most time markets modeled in this way exist in a sort of dynamic disequilibrium.
Based on such dynamics, one line of research claims to have identified robust precursory signatures in price behaviour in the buildup of a bubble[29]. This can be evident months or even years before the bubble bursts. We are all familiar with the general pattern of up trending and accelerating price changes as a bubble forms but it is only apparent (at least to most of us) after the event when the critical point is reached and prices crash. Importantly, researchers have found that the bubble price trajectory appears to be modulated by a wave of increasing frequency as prices peak, a log-periodic signal in fact. This characteristic wave acts like a sort of homing signal that pinpoints the critical point. The build up can be represented mathematically and with the adjustment of a few parameters the formula seems to fit price data from a great many bubbles.
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| Prices of IBM in the run up to the March 2000 sell-off overlaid with predictive signal |
The thesis is that this wave pattern is the result of emergent behaviour between market participants as they apply different strategies. At the simplest level of explanation trend following behaviour may bid prices up, and others who may view the market as overvalued may try to sell the market down. Like some sort of tightly contested tug of war, the competing sentiments move and sway at an increasing rate until, by a group consensus the sellers carry the day and the critical point is reached. This has considerable resonance with Galbraith’s description of the months leading up to the 1929 crash The tell-tale signature has been found in a host of bubbles including the Crashes of 1929 and 1987 and many of the emerging market bubbles. The author of the research observes:
“The October 1929 and October 1987 crashes thus exhibit two similar precursory patterns on the Dow Jones Index, starting respectively 2.5 and 8 years before them. It is thus a striking observation that essentially similar crashes have punctuated the 20th century, notwithstanding tremendous changes in all imaginable ways of life and work. The only thing that has probably changed little is the way humans think and behave.”
Probably the most famous agent based market simulator is the Santa Fe Institute Artificial Markets Model. This has been used to conduct several revealing experiments concerning market dynamics.
Developed by Brian Arthur, John Holland, Blake LeBaron, Richard Palmer, and Paul Taylor, the market consists of a population of heterogeneous agents that buy, sell, and hold stocks and bonds. An agent’s trading decisions are made on the basis of his beliefs about whether the stock's price and dividend is likely to go up or down, and those beliefs are determined by a set of market forecasting rules that are continually being assessed. Over time an agent's set of market forecasting rules evolve under the action of a genetic algorithm (GA). The rules that work best survive, the ones that fare less well are discarded.
One experiment[30] showed that varying the rate at which individual agents learn new investment strategies reveals two different kinds of overall market behavior. If investment strategies evolve slowly, i.e. when the GA-invocation interval is large resulting in forecasting rules evolving relatively slowly, prices are more stable; evolved forecasting rules are simple; levels of technical trading are low; trading volumes are low; and there is little evidence of nonlinearity. The behavior resembles the predictions of the efficient markets theory, and is termed the "Rational Expectations Regime."
On the other hand, when the GA-invocation interval is small, it results in forecasting rules evolving relatively quickly, and the variance of the price time series is relatively high; the evolved rules are complex; levels of technical trading are high; trading volumes are higher; and there is strong evidence of nonlinearity. This regime is called the "Complex Regime."
Another experiment conducted by Joshi, Parker, and Bedau involved game theory[31]. The researchers attempted to find the optimal rate at which traders should revise their repertoire of market-forecasting rules using the GA. They showed that the market has only one symmetric Nash equilibrium[ii], and that this lay in the "Complex Regime." They concluded that the Nash equilibrium was "sub-optimal" because in this regime the wealth accumulated by agents was lower than in the Rational Expectations Regime, the asset was riskier (prices were less stable), and the market was noisier.
These results suggest that financial markets can end up in situations analogous to a multi-person Prisoner's Dilemma game[iii] in which frequent revision of forecasting rules can lead to increased price variability and thus reduced overall earnings. Keynes would have loved this model!
Echoing Keynes insights, this line of research argues that asset markets have a recursive nature in that agents’ expectations are formed on the basis of their anticipations of other agents’ expectations, which precludes expectations being formed by deductive means. Instead traders continually explore expectational models, buy or sell on the basis of those that perform best, and confirm or discard these according to their performance. Thus individual beliefs or expectations become endogenous to the market, and constantly compete within an ecology of others’ beliefs or expectations. The ecology of beliefs coevolves over time.
Computer experiments along these lines explain why traders often believe in such concepts as technical trading, “market psychology,” and bandwagon effects, while academic theorists believe in market efficiency and a lack of speculative opportunities. Both views are shown to be correct, but within different regimes. Within a regime where investors explore alternative expectational models at a low rate, the market settles into the rational-expectations equilibrium of the efficient-market school. Within a regime where the rate of exploration of alternative expectations is higher, the market self-organizes into a complex pattern. It acquires a rich psychology, technical trading emerges, and temporary bubbles and crashes occur.
A dangerous walk
The instability of asset prices bears the hallmark of catastrophic behaviour[32]. Originated by the French mathematician Rene Thom in the 1960s, catastrophe theory provides a useful means to explain, in qualitative terms, the dynamics of systems characterized by sudden shifts in behavior arising from small changes in circumstances.
Using the jargon, catastrophes are bifurcations between different equilibria.
Catastrophes can be classified according to how many control parameters are being simultaneously varied. For example, if there are two controls, then one finds the most common type, called a "cusp" catastrophe.
A cusp is easily pictured by scrunching up a piece of paper as shown below.
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| A two factor cusp |
The resulting topology provides a setting in which a class of catastrophic scenarios can be described. If we imagine the topography to model, for example, a physical landscape, we can see a cliff-like structure (a cusp) rising out of undulating slopes. It would not be advisable to wander about this landscape in the dark!
It can be enlightening and challenging to try to explain the gyrations of asset prices in financial markets in terms of a two factor cusp model. Can a plausible story be worked up? What two factors could be central to the plot? My first thoughts were greed and fear. Drawing inspiration from our sugar stock story one can depict greed as the factor which caused Thomas W Lawson to buy 20,000 shares of his own company in an attempt to bid up the value of his stock. Fear of missing out on a good thing brought others in to feed the buying frenzy. It was also fear of great and instant losses that drove the shorts to scramble for cover, which increased the buying panic.
On further reflection I have selected speculation and market sentiment. It seems to me that excessive speculative activity in the market is a useful proxy for greed, the pursuit of something for nothing, the quest for a free lunch. Market sentiment also seems to be a powerful factor. It is unlikely that Mr. Thomas would have succeeded in bidding up the price of his sugar stock if market sentiment had not been, to use his words, “rendolent of opportunities.” Crowd behaviour seems to play a significant role in market behavior. Sentiment and the madness of crowds seem to be intimately entwined. When the market is, as it were, charged up through speculative fervour, it only needs a slight change in sentiment to nudge it in one direction or the other.
The thesis we are exploring therefore is that catastrophic behavior of asset prices in capital markets can be described by moving about cusp topography with speculation and market sentiment as defining factors.
First let us walk a path where market speculation is low, and market sentiment varies between bearish and bullish. This path suggests that asset prices are not overly dependent on market sentiment; the journey appears to be safe with no surprises in store. In the real world if companies perform well and risk adjusted equity returns beat high quality bond returns, money flows to equities and a bullish stock market sentiment prevails. Prices may trade at a slight premium to the discounted sum of future equity returns. If prices start to lose touch with fundamental values they will be corrected by investors of the Ben Graham School, who sell from their portfolios stocks which they consider are overpriced. Except for this, stocks are sold only when individuals require cash for such exigencies as their daughter’s wedding, or if bad news leads to a view that fundamentals my take a turn for the worse Market churn is low. Buy and hold strategies prevail. Most of the returns come from dividend income rather than capital gains. Companies are safe in the knowledge that they can tap the market at most times, so new issues come in a steady stream driven by business needs rather than market cycles. If bad news applies to the market as a whole, and expected returns fall below high quality bond yields, bearish sentiment may cause stock prices to be marked down across the board and a mass movement of money from equities to bonds. Equity prices will trade at a discount to fundamental valuations, but falls will be limited by bargain hunters again of the Ben Graham School. Generally market prices smoothly adjust to fundamental values which, often as not, tend over the long term to trend steadily upwards, the very basis for traditional buy and hold strategies. Market movements tend to reflect news relating to changes in fundamentals. In the absence of such news, changes in market direction are not predictable, in the best tradition of the Efficient Markets Hypothesis.
Of course these are not the markets we know.
Today’s markets are characterised by a great variety of speculative activities some ingenious, some more akin to Thomas W Lawson’s endeavours, but all designed to achieve more, often a good deal more than average returns. Achieving more than average returns means taking on commensurately more risk as surely as night follows day. Risk can be moved about but it appears to be conserved. Speculative activities can charge the system up with risk. They can also act like unconstrained positive feedback causing runaway prices or threatening to block the system. Positive feedback is not a good thing. Unchecked it can reap havoc.
So what qualifies as speculative activity?
We have seen that no less a leading light than John Bogle has labeled mutual fund managers as speculators, pointing to the increasing churn rate of mutual fund portfolios.
Given the huge assets in their care, this is worrying. Well at least we say to ourselves passive funds are a stabilising force. But on reflection is this really the case? Are not such fund management styles merely trend following on a grand scale? The manager who invests in say the S&P 500 is delegating stock selection to a committee at Standard and Poors who meet infrequently to consider additions and deletions to the index using very basic and unchanging criteria. Like a cloistered club new members join when old ones die. New members, by association, can gain instant credence which is reflected in a substantial rise in their stock price, the so called index effect[33].If the index trends up money flows into the funds, more stock is bought and the upward movement is reinforced. If the index trends down, money is withdrawn, stocks are sold mechanically so accelerating the downward movement.
What about the huge and burgeoning arbitrage trading by the big investment banks and hedge funds? As we have seen, because of the huge leverage involved and other technicalities, these activities can act more like destabilising positive feedback, than restoring forces, especially when there is a shock to the system.
The big highly leveraged macro and directional traders can also be a source of positive feedback.
Finally the sellers of portfolio and credit risk insurance can also be expected to act like positive feedback traders as they use public markets to dynamically hedge their risks
With all this destabilising feedback it is not surprising that there are pricing inefficiencies. Of course gross market inefficiency and volatility provides the spur for technical and trend following traders. Yet more positive feedback!
In all of this the minority of buy and hold traders seem to be awash in a sea of speculation.
Whilst speculation has always been an inherent part of the capital markets game, it does appear to be growing by leaps and bounds, and has indeed become an intrinsic and institutionalised part of today’s large and organised markets.
Let us take another walk. This time assume that we have lived through a long period of bearish sentiment due to previous market excesses. There has been a severe loss of capital for many and markets have been for a long time stagnant and depressed. Now painful memories are beginning to fade. The economy has bounced back and commerce again is on the rise. There is feeling of a new era where exciting and invigorated companies have risen from past ashes. New business models abound. Infinitely improved technologies work their magic. Fresh and hungry investors are about. Imagine it is May and the beginning of bullish sentiment is in the air.
Like it or not we will find that we are drawn to a well trodden path. We are driven somewhat involuntarily up a steep incline, a consequence of our market designs. Prices rise quickly out of stagnation, bullish sentiment is reinforced. The long dormant smart money jumps on board for the ride. The macro traders lay their bets. Large amounts of ordinary money flow into equity mutual funds and is mechanically allocated to re-inflate sagging benchmarks. The indices perk up. The pundits perk up. The S&P 500 graph shoots up. Technical traders lay their rules on the graphs and project the future, an upward trending line. More funds flow to the rising icon in a virtuous circle. The machine starts to come alive. 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 for stock increases and is met by a ready supply on easy terms, backed by collateral of rising value. The ready and unconstrained flow of paper fuels rampant and pent-up M & A activity. The profits fuel proprietary trading. Bank lending rises sharply. Banks lay off their lending risks by buying credit derivatives from the big insurers. Paper millionaires pour money into hedge funds. Intricate webs of bets are put on. Hedge funds become an asset class. Paper fueled shooting stars join the benchmark indices. Active mutual funds churn their inflating portfolios at an accelerating rate in an effort to beat the benchmarks. Stock market volumes rise to new highs. Profit takers come out in force. Volatility increases. The volatility traders come out in force. Volatility increases yet more. The hazard rate increases. Price rises accelerate. Late comers join the walking throng. Early arrivers nervously start to retrace their steps.
We are now in a very dangerous place.
Market sentiment is rampantly bullish and the speculators are out in force. The market is well and truly pumped up with risk. It is like a tightly coiled spring. Prices have lost touch with any rational measure. A huge amount of speculative capital is chasing ambitious and unsustainable returns.
Our map indicates that sharp and sudden movements in asset prices can occur if market sentiment drifts in a bearish direction.
The smart money starts to sell futures in earnest. The futures markets trade at a slight discount to the cash markets. The arbitragers buy futures and sell stock into currently liquid markets. They trade large. The cash markets start to trend down. Disbelief is no longer in suspension. Market sentiment moves sharply in the bearish direction. The shorts come out in force. Asset prices now trend sharply downwards. Margin calls increase as collateral is marked to a falling market. Enforced selling ensues. Fear driven trading infects all asset classes in all parts of the globe. There is no place to hide. Spreads widen across the board. Liquidity black holes abound. The indexed mutual funds sell the market down. The big investment banks dynamically hedge portfolio insurance exposure and sell the market down. The big credit default insurers sell the market down. Distressed hedge funds sell the market down. Some blow up. Liquidity now evaporates even in the blue chips and gilts. Prices gap down. A selling frenzy turns to outright panic to sell out at all costs. We cannot get off what has now become a route-march to oblivion.
Memories fade. New investors set forth again. This time the walk has become a mechanised roller coaster ride.
It is fast and thrilling…
The sage Keynes is looking down on us and smiling wryly.
[i] It should perhaps be noted that the large returns were made at a time when the market generally was on the rise. For example the S&P 500 returned some 33% in 1997.
[ii] The outcome of a game that occurs when player A takes the best possible action given the action of player B and player B takes the best possible action given the action of player A.
[iii] Cooperation is usually analysed in game theory by means of a non-zero-sum game called the "Prisoner's Dilemma" (Axelrod, 1984). The two players in the game can choose between two moves, either "cooperate" or "defect". The idea is that each player gains when both cooperate, but if only one of them cooperates, the other one, who defects, will gain more
[1] The Volatility of Financial Markets, Speech by Ms Tumpel Gugerell, Member of the Executive Board of the European Central Bank, July 2003.
[2] John Maynard Keynes, The General Theory of Employment, Interest and Money, Chapter 12. The State of Long-Term Expectation, 1936.
[3] The Behavior of Stock Market Prices, Eugene F Fama, Journal of Business, January 1965.
[4] The Analysis of Economic Time Series, Maurice G Kendall, Journal of the Royal Statistical Society Part 1 1953.
[5] Spectral Analysis of New York Stock Prices, C W J Granger and O Morgenstern, Kyklos, 16 (1963)
[6] The Random Walk Hypothesis of Stock Marker Behavior, Michael D Godfrey, C W J Granger and O Morgenstern, Kyklos 17, 1964.
[7] Price Movements in Speculative Markets; Trends or Random Walk, Sidney S Alexander Industrial Management Review, May 1961.
[8] "Proof that Properly Anticipated Prices Fluctuate Randomly", Paul A Samuelson, 1965, Industrial Management Review
[9] For example see Efficient Capital Markets; A Review of Theory and Empirical Work, Eugene F Fama, Journal of Finance Volume 25, Issue 2, May 1970
[10] ICI fund management handbook
[11] Beyond Greed and Fear, H Shefrin, Harvard Business School Press, 2000
[12] The Performance of Mutual Funds in the Period 1955-64, Michael Jensen, Journal of Finance May 1968.
[13] On Persistence in Mutual Fund Performance, M Carhart, Journal of Finance 1997.
[14] Speech before the Harvard Club of Boston, the Harvard Business School Association of Boston, and the Boston Security Analysts Society Boston, Massachusetts January 14, 2003
[15] The Warren Buffet Portfolio, Robert Hagstrom, Wiley 1999.
[16] The Alchemy of Finance, George Soros, Wiley, 1987.
[17] Irrational Exuberance, Robert J Schiller, Princeton, 2000.
[18] BIS 73rd Annual Report
[19] For example see Beyond Greed and Fear, Shefrin.
[20] Prospect Theory and Asset Prices, Quarterly Journal of Economic, Feb 2001, Barberis, Huang, Santos.
[21] For example see When Genius Failed, R Lowenstein, Fourth Estate, 2002.
[22] Courtesans of Capitalism, Peter Temple, Wiley 2001.
[23] Implications of the Growth of Hedge Funds, SEC September 2003.
[24] FSA Financial Risk Outlook, 2004
[25] For example see Capital Ideas and Market Realities, Bruce Jacobs, Blackwell, 1999.
[26] For example see Liquidity Black Holes: Understanding, Quantifying and Managing Financial Liquidity Risk, Risk Books December 2003, edited by Avinash Persaud. Also see Where have all the Financial Risks Gone? Gresham College Lecture by the same author, November 2002.
[27] John Kenneth Galbraith , The Atlantic Monthly; January, 1987; The 1929 Parallel; Volume 259, No. 1; pages 62-66. See also The Great Crash, 1929 , Boston Houghton Mifflin Co, and A Short History of Financial Euphoria, Penguin Books 1990.
[28] Inductive Reasoning and Bounded Rationality (The El Farol Problem), W. Brian Arthur, Stanford University and Santa Fe Institute Published in Amer. Econ. Review (Papers and Proceedings), 84, 406, 1994.
[29] Why Stock Markets Crash, Didier Sornette, Princeton Press, 2003.
[30].Asset pricing under endogenous expectations in an artificial stock market. Arthur, W. B., J. H. Holland, B. LeBaron, R. Palmer, P. Tayler. 1997. In The Economy as an Evolving, Complex System II, W. B. Arthur, D. Lane, and S. N. Durlauf, eds., Menlo Park: Addison-Wesley. Also published as Santa Fe Institute Paper 96-12-093. See also Building the Santa Fe Artificial Stock Market, Blake LeBaron, Brandeis University, June 2002.
[31] An Explanation of Generic Behavior in an Evolving Financial Market, Shareen Joshi, Departments of Mathematics and Economics, Reed College, December 14, 1998.
[32] For example see Catastrophe Theory, Alexander Woodstock and Monte Davis, Penguin Books, 1980.
[33] See for example The Mysterious Growing Value of S&P 500 Membership Morck R and Yang F (2002), NBER working Paper No w 8654.
