In support of lemmings

The article Retirement fund managers behave 'like lemmings' in today's FT caught my eye, not because of the subject matter, though retirement fund managers do indeed interest me, but because of the lemming analogy. 

Now, it is unclear whether the analogy is the FT's Chris Flood's or the Cass Business School's Professor David Blake, the writer of the report cited in the article. I suspect given the use of inverted commas in the headline it is Professor Blake's. Regardless, it is wrong. Lemmings do not herd. They do not en masse commit suicide by jumping over cliffs into the ocean. They never have and they never will.

The myth about lemmings originated from a 1958 Disney documentary 'White Wilderness'. The filmmakers could not understand why lemming populations occasionally exploded and just as quickly collapsed so made up the mass suicide story, staging the well-known scene in which hundreds of lemmings are seen running over a cliff. As the lemmings tumble, the narrator tells us that: 

"A kind of compulsion seizes each tiny rodent and, carried along by an unreasoning hysteria, each falls into step for a march that will take them to a strange destiny. That destiny is to jump into the ocean. They've become victims of an obsession — a one-track thought: 'Move on! Move on!' This is the last chance to turn back, yet over they go, casting themselves out bodily into space ... and so is acted out the legend of mass suicide."

The truth, as is often the case, is a little more mundane.

Population sizes of animals that are preyed upon like lemmings are described by the Lokta-Volterra equation. Without needing to get technical, what this means is that there are certain situations in which populations can explode in size, either because of short gestation periods, large number of offspring per birth, abundance of food, lack of predators or good weather. However, the environment of the animal in question may not be able to support a large population, either because of lack of food, poor weather, increase in predators etc, so numbers collapse.

Disney it seems did not know what explained the collapse of lemming populations so with the help of some imported lemmings, clever camera angles and turntables to induce the frenzied activity, came up with their own explanation.

It is possible of course that in citing lemmings Professor Blake meant that retirement fund managers were procreating like crazy but I doubt it.

Active management and the predictability of markets #4

These recent posts on the subject of active management have sought to distill the work of those who have found pattern in asset prices and to consider what relevance their work has with respect to today's markets. In this post, I look at asset price bubbles and the work of theoretical physicist turned bubble-spotter, Didier Sornette.

Former Federal Reserve governors Alan Greenspan and Ben Bernanke both said that it was impossible to spot bubbles in asset prices until after they had burst. It is possible they believed this. More likely, they realised that an admission to the contrary would impose on them a responsibility to pop bubbles, perhaps complicating or, at worst, endangering their key objectives with respect to inflation and employment.

Sornette founded the Financial Crisis Observatory (FCO) in the aftermath of the 2008/9 financial crisis. He wanted to understand how a few hundred billion of losses in one small corner area of the financial world — US subprime lending — triggered a US$5 trillion contraction in world GDP and almost US$30 trillion of losses in global stock market capitalisation. Furthermore, was the carnage directly related to the 30 or so years of stability — known as the Great Moderation —that preceded it?

The FCO was established as "a scientific platform aimed at testing and quantifying rigorously, in a systematic way and on a large scale the hypothesis that financial markets exhibit a degree of inefficiency and a potential for predictability, especially during regimes when bubbles develop." In other words, can one spot asset bubbles and predict when they'll burst?

Use of the word bubble with respect to financial markets dates back to the 1720 and the passing in June of that year by the British parliament of The Bubble Act, a response to the 87% collapse in the stock price of the South Sea Company and consequent bankruptcy of numerous and important investors. Since then, bubbles — or, as they are also known, asset bubbles, financial bubbles, speculative bubbles — have been defined in numerous different ways but all seem to relate in some way to prices that are far above intrinsic value.

Yale's Robert Shiller defined a speculative bubble as "a social epidemic whose contagion is mediated by price movements. News of price increase enriches the early investors, creating word-of-mouth stories about their successes, which stir envy and interest. The excitement then lures more and more people into the market, which causes prices to increase further, attracting yet more people and fueling "new era" stories, and so on, in successive feedback loops as the bubble grows. After the bubble bursts, the same contagion fuels a precipitous collapse, as falling prices cause more and more people to exit the market, and to magnify negative stories about the economy."

Sornette's own, and simpler, definition of bubbles is that they are "significant persistent deviations from fundamental value".

It is the study of complex systems that links the financial world with that of theoretical physics and thus what attracted Sornette to the former. The weather and the stock market may not at first appear related but both are driven by a vast multitude of positive and negative feedback loops that can be described using a common framework.

Sornette and his colleagues at the FCO developed a theory called "dragon-kings" as a framework for understanding asset bubbles. Unlike so-called black swans — events that come completely out of the blue — dragon kings are catastrophic occurrences but ones

whose origins are very much traceable. 

In financial markets, dragon kings are evidenced by price movements that fall far outside a normal expected probability. The term dragon king is a reference both to the mythical creature falling far outside the normal classification scheme —Sornette himself describes dragons as "extraordinary animals of extraordinary properties" — and to the King Effect, in which a simple linear relationship describes the distribution of wealth of all members of a society other than those at the very top. According to Sornette, "The root mechanism of a dragon king is a slow maturation towards instability, which is the bubble, and the climax of the bubble is often the crash."

Getting a little more technical, one particular signal that a bubble is developing is super-exponential growth with positive feedback. Rather than being followed by a price reversal as is often the case, a 1% price rise instead triggers a 2% price rise which in turn triggers a 4% price rise, etc.

In the real world, of course, things are not so simple, but Sornette's theoretical models not only appear to mimic closely the growth phase of financial asset bubbles but also to define a finite-time singularity, the point at which a bubble bursts. This bursting may be quick, a crash, or slow, a plateau. Either way, according to Sornette, "the information about the critical time is contained in the early development of this super-exponential growth."

It appears that Sornette has had some success in recent years in identifying ex ante a number of asset bubbles. In September 2007 he predicted that the bubble in Hong Kong and Chinese shares would "change regime" by the end on the year and that there "might be a crash". More recently, on 17 May last year, he noted that the US stock market was on an unsustainable trend and that there would be a correction — as indeed there was — but that this was only part of a "massive bubble in the making".

Perhaps in response to criticism, and to add rigour to his approach, Sornette now encrypts his predictions, posts them on an international archive, then releases a public key six months later. Sornette now regularly posts on his website an FCO Cockpit — an assessment of bubble tendencies of 435 systemic assets or indices. The latest, dated 1 April, noted that his proprietary bubble risk indices were turning red for Spanish, Italian and Irish bonds, as well as for European financial services subordinated bonds, reflecting a belief that "the European sovereign debt crisis is over". 

In equity land, Portuguese and Egyptian shares were flashing red. Notably, price action in the US in February and March had taken some of the "bubble pressure" off the likes of Amazon, Netflix and Testa, though Life Sciences Tools and Services, Pharamceuticals, and Healthcare Providers and Services sectors were still exhibiting strong bubble signs. All of these to varying degrees have seen some sort of correction.

Perhaps the main argument against the notion that it is possible to identify bubbles and predict when they'll burst is that if that were indeed possible, investors would anticipate them such that they'd never have a chance to develop in the first place. However, that assumes investors always behave rationally whereas the reality is that at times, and en masse, they don't. Maybe that is what Sornette's models have going for them.

Active management and the predictability of markets #3

The first two posts on market predictability focused largely on how asset classes behave over time. This post looks at patterns within asset classes, also known as cross sectional returns. Specifically, I look at equity markets and a factor very close to my heart, corporate governance.

I believe that well-governed companies produce better returns for shareholders over time than poorly-governed companies. On its own however this belief would not be much use as it says nothing about the extent to which differences in governance are reflected in share prices. Thus, I also believe that good governance is a quality that is systematically under-appreciated by investors.

I think of corporate governance as the extent to which decisions are taken in the interests of all stakeholders. Good governance means that all stakeholders are treated fairly. Poor governance means that some stakeholders are prioritized at the expense of others. As investors, it is important to ensure that one will get a fair share of revenues and to continue checking once invested. 

But I think it makes good investment sense too. If, as a minority shareholder, you are not getting your fair share of the revenues, it follows that stronger revenue growth has to make up the deficit, a big ask by any standard.

History is littered with stories of big corporate failures but poor governance only rarely ends in bankruptcy. More often than not it happens insidiously, and investors remain frustrated by the poor performance, but essentially unaware of its cause.

Governance can be poor at companies with large controlling shareholders. Minority shareholders in Essar Energy have been angered recently by what appears to be a cynical move by 78% owner Essar Global Fund Limited to take advantage of the 84% fall in the share price and bid for the shares it doesn't own. Opinion is split between those who argue there should be laws in place to protect investors from such predatory action and those who suggest that investors in the company's IPO in 2010 only have themselves to blame.

Regardless of your stance, research conducted by S&P Capital IQ for the FT about the performance of companies with a dominant shareholder has something for both sides. The median return over five years of 8,000 listed companies in which a single investor owned more than 50% was 60% compared with 116.2% for the MSCI World Index. Stripping out penny stocks that distort the data and you're still looking at a median return of 99.1%, 17.1 percentage points behind the index.

The FT article went on to note that "While active fund managers have the power to sidestep companies with dubious owners and ropey corporate governance, passive funds have no choice but to hold such stocks if they are a constituent of the index they track." And by the time such stocks are driven out of the index because of poor performance, the damage to passive funds will already have been done.

The 2003 paper Corporate Governance and Equity Prices written by Paul Gompers, Joy Ishii and Andrew Metrick also provides strong support for screening stocks on the basis of corporate governance measures. Stocks with the best governance based on 24 factors outperformed those with the worst governance by an astonishing 8.5 percentage points per annum. They also found that "firms with stronger shareholder rights had higher firm value, higher profits, higher sales growth, lower capital expenditures, and made fewer corporate acquisitions." These findings are supportive of my two beliefs that not only does better governance produce better corporate performance, but that this better performance is under-appreciated by investors.

Countries from Brazil to Japan have in recent years begun to promote good governance by constructing indices for better governed companies only. Brazil's Corporate Governance Index has been in existence only since June 2001 but it has produced a total US$ return over that time of 600.5% versus 220.2% for the broader Ibovespa index. 

Japan's Prime Minister Abe has followed suit, proposing a similar index for well-governed Japanese companies as part of his so-called Three Arrows initiative to breathe life into the economy.  The JPX-Nikkei 400 members are chosen based on return on equity and cumulative operating profit, which each account for 40 percent of the selection criteria. Market value makes up the remaining 20 percent. Subsequently, companies that don't meet corporate-governance criteria may be replaced. For a country that has for so long ignored the rights of minority shareholders, the creation of this index is a ground-breaking move.

While it is understandable why better-governed companies produce better business performance, it is less clear why such superiority is not rewarded by the market and thus represents a price anomaly to be taken advantage of. Perhaps it is because good governance is part of a company's culture and thus something that endures far longer than investors are prepared to admit. It may also be the case that companies that are not acquisitive nor incur large capital expenditures do not tend to make the headlines and as a result do not attract as much investor attention.

Whatever the reason, the tortoises of the corporate world may not have the glamour of the hare-like headline makers, but they do tend to produce better returns for shareholders.

Active management and the predictability of markets #2

In this second post on 'market predictability' I look at some of Prof Robert Shiller's work. Shiller was a co-winner of this year's Economics Nobel Prize along with Prof Eugene Fama (whose work I considered in the last post). To many it seemed a mistake - or at least a contradiction - that these two shared the prize. Fama is best known for the finding that markets are essentially efficient, or rather that they are once trading costs are taken account of. Shiller on the other hand found the opposite, that there are patterns discernible enough to profit from. How could they both win the prize having derived diametrically-opposed results?!

Although Fama is known for his early work, which labeled him as a believer in efficient markets, his later work revealed more pronounced patterns that he nowadays seeks to profit from through his work with Dimensional Advisors. These patterns relate to the size and valuation of stocks (he found that small caps tend to outperform large caps and high book-to-price stocks outperform low book-to-price ones).

In a 1981 paper, Shiller showed that stock prices move much more than they should if they were purely a function of subsequent changes in dividends (also known as the "efficient markets model".) Later, in 1984, he showed that there was a positive correlation between the current dividend yield and subsequent returns. In other words, when the dividend yield was high, the subsequent one year price movement was higher than normal, contrary to the efficient markets model which implied that "a high current yield should correspond to an expected capital loss to offset the current yield".

Somewhat ironically, Fama, in collaboration with Kenneth French, showed in a 1988 paper that dividend yields had even greater predictive power over longer time frames. While dividend yields explained 15% of subsequent one year returns, over five years they explained 60%.

Shiller's work on asset prices, and in particular his 1984 paper, "Stock Prices and Social Dynamics", paved the way for the emergence of the field of behavioural finance. Indeed, although the term "animal spirits" was coined by John Maynard Keynes in his 1936 publication, "The General Theory of Employment, Interest and Money", it was popularised only later by Shiller himself and a colleague George Akerlof in their 2009 book "Animal Spirits: How Human Psychology Drives the Economy, and Why It Matters for Global Capitalism".

That markets are not rational or efficient now seems obvious though it took several decades to challenge the widely accepted principle that human beings, the agents of markets and economic systems, make rational decisions. Charlie Munger, Warren Buffett's right hand man, famously remarked "If it isn't behavioral, what the hell is it?" though this was in reference to economics rather than financial markets.

Although not mentioned in the paper that provided the background to the Nobel 2013 award, Shiller is also now associated with another predictive indicator, the cyclically-adjusted price-to-earnings-ratio (CAPE), or the Shiller P/E. CAPE is calculated by dividing the current price by the average 10 year real earnings and is based on the work of Benjamin Graham and David Dodd who argued in their 1934 classic, Security Analysis, that more meaning could be garnered by using smoothed earnings rather than current earnings, since when earnings were depressed the market would anticipate them recovering and thus trade on a higher multiple. Taking the ten year average meant that one should always or at least most of the time be including both a peak and a trough in earnings and thus keep comparisons between current CAPE and historic CAPEs on a like-for-like basis.

So, what are current dividend yields and Shiller P/Es telling us about likely future returns from equity markets? Annoyingly little, if Robert Shiller's own words are anything to go by. Speaking earlier this year in Davos, he said that his "CAPE ratio [for the US equity market] is over 25 which by historical standards is high but is not record high; it got up to 46 in the year 2000." In other words, over the long term, equity returns will be below their historic average in the long term but in the short term could outpace it as the CAPE continues to rise towards its historic high.

There is also a reasonably strong inverse relationship between the CAPE and the inflation rate (other than when inflation is negative) so it is possible that if central banks are able to stop the world from slipping into deflation and weak aggregate demand prevents inflation from accelerating sharply, a higher CAPE would be justified.

Prof Jeremy Siegel, famous for his 1994 classic Stocks for the Long Run, is another fan of the ratio but argues that the data on which it is now based are unreliable. Adding back write-downs incurred by financial firms in 2008 and 2009 raises the ten year average and thus lowers the CAPE to a level which he says suggests US equities are still cheap.

John Hussman of US firm Hussman Funds also argues that earnings have been distorted (downwards) by accounting standards such as FASB 142, introduced in 2001. This standard "offers guidelines on adjusting the value of intangible assets, instead of keeping those investments on the books at cost and gradually amortizing the value over time. It's argued that during the last couple of recessions this new accounting rule has caused companies to aggressively write down the value of their intangible assets, impacting earnings, therefore pushing profits lower, and biasing P/E ratios (like the CAPE) higher." However, Hussman finds plenty of other measures that suggest US equities are now overvalued.

The conclusions of both Shiller's and Fama's work is that markets are most or only predictable at valuation extremes. Although it is hard to know whether market valuations will reach or even exceed previous extremes, it is fair to say that they are currently a long way from them. While this does not therefore support a case for being bearish, nor does it support one for being particularly bullish. That, sadly, is often the way with markets.

Active management and the predictability of markets #1

That it is possible to add substantially more value to customers' portfolios than is subtracted from them in fees is the basis of the entire active management industry. The debate between those who believe that markets are efficient and thus unpredictable and those who don't will continue to rage on, and active managers should seek to be part of it.

The battle lines in this debate, however, are drawn in a somewhat puzzling way. To the passive world, all those seeking to 'beat the market' are fools. Yet to the active world, the passive world's endeavours are far from futile. The apparent anomaly lies in differences of opinion with respect to the nature of the 'game' being played. 

To the passive world, investing is a game of luck, so by definition theirs is the only worthwhile approach and accordingly they must disparage all others. To the active world, on the other hand, investing is a game of skill, in which there is no 'house', only other players.

If an active manager can be better than three quarters of its competition, it will almost certainly generate returns, net of fees, well in excess of the relevant index or passive equivalent, and thus over time respectable in absolute terms. The challenge is thus to be more skilful than other active managers, then to clearly articulate the approach adopted to customers (success for an active manager relies as much on the power of persuasion as the power of prediction.)

As mentioned, the passive world has something to offer because index funds do what they say they will - track an index. Furthermore, there will always be fund investors who lack the time, tools or inclination to identify skilful active managers and thus for whom an index fund is the sensible option.

It is somewhat ironic however that the constituents of index funds, namely companies, are all trying to do one thing: beat each other. Few would question that this competition is anything other than a game of skill and hard work. The better companies get to the top and tend to stay there, whether in toothpaste, passenger jets, active management or passive management. Let's be clear, Vanguard is not seeking, like its products, to be average but to beat iShares.

It would be nice if we lived in a world in which all companies win. Until then, active managers must seek to beat their competition and in so doing give customers value for money. 

This post looks at the work of recent Economics Nobel Laureate Professor Eugene Fama, the "father of modern finance". Although it was Fama who first popularized the idea in 1970 that markets are efficient, its origin goes back as far as French mathematician Louis Bachelier and his 1900 PhD thesis The Theory of Speculation. Bachelier is credited with being the first to model mathematically the random process known as Brownian Motion, and to associate it with stock prices.

60 or so years later, and following a number of other empirical studies, Fama set out to test systematically whether there were identifiable patterns (non-randomness) in stock prices. In 1965 he reported that shorter term returns were somewhat predictable from previous returns — they had a tendency to move in the same direction — but that the relationship was quite weak. Later, Fama stated that these patterns were so faint that attempts to exploit them would be wiped out by trading costs. This no-arbitrage model formed the basis of the Efficient Market Hypothesis.

In the decades since Fama's early work, there have been countless other empirical studies published that looked for patterns in stock prices and markets. One might think that if stock prices are essentially unpredictable over short timeframes then they are even more unpredictable over longer ones. However, this is not the case. Indeed it was Fama himself who in 1977 showed that the short-term interest rate could be used to forecast the return on the stock market.

If prices follow a random walk, then their variance (the square of the standard deviation or volatility) over two year periods should be twice the variance over one year and so forth. In fact, for both stocks and bonds, this is not the case. However, unlike short-term returns which Fama had shown exhibit slight momentum tendencies, longer-term returns are mean reverting (variance over two years is less than variance over one year). 

To put this into English, if you toss a coin ten times, there is a certain probability that you will end up with five heads and five tails. However, if the coin is mean reverting, meaning that following a head the coin is more likely to land tails (and vice versa), the probability of ending up with five heads and five tails is higher.

In recent years more and more pattern within stock prices and markets has been revealed, both in short term and longer-term movements. Fama is now a consultant to Dimensional Fund Advisors, a firm that structures funds that seek to take advantage of longer-term patterns such as low price-to-book companies outperforming high price-to-­book companies. 

Mastering the short term is Jim Simons and the firm he founded, Renaissance Technologies. On a per employee basis, Renaissance has the third largest super computer in the world, one which is able to delve far far deeper into price movements than the devices that Fama used in the 1960s. The annualised returns over a number of years of his Renaissance Medallion Fund, now closed to outsiders, were spectacular.

Intuitively, it makes sense to me that the Efficient Market Hypothesis is bunkum. Whether within markets or outside them, all events are a function of what came before. Club hits ball, ball hits tree. The key to successful active investing must therefore be to try to understand and exploit that function. That some are more able to do this than others seems completely natural to me. Like I said, investing is a game of skill not luck.

For better investment results, concentrate

(Published in the Financial Times on 29 June 2014)

As the Financial Times' John Authers rightly points out, "active share" — the portion of a fund that differs from its benchmark —should never be used in isolation to assess funds ("Active fund managers are closet index huggers", March 12). The notion that there exists a simple measure to predict performance is clearly absurd.

Furthermore, whether or not it should be used in conjunction with other tools is also contentious. Research by Martijn Cremers, professor of finance at the University of Notre Dame, and Antti Petajisto, a portfolio manager at BlackRock and former assistant professor of finance at Yale, found that, net of costs, high active share funds on average performed better than index funds, which in turn performed better than low active share funds. This was certainly an interesting conclusion, but why should it be true that high active share funds tend to perform well?

Ross Miller, finance professor at the State University of New York, devised a clever way to demonstrate why closet index funds were a bad idea. His insight was that any fund could be divided into two parts: a passive portion that correlated 100 per cent with the benchmark and an active portion that was 0 per cent correlated.

By assigning typical passive fund fees to the passive portion one could then calculate the effective fee (the actual fee less the passive fee) that one was paying for the active portion.

In the case of the benchmark huggers, the active fee was so high — in some cases as high as 7 per cent — that the chances of producing sufficient alpha, or excess returns, to cover it as well as leaving a big chunk for unit holders were negligible.

High active share funds are therefore the ones giving themselves a chance to produce sufficient alpha, but why do they also tend to succeed in this endeavour?

There are essentially two ways to get a high active share: run a fairly concentrated portfolio, taking little notice of benchmark constituent weights, or run a diversified portfolio full of stocks that are not in the benchmark. There are few if any funds that fall into the latter category, so the argument is really about why concentrated portfolios are a good idea.

Skill, and thus good performance, is about first spotting and then taking advantage of price anomalies. It is other investors — "the market" — that create the price anomalies in the first place, so good performance will always be at the expense of others. Alpha generation is after all a zero-sum game.

The behavioural trait known as herding from time to time takes prices to levels that, with analysis, can be declared cheap or expensive. Such mis-valuations — or mispricings — can be tiny ones that correct in a few seconds or hours, or bigger ones that correct over a few years. Jim Simons, founder of hedge fund Renaissance Technologies, uses a very powerful and very quick computer to spot the tiny ones before anyone else. Others are more interested in the longer ones.

Longer-term price anomalies are well documented. Sanjoy Basu, former professor of finance at McMaster University in Ontario, and Robert Shiller, professor of economics at Yale, found that stocks with high dividend yields outperform stocks with low dividend yields. US economist Eugene Fama and Kenneth French, professor of finance at Dartmouth College, showed that this predictability increased with time: while over one year the dividend yield explained 15 per cent of the variation in excess returns, over five years it explained 60 per cent.

It seems that investors systematically overestimate the extent to which growth stocks will grow. Since it is growth stocks that tend to make the headlines with stories of expansion and acquisition, it is hardly surprising that this attention can cause overvaluation.

Corporate governance is another factor that gets systematically mispriced. Paul Gompers, professor of business administration at Harvard, Joy Ishii, assistant professor of finance at Stanford, and Andrew Metrick, professor of finance at Yale, found that the stocks of companies with good corporate governance outperformed those with poor corporate governance by 8.5 per cent per annum. Given that the well-governed companies were ones that had lower levels of capital expenditure and made fewer acquisitions, this anomaly is perhaps also explained by an interest in newspaper headlines.

Armed with this evidence, and having identified potential winners, one then has to decide how much to commit to each. Here we turn to mathematician John Kelly and his work on horse betting. He devised a very simple formula, known as the Kelly Criterion, to determine what percentage of your purse to bet on a particular horse, the equivalent perhaps of how much of your portfolio to invest in a particular stock. If the market odds of a horse winning were 5o per cent but you had an edge of some sort and believed its chances were 55 per cent, the formula said you should bet 10 per cent of your purse to maximise your winnings.

The empirical findings with respect to dividend yields and corporate governance are so strong that one should consider them to represent a considerable edge. While it is impossible to put a number on precisely what that edge might be, the evidence strongly supports the case for putting 10 per cent in a thoroughly researched, well-governed, high-yielding stock, not 1 per cent.

Skilled managers do exist

(Published in the Financial Times on 27 January 2013)

John Authers asserts (Quest for test of investment skill persists, January 11) that nobody can tell which investors are more skilled than others and that active fund managers are unaware of their skills. 

These assertions are wrong. I suggest - with statistics on my side - that Berkshire Hathaway’s Warren Buffett and Renaissance Technologies’ Jim Simons are more skilled than most and furthermore that there are others who, with a little work, can be identified. I also know that at Aberdeen we are aware where we possess skill and - more pertinently - where we not.

Knowing where you possess skill however requires knowing what it is. Simply, investment skill involves identifying non-randomness in financial markets, then profiting from it. It is about knowing the difference between what is predictable and what is not. It is about understanding where and when one has an edge and then swooping in for the kill.

The sad fact is that the vast majority of investors waste their energies and capital guessing the equivalent of which side a coin will land, often supported by written and verbal justification that is both sincere and articulate.

The key to investing is knowing when the odds of a coin landing heads have increased to, say, 70 per cent or 80 per cent. And this is where serial mean reversion comes in. 

Occasionally, random walks take asset prices so far away from their mean or trend that they are pulled back towards it rather than continuing in a random fashion. If a coin lands heads 10 times in a row, the odds of a tail on the next throw are still 50 per cent. In the world of investing however, it may be 70 or 80 per cent. Put another way, despite the ubiquitous disclaimer, past performance can sometimes be a guide to the future.

Identifying pattern is very much what the two aforementioned maestros do in their own different ways. Mr Buffett’s edge, in my humble opinion, has been his remarkable understanding of human nature, both its strengths and its weaknesses, combined with discipline, patience, honesty and a very good grasp of statistics. Mr Simons, on the other hand, is a brilliant mathematician and has smarter and faster computers than anyone else. While Mr Buffett is the king of predicting share prices over 10 years, Mr Simons is unrivalled over 10 minutes.

Mr Buffett and Mr Simons are rare birds yet many still believe themselves to be good investors when the facts may tell a blatantly different story. The reason for this is that we humans evolved a survival mechanism to believe that we are better than we actually are. A timid approach to facing down a sabre-toothed tiger or attracting a cave mate would have been disastrous. Furthermore, we have an asymmetrical ability to blame our failures on (bad) luck but to attribute our successes to skill, a bias termed the fundamental attribution error. Thus you only need a couple of successes among all the failures to think you are a skilful investor.

If you have correctly identified an edge, the next step is to know how to use it. Question: if you have a biased coin that you know has a 6o per cent chance of landing heads and you are playing with someone who does not know the coin is biased, what percentage of your bankroll should you bet each round in order to increase your wealth over time?

If you bet nothing, you are wasting your edge and your wealth will remain the same. If you bet your entire purse, there is a 40 per cent chance the coin will come up tails, and you will lose everything and be out of the game (even with the bias, the chance of there being one tail in 10 tosses is 99 per cent.) So the optimal percentage must be somewhere between 0 per cent and 100 per cent. 

The answer, in fact, is 20 per cent. Bet 21 per cent or 19 per cent and over time you will end up less wealthy than if you bet 20 per cent. If you want to know the formula, google the term Kelly betting criterion.

How does this apply to investing? In Mr Buffett’s case, he of course understands that to put all one’s eggs in one basket is foolish, but also that being overloaded with baskets will wear you out. The efficient market hypothesis asserts that you should diversify as much as possible to eliminate stock specific risks. Mr Buffett on the other hand actively seeks out stock specific risk because he knows that is where his edge lies. As he has noted: Wide diversification is for people who do not know what they are doing.

Does Mr Buffett know precisely what his odds are? Of course not. What he does know is that he has a good feel for where a company will be in 10 or 20 years’ time, giving him the confidence to run a concentrated portfolio. There is much we can learn from him, though I am not the first to suggest that.