Patience and Finance

Looking at patience in financial decision making


In the East, it is said:
“One moment of patience may ward off great disaster. One moment of impatience may ruin a whole life.” [Chinese Proverb]

In the West, it is said:
“I often make more money when I am snoozing than when I am active.” [Warren Buffett]

These observations have common conceptual roots. Underlying both lies patience. Patience, or its alter ego impatience, is a key factor shaping inter-temporal decisions.

Whether to save or spend, trade or invest, work or quit, stick or twist. As such, patience has important implications for the evolution of economic and social systems. This paper considers the role of patience in decision-making, in particular financial decision-making.

Impatience is no stranger to economics. It was discussed by Neo-Classical economists, such as Marshall, Fisher and Pigou writing over a century ago. Pigou memorably described the tendency of humans to discount excessively future outcomes as a “defective telescopic faculty”. Today, research has gone one step further: discounting is not just myopic but inconsistent through time. This has been given a somewhat less memorable, if mathematically more accurate, moniker by economists – “hyberbolic discounting”.

Hyperbolic discounting describes how people’s preferences alter as distant outcomes become closer to the present. Concretely, imagine a person who prefers $100 in ten years’ time to $90 in nine years’ time. With hyperbolic preferences, this same person would also favour $90 in one year’s time to $100 in two year’s time. They exhibit inconsistencies in decision-making across time, or so-called preference reversals. The implications of such behaviour are potentially far-reaching. The patient planner becomes a spontaneous doer when outcomes are within reach. The cautious saver becomes a reckless spender when nest eggs are close to hatching. The long-term investor becomes a short-term speculator if assets can be cashed. As temptation beckons, the devil on one shoulder whispers more seductively than the angel on the other. Preferences switch as the distant becomes instant.

Self-improving cycles
If preferences evolve over time, this gives rise to the possibility of self-reinforcing patterns of behaviour. Such evolutionary trends have been extensively studied by sociologists, psychologists and even some economists. These studies confirm the old aphorism: virtue is its own reward. Specifically, patience is capable of setting in train a cycle of self-improving behaviour in individuals, economic and social systems.

Latterly, models of economic systems have got in on the act. Growth, too, can be self-improving or endogenous – for example, because investment in human capital is self-reinforcing. Working, like dieting, is good for self-esteem and long-term productivity. Idling, like over-eating, is bad. History suggests a strongly self-reinforcing relationship between saving and growth. That is probably why cross-country studies point to such strong growth enhancing effects of financial deepening.

Self-destructive cycles
Just as patience can self-generate, so too can impatience. And while patience generates self-improving cycles, its alter ego can create self-destructive cycles. Addiction is the classic self-destructive cycle. Drugs and alcohol chemically alter the balance of the double-self, increasing the value of instant gratification. This shortens time horizons, increasing further the value of instant gratification in a downward spiral. Unless arrested, this unfulfilling equilibrium becomes self-fulfilling.

As with self-improving cycles, these self-destructive spirals have a social dimension. Bad behaviours rub off just as much as good, with three degrees of influence. It is not just happiness, diet tips and gym membership cards which pass between friends. So too do depression, chocolate cake recipes and membership of addiction clinics. As patience is contagious, impatience is infectious.

So self-destructive cycles in social systems are the result of a neurological seed nurtured by sociological forces. Self-destruction, like self-improvement, is part nature, part nurture. Finance has both these raw ingredients. Most traders’ brains harbour the impatience gene. Often, they harbour little else. And traders’ behaviour is shaped every bit as much by the footfall of their friends in the herd. So, in theory, we might expect similar cycles of self-destruction and self-improvement in finance.

Gresham’s Law in finance

To illustrate these theoretical dynamics in action, consider a sketch model. Imagine three classes of investor:

• an impatient short-term speculator, who follows the momentum of the herd, buying when prices are rising and selling when they fall;

• a patient long-term investor, who invests according to whereprices are reltive to their long-term fundamentals;

• an untested investor, who can mimic either the speculator or the long-term investor, but whose performance either way is assessed at frequent intervals by end-investors who withdraw or maintain funds accordingly.

Market prices in this model are buffeted by two winds. Momentum-based speculators cause deviations from fundamentals, while long-term investors drive prices back towards fundamentals. These are the double-selves of the financial brain, the patience and impatience genes.

And as in social systems, the balance of these two genetic types results in two very different evolutionary equilibria. Under one equilibrium, patience wins the day. When long-term investors start in the ascendency, prices tend to correct towards fundamentals. The performance of untested investors pursuing momentum strategies falters, while those pursuing long term strategies flourish. The fraction of long-term investors rises. The self-correcting tendencies of market prices are thus reinforced, further supporting long-term investors. The patience gene thrives, the impatience gene dies. Natural selection results in a self-improving cycle, as with dieting, happiness and exercise.

But there is a second equilibrium where this cycle operates in reverse gear. With a large fraction of momentum traders, prices deviate persistently from fundamentals. Among untested investors, momentum strategies now flourish while long term fundamentalists fail. The speculative balance of investors rises, increasing the degree of misalignment in prices. The patience gene falls into terminal decline. Natural selection results in a self-destructive cycle, as with drug, alcohol and food addiction.

These self-destructive dynamics would have been familiar to economist, and sometime investor, John Maynard Keynes. He quipped, “Markets can remain irrational for longer than you or I can remain solvent”. In the sketch model, a Keynesian dynamic selection process is at work. Myopic finance bankrupts the long-sighted.

This echoes an earlier evolutionary game in finance – Gresham’s Law. Named after English financier Sir Thomas Gresham in the 16th century, this refers to the tendency for bad money to drive out good. Today, finance faces its own Gresham’s dilemma – the patient or impatient path. Innovation has, of course, transformed finance over the intervening years. Liberalisation has resulted in far greater information and liquidity in financial markets. Perhaps these developments have helped good finance drive out bad, nudging money towards the patience path? Not necessarily.

Take information. In an evolutionary game, information is a double-edged sword. It supports the cause of the long-term investor, by allowing them more easily to compare prices with fundamentals. But it also tests the patience of the untested investor subject to regular performance evaluation. Anecdotally at least, performance evaluation intervals have progressively shortened. Over recent decades, companies have migrated from annual general meetings, to a six monthly or quarterly reporting cycle to today’s steady stream of within-cycle trading updates. In finance, information is in general a good thing. But in finance, as in life, it is possible to have too much of a good thing.

Liquidity is similarly double-edged. It reduces the impact of momentum trading on prices, thereby increasing market efficiency. But it also reduces the costs of pursuing such strategies. In other words, liquidity unlocks the impatience gene. Investors whose judgement is wrong, but whose timing is right, can lock in immediate gains. Liquidity, too, can pollute the gene pool by allowing the impatient to prosper. Like information, liquidity can be too much of a good thing.

Patience in finance
There is ample evidence, theoretical and empirical, of self-improving financial cycles. From the Medici banks in Italy in the 13th century to the joint stock banks of the 19th century to the explosion of capital market finance in the latter part of the 20th century. Today, China provides no better example of that self-improving cycle in motion.

But can financial systems overshoot onto the impatient path, where too much liquidity and information unlock the impatience gene and its ugly progeny. Along that path lies excess – excess trading, excess credit and excess volatility. What evidence exists on these phenomena?

Patience and puzzles
One source is the enormous literature on financial market efficiency. If markets were efficient, asset prices would mirror fundamentals. This would be indirect evidence against impatience, which tends to cause prices to deviate persistently from equilibrium. In fact, empirical finance is full of puzzles – economist code for deviations from market efficiency. And, interestingly, many of these observed puzzles are consistent with impatient dynamics.

Patience and efficiency
If impatience in the financial system is growing, there should be evidence of financial prices having become more volatile and more divorced from fundamentals over time. Excess volatility and misalignment would rise alongside short-termism, with market efficiency the casualty. What does the evidence suggest?


Fig.1 plots equity prices in the US back to 1880, relative to a model-based measure of equity market fundamentals based on discounted expected future profit streams. Fig.2 shows a measure of excess volatility in these series over time (a moving average of the ratio of actual to fundamentals-based volatility), while Fig.3 shows a measure of price misalignment (the absolute deviation of prices from fundamentals, expressed as a percentage of prices).


Fig.2 suggests that, on average over the past century, US stock prices have been over three times more volatile than fundamentals, confirming the excess volatility hypothesis. But the trend in the degree of excess volatility is also telling. Up until the 1960s, prices were around twice as volatile as fundamentals. Since 1990, they have been anywhere between six and ten times more volatile. Excess volatility in equity prices has risen as financial innovation has taken off.


The pattern is much the same with measures of misalignment. Up until 1960s, the average absolute deviation of US equity prices from fundamentals was just over 20%. Since 1990s, the average absolute deviation has been well over 100%. Fig.4 presents the same evidence for UK equity prices since 1920. While less dramatic, the patterns are much the same. Misalignment correlates with innovation and liquidity.


Patience and profits
To bring these market inefficiencies to life, consider a simple experiment to gauge the relative performance of momentum and long-term investors. Both are assumed to follow a simple strategy: the speculator buys (sells) when prices have risen (fallen) in the previous period; the fundamentalist buys (sells) when prices are low (high) relative to fundamentals.


Portfolios are evaluated and re-optimised on a monthly basis, based on a $1 initial stake. How would these strategies have fared historically? Fig.5 and Fig.6 show cumulative returns to these strategies in the US and UK. They suggest a dramatic evolutionary pattern. The speculator’s $1 stake in US equities in 1880 would by 2009 have grown to over $50,000. The fundamentalist’s same $1 stake would have fallen to be worth around 11 cents. Impatience would have trumped patience by a factor of half a million.


This out-performance is mirrored in the UK, if less dramatically (Fig.6). Starting in 1920, the value of the speculator’s £1 stake would have risen to around £1.56, while the fundamentalists’ stake would have fallen to 32 pence. Momentum would have mopped the floor with fundamentals. The sheep would have defeated the goats.

In an evolutionary game, these profit profiles would alter the balance of investors. Impatient investors would have profited and thrived, while patient investors would have lost and died. Nature would have deselected the patience gene. As Keynes predicted, market inefficiencies would have supported the myopic and irrational at the expense of the solvency of the far-sighted.

Patience and trading
If impatience strategies flourish, we would expect this to be reflected in a secular fall in the average duration of asset holdings, as the fraction of short-term investors rises. Again, what does the evidence suggest?


Fig.7 plots the average holding period of investors in the US NYSE index since 1940. This is estimated by simply looking at the ratio of the market value of the shares outstanding to the value of shares traded in any given year. It suggests a striking pattern. In 1940, the mean duration of US equity holdings by investors was around seven years. For the next 35 years up until the mid-1970s, this average holding period was little changed. But in the subsequent 35 years average holding periods have fallen secularly. By the time of the stock market crash in 1987, the average duration of US equity holdings had fallen to under two years. By the turn of the century, it had fallen below one year. By 2007, it was around seven months. Impatience is mounting.


Fig.8 shows the average duration of equity holdings across a wider set of international equity markets over the past 15 years. The trends are much the same. Average holding periods have fallen. Today, they are typically below one year. For the Shanghai stock index, the mean duration is closer to six months.

Some investors have bucked this trend. Warren Buffett told Berkshire Hathaway investors in 1988 “our favourite holding period is forever”. But for an increasing fraction of the financial world, the favoured investment horizon seems to be whenever.

A number of structural factors help account for these trends, some of them positive. Transactions costs in equity markets have fallen significantly. This has encouraged growth in a particular class of investor – high-frequency traders. While HFTs are not new, their speed of execution has undergone a quantum leap. A decade ago, the execution interval for HFTs was seconds. Advances in technology mean today’s HFTs operate in milli- or micro-seconds. Tomorrow’s may operate in nano-seconds.

HFTs operate in size as well at speed. HFT firms are believed to account for more than 70% of all trading volume in US equities, 40% of volumes in US futures and 20% of volumes in US options. In Europe, HFTs account for around 30-40% of volumes in equities and futures. These fractions have risen from single figures as recently as a few years ago. And they look set to continue to rise.

Asia is not immune from these trends. HFT is believed to account for between 5-10% of Asian equity volumes. In China, HFT is still in its infancy. But market contacts suggest as much as 80-90% of trading on the Shanghai stock exchange may be done by day-traders, many small retail investors. Impatience is socially, as well as technologically, contagious.

This evolution of trading appears already to have had an effect on financial market dynamics. On 6th May 2010, the price of more than 200 securities fell by over 50% between 2.00pm and 2.45pm. At 2.47pm, Accenture shares traded for around seven seconds at a price of 1 cent, a loss of market value close to 100%. No significant economic or political news was released during this period.

The causes and consequences of this “flash crash” are noclearer now than at the time. But it is known that a number of large HFT trading positions coincided with these chaotic dynamics. In response, market-makers and liquidity-providers withdrew.

Gresham’s Law re-emerged as bad money drove out good, its effects now taking milli-seconds rather than months. Trading in securities generated trading insecurities. The impatient world was found, under stress, to be an uncertain and fragile one.

Patience and dividends
Another way of gauging short-termism is to look at investors’ implied preferences for income today (dividends) over income tomorrow (retained earnings). In theory, investors should be indifferent between these options, as the dividend payout ratio ought not to affect the value of a firm. Empirical evidence suggests, however, strong evidence of high and sticky dividend payout ratios, almost irrespective of profits. Moreover, dividends appear to be becoming stickier over time.

Between 1825 and 1870, a study of over 500 NYSE listed firms found that dividend increases and decreases were roughly equally split. Dividend reductions occurred just less than 50% of the time, as might be expected. Similar behaviour has been found among UK quoted firms during the 19th century.

Now fast forward a century. Dividend behaviour has altered dramatically. Between 1980 and 2010, the world’s largest 200 companies reduced dividends only 8% of the time. This was despite dividends being greater than earnings in over 10% of cases – and, indeed, dividends being positive despite negative earnings in 5% of cases. Over recent years, earnings have been more than six times more volatile than dividends. Berkshire Hathaway has again bucked the trend. Since 1967, it has paid dividends only once. And that may have been once too often for Buffett: “I must have been in the bathroom when the dividend was declared”.

Patience and discounting
A more direct test of short-termism would involve estimating directly the discount rate people assign to future outcomes. Conducting your own test is fairly simple. Ask your friends how they would feel if the price of their favourite luxury good were to rise by 10%. Then ask them how they would feel if the price of their house were to rise by 10%. The first is likely to meet with a frown, the second a smile. In general, people dislike goods price inflation, but like asset price inflation.

This feels rational right? Wrong. These perceptions suggest a sub-conscious myopia. Higher goods prices cut today’s disposable income. Higher asset prices cut tomorrow’s disposable income. So disliking goods price inflation and liking asset price inflation suggests a potential time-inconsistency in preferences. It is leaving as a bequest for your children the mortgage but not the house. It is possible to test more formally the evolution of discount rates by extracting them from the prices of financial assets, such as equity prices, using asset pricing theory. This suggests that discount rates in asset prices are higher, often much higher, than implied by rational expectations theory, consistent with short-termism.

For example, in studies of UK companies it has been found that actual annual discount rates can be materially, perhaps as much as 300%, higher than their rational value. Or, put differently, cash flows four years ahead are discounted at rates more appropriate for cash flows six to 10 years ahead.

Equivalently, studies have found that future cash flows are undervalued by investors. These effects compound over time. So if cash flows five months ahead are undervalued by 5% today, those occurring five years ahead are undervalued by 40% today. This finding is common, although not uniform, across countries. It also appears to have grown in the second half of the 20th century.

Evidence from the US over the period since 1880 suggests a similar pattern. Stock market evidence suggests that agents may be undervaluing cash flows by up to 40% each year. Or, put differently, if cash flows six months ahead are undervalued by 20%, those occurring five years ahead may be undervalued by up to 90%. The stock market appears to be a quite defective Pigouvian telescope.

Patience and jobs
If impatience is part nature, part nurture, it ought to have implications beyond finance. So take another key inter-temporal decision – the choice of job. Like financial assets, the market in employment is likely to have become more liquid and information efficient over time, facilitated by the growth of job search services. But as with finance, information and liquidity has the potential to cause over-trading.

Consider, for example, the market for CEOs. Their positions are likely to be particularly at risk from short-term performance evaluation in capital markets. And as with holding periods for financial investments, CEO tenure patterns have changed strikingly over recent decades.

In 1995, the mean duration of departing CEOs from the world’s largest 2,500 companies was just less than a decade. Since then it has declined. By 2000, it had fallen to just over eight years. By 2009, it had fallen to around six years. This pattern is replicated across regions, but is marked in North America and non-Japan Asia.

Patience and public policy
This evidence is no more than illustrative. But it does point to the potentially adverse side-effects of improved information and liquidity in markets. The public good of information and liquidity may unleash the public bad of myopia and volatility. So what are the potential public policy implications? These include:

(a) Countries, like China, embarking on financial liberalisation need to walk a fine line. On one side of this line is the self-improving cycle of increased saving, investment and growth – the patience path. On the other is the self destructive path of increased volatility and consumption – the impatient path. China today is an intriguing mix of the two paths. Patience is the dominant gene in the high savings rates of households and corporations. Yet the impatience gene is dominant in the behaviour of frothy equity and property markets. Finance in China is being buffeted by opposing winds – the mild east and the wild west. Dynastically, it is part Ming, part Yuan. China today is proof that financial innovation can be a double-edged sword. It is important to keep on the right side of that sword. That calls for careful sequencing of financial reform, in China and elsewhere.

(b) If excess volatility in market prices is a distortionary tax on long-duration investments, policy measures may be needed to offset this distortion. Pigou’s defective telescope may need to be repaired, perhaps reversed. One way of doing so is to provide incentives for longer-duration asset holdings. Another would be to introduce disincentive devices for short-termist behaviour: holding period-related levies on financial investments is one such example. A third potential instrument is governance – for example, some have proposed that voting rights and the appointment of board members could be made conditional on the duration of equity holdings.

(c) Impatient preferences can be constrained by pre-commitment devices – diets, exercise regimes, tattoos of your partner’s name. The financial equivalents include trust and pension funds, Christmas Clubs and pre-nuptial agreements. Some economists have called these “golden egg” investments – investments which cannot be realised quickly, so that temptation is constrained. Pre-commitment can also work for non-financial contracts. For example, job contracts could be based on long-duration performance measures. These contracts may require a public policy “nudge”. For example, savings schemes might require people to opt out rather than opt in.

(d) Institutional arrangements, and policy frameworks, are another such pre-commitment device. They are a means of resisting the temptation to place short- over long-term policy objectives. Government’s policy preferences, which are derived from people’s preferences, can be hyperbolic too. That is the essence of the policy time-consistency problem. A solution to that problem is to delegate policy to a patient, low discount rate agent. Because central banks have very long horizons, they fit the bill. Increasingly over the course of the past century, central banks have been chosen to safeguard the long-run objectives of price and financial stability, as a means of leaning against short-termist temptations.

To illustrate some of the benefits of pre-commitment and long-duration investment, imagine having placed that $1 stake in 1967 with an investment firm whose motto was “our favourite holding period is forever”. By 2009, that long-term investor’s stake would have risen to $2650. Over the same period, the momentum traders’ stake would have returned $75. Buy-and-hold would have out-performed bought-and-sold by a factor of around 36.

How different the world may have looked. Fundamentals would have triumphed over momentum. The sheep would have been herded by the goats. Facing a losing streak, speculators may have gone the same way as despairing Dick Fuld or the ravenous robin. The gene pool may have been cleansed of the impatient. Patience may have helped ward off great disaster, the like of which we have recently seen.

Just as patience can ward off great disaster, impatience can ruin a whole life. Generations of dieters and addicts are testament to that. So too is finance, not least in the light of the crisis. It is important finance sticks to the patient evolutionary path. To do so, the fidgeting fingers of the invisible hand may need a steadying arm.

Andrew Haldane is Executive Director, Financial Stability, at the Bank of England. This is an abridged version of a paper he presented to the Oxford China Business Forum in Beijing on 2 September 2010. The author is grateful to Geoff Coppins, Richard Davies, Salina Ladha, Pippa Lowe, Gareth Murphy, Rhiannon Sowerbutts, Nick Vause and Iain de Weymarn for background research and comments.