Mr Galton’s Machine

From my book Financial Speculation

Francis Galton was the epitome of the wealthy upper class Englishman during the Victorian era, a polymath with a high degree of curiosity and a private income, he spent his entire life investigating and researching new ideas. His range of interests was diverse enough to encompass criminology, where he helped pioneer finger-printing techniques, weather patterns, where he devised the classification of cyclonic and anti-cyclonic weather systems; and he even conducted experiments to test the efficacy of prayer – though his results were not very encouraging on that front. And of more direct relevance to our interest in finance he spent a great deal of time looking at statistics and probability.

Whilst looking for ways to enliven his lectures on statistics Galton developed in the mid 1870’s a simple mechanical device he named a quincunx. The apparatus which he first demonstrated at the Royal Institution in London comprised a wooden box with a glass front and a funnel at the top. Metals balls of equal size and weight are dropped via the funnel to fall through a number of rows of pins spaced equally in the box. Each row was offset from the previous row so that the pins sat between the gaps of the row above. These pins then deflect each falling metal ball to the left or right with equal probability and at the bottom of the box each metal ball finished by falling into one of a number of compartments. After a number of metal balls are dropped through this device a pattern in the compartments below starts to emerge. The balls start to describe a binomial distribution which with a large number of rows approximates to our previous curve – the normal distribution.

With this device Galton sought to demonstrate that seemingly random events or facts do in fact tend to arrange themselves into a distribution. So it would appear that the distribution curve we examined earlier is a natural occurrence that appears even when seemingly random events take place. Galton went on to do a large number of experiments that looked to see if in fact distributions did appear in natural life. His researches conclusively proved that they do, and furthermore the outcomes were often quite close to the normal pattern described by the quincunx.

At this point we can depart from Francis Galton but use his ideas and clever box like device to look at financial derivatives. Derivatives have been around since finance began, some claim there is a reference in Aristotle to an option like instrument, and certainly by the Middle Ages very crude option like transactions were being executed. As we saw earlier with the story of Russell Sage, by the second half of the nineteenth century stock options were starting to emerge as a recognised, although specialist and niche, financial market. Of course options really took off with the publication of the Black-Scholes formula in 1973, which for the first time sought to accurately value options. The financial de-regulation of the late 1970’ and early 1980’s really boosted derivative trading and nowadays the global market has expanded massively. It is estimated by the latest (June 2008) Bank for International Settlements report to have an outstanding nominal value in excess of US$680 trillion. This is a truly eye watering number. To give you an idea of just how large – A trillion (being one million millions in modern usage) can be expressed in a number of ways – there are a trillion seconds in 31,710 years!

The Black-Scholes formula was just the start of a series of equations that sought to value and price options, and still remains one of the best known in the business, to calculate it, we need the following inputs:
1. The time to expiry of the instrument
2. The asset price; i.e. the stock, commodity or currency price
3. The strike price
4. The implied volatility of the instrument
5. The so called risk free interest rate – typically the yield on low risk short maturity government securities. E.g. 90 Day Treasury Notes

From these basic inputs we can get an option valuation, but it comes with a number of conditions and caveats, namely:

1. The asset price follows a log normal random walk
2. The risk free interest rate and volatility are known functions of time
3. No transaction costs in hedging portfolio
4. No dividends paid during the life of the option
5. No arbitrage possibilities
6. Continuous trading of underlying asset
7. Underlying asset can be sold short

A number of important problems strike one about these conditions; first and foremost an enormous assumption is being made that the underlying instrument is continuously traded, this of course ignores that most dangerous of foes – lack of liquidity. Secondly in the real world, brokerage, bid offer spreads, slippage (effectively the monetary cost of less than perfect liquidity) and taxes all loom large. In fact as we will see these charges can be quite punishing. So whilst Black-Scholes gives us the first serious approximation for pricing options risk it is hemmed in by a number of limitations. In fact it is probably true to say that it is more important to understand these limitations than to necessarily worry about the underlying maths. Risk assessment is not just about cold equations, the judgements we make about the softer more fuzzy elements of the decision process are often much more important. It is unlikely the maths alone will protect us – we have to know the context in which the result was calculated.

quincunx

But let us go back to Mr. Galton’s box with its pins and metal balls, as it can produce a useful mental picture with which to consider and understand option pricing. Consider Chart Nine. The position of the funnel represents the current price of the underlying instrument; move it to the left to decrease the price; move it to the right to increase the price. Every row of pins is an increment in time, one day say, and the number of rows represents the time to maturity. The horizontal distance between neighbouring pins represents the volatility; moving the pins further apart increases volatility; moving them together decreases volatility. The figure shows the passage of one ball as it bumps down onto a pin and has to go either right or left, before falling to the next row. This represents the daily price movement of the underlying instrument and the movement of the option by one day towards maturity. At the bottom, the ball will drop into a box. The boxes are divided into two groups by the strike price. The boxes to the left hold winners for owners of put options; the boxes to the right hold winners for owners of call options. In each case, the boxes furthest from the strike price are the most valuable. Increase the strike price and there are more put winner boxes; decrease the strike price and there are more call winner boxes. When we drop a large number of balls, they finish up (expire) in the boxes distributed in the bell shaped curve that we met earlier. For the mathematically inclined, this requires us to deal in logarithms of prices, rather than the prices themselves, but ignoring this does not affect overall picture.

Many aspects of option behaviour can be understood from this model. In the example in the figure, the put option is ‘in the money’, while the call option is ‘out of the money’. You can see that adding more rows of pins (increasing the time to maturity) increases the number of winners that are far from the strike price, so generally increasing the value of the option. Increasing the distance between the pins (raising the volatility) has the same qualitative effect. The model also highlights the arbitrary nature of the underlying assumptions of the Black-Scholes formula. For example, why should all the pins be equi-distant?

 

Now in a way this is all just a parlour game it’s not meant to be a serious substitute for Black-Scholes or any of the myriad successor mathematical formulae for options and alike; but it does provide us once again with a quite vivid picture of option risk and a broad idea of how prices react in the three dimensional landscape of derivatives risk.

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The Illusion Of Control

Experienced investors know that that markets are often difficult to read and can be very fickle, also they can be extremely unforgiving if our judgement is not spot on. We also know that humans have a very strong desire for certainty; the research by Abraham Maslow on The Hierarchy of Hygiene factors demonstrates how certainty plays an enormous part in our lives and is an important component of our well-being.

So the investor is faced with two incompatible forces, the inherent uncertainty and instability of the marketplace and a deeply held personal desire for certainty, comfort and predictability. This tension is absolutely central to how we address markets, their volatility and perceived risk. The most common “coping strategy” in such circumstances is to adopt a mode of thinking called The Illusion of Control. By this I mean we seek ways to convince ourselves we are on top of things, and that we can, through superior skill, knowledge and self-assessed ability stay on top of any sudden shocks or volatility. In fact we often fool ourselves into believing that we can start to influence events or at the very least we “knew that was going to happen”.

One tell-tale sign of trouble is that we tend to underestimate the role of chance in human affairs and to wrongly believe games of chance to be games of skill. Many readers will know of the Gambler’s Fallacy and the false hope of the winning streak or hot hand in a game of chance. Here we try to super impose our own internal certainties on to outside events – in this case (gambling) where the game is specifically designed for us to lose money! Surely we know you cannot predict the next in the series of heads or tails – but a long run of say heads can create an overwhelming belief the next time it “must” be tails!

Also we should note that both novices and those who believe themselves expert in a field are all prone to overestimate their own abilities – research shows novices’ ignorance often blinds them to their lack of expertise, and equally galling, the expert in a field is often very unwilling to change their views, even in the face of solid facts!

So what can we do to try and straighten out our investment decision making?

The key lies in two characteristics we need to develop – firstly to acknowledge that we have no special insight when looking at a financial market – we may of course analyse a forgotten corner and therefore have more information than our competitors, but that doesn’t mean that we have an unassailable advantage – maybe just a small edge. That edge can be important but only if we keep strong controls in place on allocation size, develop a sensible stop loss strategy and realistic expectations of profit targets.

Secondly we are all experts at only hearing what we want to hear – the market place is full of information, news, rumours and gossip and we can fall into the trap of cherry picking this to find the facts that suit our position. One way to overcome this maybe to just reduce the overall amount of information we try to read and process – this is really a case of where less is more.

Three Thoughts for Investors
1. Guard against over confidence – this usually shows itself in taking greater and greater risks. Investors should always use strict portfolio management rules. The temptation to think this is “The Big One” can be fatal – fortunes are not make (and kept) by single dead certain investments. Your aim should be to invest in consistent risk adjusted size and to aim to win on a ratio of 2 to 1. In time this would be an extremely successful strategy.

2. Don’t confuse accuracy of information with greater performance. A lot of behavioural research points out that investors get plenty of additional confidence and comfort from more and more information but there is little evidence that it improves the accuracy of their predictions.

3. Most bad investment decisions and behaviour can be really helped by keeping an accurate decision journal – this is a difficult discipline, but writing down one’s reasons for an investment and keeping accurate records of what went right and crucially what went wrong can be a powerful tool in focussing the mind, and reminding ourselves we are not Masters of the Universe!

The Sticky Balance

Even a cursory glance at how financial markets digest information quickly shows that they are erratic, and prone to either over or under reaction. The information process is not smooth and continuous; new facts, opinions, rumour, and news usually enters the market in a haphazard manner, after which the market reacts. This usually happens in a rather jerky and ill-defined way, this is where the information inefficiencies lie; and from these inefficiencies the bright, well informed and, yes once in a while the lucky, can profit.

One way to consider how information hits the market is to imagine a set of balance scales, with the pans holding piles of information; one pan holds any positive information about the market, the other anything negative. News, rumours and plain facts drop constantly into one or other of these pans, leading to an overall balancing position that represents the net emotion and thinking of the market. But there is a twist, our imaginary scales are sticky, so don’t always react straightaway when a new piece of data or information is dropped into one of the pans. Then quite suddenly the scales may shift as the ‘stickiness’ gives way. This is pretty much what happens when markets try to digest news, there is no smooth information flow; at the risk of stating the obvious the trick is to try and anticipate when the scales (i.e. the market realisation) suddenly tip and change.

The news and information is not important in itself, it is market the reaction, or lack of, that is the key. In markets it is often the tiniest movement or change, the lightest of last straws on the camels back if you like, that sets forth the cascading market move.

Prediction & The 2006 World Cup

Back in 2002 Brazil won the World Cup, which is exactly what was expected. Why, because they were the favourites? Well no actually they weren’t, in fact there were other much more fancied teams, but all of these crashed out of the competition fairly early on. But of course Brazil were bound to win the cup; it was in the numbers. What? Well in the few weeks leading up to the competition in the Far East, somebody noticed the following little relationship:
Brazil had previously won the World Cup in 1994, and before that in 1970. If you add 1994 to 1970 you have a total of 3964.
Argentina won the World Cup last in 1986, and before that in 1978. If you add 1986 to 1978 you have a total of 3964.
Germany last won the World Cup in 1990, and before that in 1974. Yes if you add those numbers together you once again get 3964.
Now for the clever (dare one say predictive) part. Applying this formula (which has been right three times before) we can take the total of 3964, deduct 2002 for this year’s competition, and get the answer 1962. Clearly whoever were champions in 1962 would win in 2002. Well Brazil won in 1962 and of course did so again this time! All of this calculation (coincidence and wishful thinking more like) came crashing down with the results of the 2006 competition. Using our trusted system (!) we could have calculated that Brazil should have won again – but unfortunately Italy ruined things by lifting the trophy.

So what’s going on with this little formula? Well in fact very little. It’s just a very nice example of coincidence, nothing more; no supernatural force is guiding the destiny of World Cup winners, the results above may just be a fluke, but they are also extremely selective. Of course it’s hard not to be impressed by the initial run of success for this little formula, but in doing so we are forgetting some very important factors. The data above is a very narrow selection, there are plenty of examples where the formula just doesn’t work, and of course as there have only been seventeen World Cup competitions, the data sample is just too small to be meaningful. Once again the human mind is impressed by statistics that are in fact insufficient and therefore probably unreliable – as was neatly demonstrated by the 2006 outcome.

Large amounts of academic research has shown time after time that we are over impressed by coincidences. We place too much faith in seemingly amazing coincidences when in fact many such events are far more commonplace than we imagine. Given the mindset of financial markets it is not surprising that many events are given undue importance or attention because they are seen as significant when in fact they are merely coincidences. It is more interesting and impressive to reel off an amazing relationship in the marketplace than to coolly stand back and see that it was just a coincidence with no serious meaning. As we observed earlier the market is gripped by meaning and relevance; events are always supposed to happen for a reason or an underlying motive. The term coincidence is rarely if ever heard in the market; it is simply not recognised as a legitimate explanation for any market move. Chance is given little house room in such an atmosphere.

Hope, Mope and Dope

We are usually taught that hope is a virtue, but in the unforgiving world of financial markets it can be a curse. When we are reduced to “hope”, it’s an admission that our investment discipline is starting to slip. Experienced investors will recognise that this also the flip side of the equally dangerous emotion of “excitement”. Let me explain.

Conventional wisdom states markets are driven by greed and fear – but I disagree. In fact they are driven by fear (on the way up) and hope (on the way down). The excitement element is the rocket fuel that drives the fear. How come?

Well let’s firstly consider a strong bull market in stocks; as the trend strengthens more and more investors pile in, previously cautious types join in as they fear missing out. After all if everyone is making money why not me? Egged on by market pundits, economists chartists et al – the fear of missing out on future spectacular gains and its accompanying excitement is just too much. Then curiously when there is no fear left in the market – prices can only go up from here – we are usually at the very top. Having climbed the wall of fear there is only one way to go – down.

When markets are on the slide its Hope that is the dominant factor – all those small losses start to snowball and investor’s instead of cutting their positions start hoping, perhaps even praying that things will turn around. This is the slippery slope leading to losing positions and in some extreme cases spectacular rogue trader fiascos. Only when all hope is extinguished and all the towels have been thrown in, can markets make a bottom and the trend change.

With this insight I think we can start to see how bubbles & crashes manifest themselves. In the downward spiral that is hope the most toxic effect is it can freeze our ability to act. We just can’t bring ourselves to cut the losing position (“after all it may come back, and I’m sure the market is wrong”). Once this spiral starts to take hold of an individual trader there are some tell-tale signs. We almost immediately lengthen our time horizon (“ohh it will recover in time”), we fail to place, or even worse, cancel stop loss orders (“I don’t want to be selling at the bottom”) and we filter out all the news and analysis around us that is contrary to our view. We become experts at only listening to news that suits our (losing) position and blame everyone except ourselves. (“The market is full of idiots!”).

Worse still extensive behavioural research suggests we feel the pain of losses at around twice the rate we feel the satisfaction of any gain. That pain paradoxically is one of the factors that keeps us clinging to losing positions. Although we feel the pain with every tick against us we convince ourselves if we can only just get back to the opening level we will have triumphed and will feel a genuine rush of relief and even ecstatic reactions. It’s the hope we can avoid that pain that destroys our rational investment plans and actions.

Will we ever learn? I’m doubtful!

Six Books for Summer

With the days getting longer and summer hoving into view here are six books about decision making and risk taking that I think will stimulate and entertain.

Against the Gods: The Remarkable Story of Risk by Peter Bernstein

The Mystery of Overend and Gurney: Adventures in the Victorian Financial Underworld by Geoffrey Elliott

The Wiki Man by Rory Sutherland

Why Information Grows: The Evolution Order from Atoms to Economies by Cesar Hidalgo

Anti-Fragile: Things that Gain from Disorder by Nassim Nicholas Taleb

Butterfly Economics: by Paul Ormerod

 

Brittle New World

It is commonplace to observe that we live in an “ever more connected” world, but are we reaching a point where we are exposed to serious risks by being over-connected?

The history of human progress illustrates how many of our greatest breakthroughs have been through advances in communication and the desire to link up, whether as individuals or organisations. From printing to the telegraph, to flying and the ability to transmit data around the globe in a flash – all have advanced trade, wealth and a general feeling of progress. But now we seem to be on the cusp of a myriad of technologies that will massively increase our connectivity, and also with the potential for serious risks if not disasters.

In little more than 30 years the internet has grown from a small exclusive network to an all pervading channel for much of our lives. For the first time in human history we can now connect to a vast global network – already half the world’s population is on the net, and this will only increase. At first this connectivity brought the usual risks associated with communication; operational failures, exposure to potential fraud and the need to invest heavily in new technology, business systems and knowledgable staff. But now the risk profile has subtly changed, the network itself, whilst a carrier of great efficiency and potential wealth, is also a risk itself.

The simple diagram below shows the danger of “over-connectivity”. Here we can see as connections increase in a network, it becomes more resilient (moving from randomness to organisation) however diminishing marginal returns eventually kick in and the network becomes stressed, brittle and ultimately prone to complete collapse. We can think of this a bit like have too many dominoes to closely together – so if one domino should fall?

complex

For those involved in risk taking and decision making, the study of Complex Systems science is going to be an important element in understanding and mitigating these future risks. Complexity looks at networks and their agents and crucially seeks to understand the flows around the network and how small changes can have very large effects. Many of our new business networks whether electronic systems, management systems or actual infrastructure (eg power supply) are now at risk of moving from stable resilience to being stressed and vulnerable. Whether it be risks of an “electronic hurricane” from cyber attacks or the unthinking connections being rolled out in the “Internet of Things” we need to be aware of the consequences.

So what to do?

Policymakers, military planners, business people and individuals need to have a much clearer idea of networks and their inherent weaknesses, and their own exposures to networks that might be overly connected or overly optimised. Far too many organisations have no deep understanding of their own networks let alone those of others to which they are exposed. This is particularly true where firms have merged and there is no end to end complete analysis of the business. Network resilience testing should be the core of operational risk management and using the new analysis techniques that are coming from biology and physics via Complex Systems science.

Sensible mediation can be pretty straightforward, It really is a case of building in gaps and circuit breakers into any system…these come however with a cost (in both monetary and short term efficiency terms) but are essential to avoid heightened vulnerabilities. Whether we are planning large complex networks or happily hooking up our fridge to the net this whole area of network resilience  is becoming of vital importance.

Suggested Further Reading

The Tangled World: Understanding Human Connections, Networks and Complexity   Gerald Ashley & Terry Lloyd     Harriman House 2011

Positive Linking: How Networks Can Revolutionise the World   Paul Ormerod Faber & Faber 2013

Risk Management – What Really Matters

This a summary of a keynote speech I gave to a conference of African Central bankers in Johannesburg, looking at what really matters in risk management.

A central question when developing a risk management strategy has to be: “Do you manage risk or just measure it?” Ironically, risk management could be said to have been one of the major contributors to the financial crisis, through the concept that financiers believed they could take on additional risk because their risk management systems had become so much more sophisticated. The more mathematical or formulaic approach to risk management has simply proven that models can never replace personal judgment.

The key to risk management is risk ‘identification’ which proposes that instead of using ever more mathematical concepts commonplace in finance one should rather look at what finance can learn from other disciplines. While diversification is a central theme of any reserves management programme, regulators may have given insufficient consideration to the fact that globalisation, hitherto typically seen as a positive factor had in fact produced some important negative factors such as unexpected convergences. These potentially include convergence of regulators and rating agencies, the commoditisation of information systems and of information providers. De facto, this results in not as much diversification occurring as central banks or fund managers had anticipated.

It results in narrowed thinking – if everyone uses the same analytics and systems, they are probably all coming up with the same trading strategies which has the effect of increasing risk when users think they are lessening it. It brings about unexpected correlations across unrelated markets. In effect, it reinforces the ‘herd instinct’ at critical times of crisis, when it is least wanted. In fact, growing regulation tends to worsen this factor: new Basel rules may simply be bringing about new levels of herd mentality and potentially increasing volatility rather than reducing it.

What experience has taught is that as connectivity increases systems become more resilient – but only up to an optimum point. As things become too connected (as today) the resilience tends to decrease in the absence of ‘fire breaks’ in systems. This in turn increases turbulence and volatility. The serious systemic risks of such a highly connected world are often invisible and unexpected. Each new crash is completely unheralded and all the vigilance in the world has hitherto not been able to prevent them. What it requires is a close look at all the linkages in the system, otherwise known as Complexity Science – thinking outside the box at linkages and the various networks organisations have.

The answer may be for risk management to become less formulaic and more judgmental. Central banks establishing risk management systems should by all means employ the traditional tools always used – but not omit personal judgment. African central banks may benefit from the mistakes made by their colleagues in developed countries – but one rule to learn well as don’t over-rely on tools.

Chartists Economists & Gurus – Part Two

A second extract from Financial Speculation

This time a couple easy (but fraudulent) prediction scams!

One quite well known prediction scam, and nowadays totally illegal, is recounted in John Allen Paulos’s excellent book Innumeracy. There are a number of versions of the idea, with Paulos illustrating the idea with stock index prediction. The following version is similar, but with a slightly stronger marketing message as the punter is shown supposed predictive genius across a number of stocks, rather than just a single index.

The would-be expert starts a stock-market commentary business and sends out free predictions to an initial group of say one thousand investors. The commentary tells one half that Stock A will rise in the next month, and the other half that it will fall. After a month the ‘losing’ five hundred are dropped from the mail shot, and the process is repeated to the group that received last months’ correct prediction. Now one half (two hundred and fifty potential punters) are told Stock B will go up and the other half that it will fall. After a few rounds of predictions you can demonstrate to a core number of potential subscribers that you have a 100% percent record, across a number of totally different stocks and stretching out over a number of months! In fact the initial mail shot could be to say ten thousand recipients, after six months, and six correct market calls in a row you would have around one hundred and fifty souls who think you can see every stock-market turn! Of course once subscribers pay up you are faced with trying to predict as successfully (likely to be impossible) or making a run for South America.

Another similar idea, and equally fraudulent, is to set up a service predicting the sex of unborn children. Simply place an advertisement in the national press advertising your service, asking for a fee and (this is the rather unpleasant part of the idea) a small urine sample. In your marketing and advertising blurb you stress that the methods used are ground-breaking, and of course guaranteed. (Everyone loves a ‘guarantee’ and rarely stops to question its value.) If for some inexplicable reason the system fails to predict the sex of the unborn child correctly the customer gets their money back. As all marketing men know, the two most powerful phrases in any business are New and Free. So you have a new product, and whilst it’s not free, it does have a money back guarantee if the service fails to make a correct prediction. So how do you make this work? Easy – Just tell every customer that the child will be a boy – around 50% of your ‘predictions’ will be correct! The twist here is of course is that you are only predicting a known outcome, but the marketing and packaging make it look like you are offering a genuine service.

Chartists Economists & Gurus

Given all the recent controversy about financial forecasting and predictions about the economy; here is an extract from Chapter Six of my book Financial Speculation.

“One inch forward lies darkness” Japanese Proverb

None of us know the future, but of course in financial markets little else is talked about. Will the latest economic figures be good? Is it true the central bank will intervene overnight? What are the chances of a take-over bid? Why is the market lower, when we expect good news next week? What will happen next? This insatiable demand for prognostication has led to a huge industry of analysts, commentators, pundits, experts and alike. In every financial market there is a veritable travelling circus of performers that seek to persuade us that they can guess, surmise and predict absolutely anything and everything – in return for a modest fee.

Much of what is said and written about in financial markets is often dreadful rubbish, but that of course doesn’t matter. As we all know, the truth doesn’t count in finance, it’s what everybody else believes that is important. As a result there are tons of amusing and bizarre stories about how rumours and misunderstandings some times grip markets. Efficient Market types usually label such behaviour as ‘noise’ and that over time random and ill-judged market moves are soon corrected. Certainly much of the ‘noise’ is created by market commentators themselves, who feed the never ending demand for information, opinion and that ultimate Grail – What will happen next? Once again we can see that the rise of cheap global communication has been a major component in this activity. The sheer omnipotence of computers, e-mail, 24 hour business television etc., has caused avalanches of comment, analysis and opinion to rain down on the marketplace. The market is full of information – but of course knowledge is much more rarely seen.

It is against this background that the financial soothsayers operate. Theirs is a business with almost infinite demand, and a client base that is usually very forgiving of their often poor predictive records. There are many different groups to choose from, they have differing methods and techniques, and frequently approach their work with almost religious fervour. Often however, the only thing that truly unites them is their barely concealed hostility towards one another. Again for the sake of good order and to try and maintain some sanity when discussing these would-be financial Merlins, let’s just remind ourselves; none of us know the future.

Chartists – Selling Maps of the Future

Charts have been around for ages – certainly since the days of Charles Dow, the American journalist and publisher who in the late 19th century, was a co-founder of the Dow Jones Index and created The Wall Street Journal. Dow recorded closing prices of thirty major industrial stocks, created the world’s first stock index and then plotted various line graphs of industry sectors, and then over a period of time created a predictive idea called Dow Theory. From this point on the chartists were in business with a vengeance. Bar charts, point and figure charts, market timing cycles, percentage moves, swing charts; a whole plethora of inventive ideas appeared, all long before the computer. In the Orient the Japanese can lay claim to their own system, Candlestick Charts; that have a history going back to the 17th Century rice market; they have also dreamt up the Kagi, Ichimoku (a particularly bizarre format) and Renko charting systems.

If one thinks about it, charts are a curious investment tool; they can only perfectly map the past. Unlike naval charts or say road maps they record a journey that cannot be revisited. Of course a stock can trade at a previous price again, but the time frame will have changed, and the precise price action is nearly always different. So financial charts cannot be used in the same way as road maps, perhaps in a way they are more like a diary of the past events that faithfully records where a share price, or commodity has been; but in truth can give no definitive answer as to the future. You cannot use a stock chart to plan your future investment journey in the same way as you might use a road map to plan a touring holiday of France, though of course many market players seem to adopt this approach. Many chartists would bridle at such a notion; this is to misrepresent their craft, their skill they claim is in the interpretation of these past moves and postulating likely scenarios going forward. In one sense they do have history on their side; financial markets do seem to repeat the same cycles and the same general patterns of events, certainly at a macro level. But the key is can charts do the same on the micro level?

Nowadays of course charting is big business, and has exploded in popularity with the advent of the personal computer. Every cheap and cheerful internet broking system offers free charts, and charting tools. Of course some market participants had been hand drawing charts long before computers, but only a dedicated band of players could be bothered to do all the donkey work. As a result most of the data that was plotted was daily information; usually the open, high low and closing prices for the stock, index, commodity, or currency that was being charted. Occasionally trading volumes were also included, and amongst futures traders the open interest data was also plotted. Now of course computing power and graphics allows almost limitless time slicing. Some people create one minute bar charts, or perhaps divide the day up into unusual time periods, all as a way to try and reveal the coming the moves in the market. Charts have also developed into technical analysis, which seeks to create and analyse essentially secondary or derivative information about the market price. This can range from simple moving averages, through a whole gamut of mathematical indicators, to some of the latest ideas involving fractals, artificial intelligence and chaos theory. In fact some have extended the art (could it be called a science?) to make predictions about time in the markets as well as prices. Not content with predicting the Y axis on the graph, many claim to know when on the X axis things will happen. This seems to be prediction on a heroic scale; and of course the punters lap it up. Imagine knowing where the price will move to, and when!

See https://www.amazon.co.uk/Financial-Speculation-Trading-financial-behaviour-ebook/dp/B0032XO5RQ