A participant may see himself as prudent, believing his large credit exposures to be diversified and therefore not dangerous. Under certain circumstances, though, an exogenous event that causes the receivable from Company A to go bad will also affect those from Companies B through Z. History teaches us that a crisis often causes problems to correlate in a manner undreamed of in more tranquil times.

Source:   Berkshire Hathaway Shareholder Letters

In banking, the recognition of a “linkage” problem was one of the reasons for the formation of the Federal Reserve System. Before the Fed was established, the failure of weak banks would sometimes put sudden and unanticipated liquidity demands on previously-strong banks, causing them to fail in turn. The Fed now insulates the strong from the troubles of the weak. But there is no central bank assigned to the job of preventing the dominoes toppling in insurance or derivatives. In these industries, firms that are fundamentally solid can become troubled simply because of the travails of other firms further down the chain. When a “chain reaction” threat exists within an industry, it pays to minimize links of any kind. That’s how we conduct our reinsurance business, and it’s one reason we are exiting derivatives.

Source:   Berkshire Hathaway Shareholder Letters

The derivatives genie is now well out of the bottle, and these instruments will almost certainly multiply in variety and number until some event makes their toxicity clear. Knowledge of how dangerous they are has already permeated the electricity and gas businesses, in which the eruption of major troubles caused the use of derivatives to diminish dramatically. Elsewhere, however, the derivatives business continues to expand unchecked. Central banks and governments have so far found no effective way to control, or even monitor, the risks posed by these contracts.

Source:   Berkshire Hathaway Shareholder Letters

Investing in junk bonds and investing in stocks are alike in certain ways: Both activities require us to make a price-value calculation and also to scan hundreds of securities to find the very few that have attractive reward/risk ratios. But there are important differences between the two disciplines as well. In stocks, we expect every commitment to work out well because we concentrate on conservatively financed businesses with strong competitive strengths, run by able and honest people. If we buy into these companies at sensible prices, losses should be rare. a. Purchasing junk bonds, we are dealing with enterprises that are far more marginal. These businesses are usually overloaded with debt and often operate in industries characterized by low returns on capital. Additionally, the quality of management is sometimes questionable. Management may even have interests that are directly counter to those of debt holders. Therefore, we expect that we will have occasional large losses in junk issues.

Source:   Berkshire Hathaway Shareholder Letters

It’s easy to identify many investment managers with great recent records. But past results, though important, do not suffice when prospective performance is being judged. How the record has been achieved is crucial, as is the manager’s understanding of – and sensitivity to – risk (which in no way should be measured by beta, the choice of too many academics). In respect to the risk criterion, we were looking for someone with a hard-to-evaluate skill: the ability to anticipate the effects of economic scenarios not previously observed.

Source:   Berkshire Hathaway Shareholder Letters

Part of the appeal of Black-Scholes to auditors and regulators is that it produces a precise number. Charlie and I can’t supply one of those. We believe the true liability of our contracts to be far lower than that calculated by Black-Scholes, but we can’t come up with an exact figure – anymore than we can come up with a precise value for GEICO, BNSF, or for Berkshire Hathaway itself. Our inability to pinpoint a number doesn’t bother us: We would rather be approximately right than precisely wrong.

Source:   Berkshire Hathaway Shareholder Letters

Leverage, of course, can be lethal to businesses as well. Companies with large debts often assume that these obligations can be refinanced as they mature. That assumption is usually valid. Occasionally, though, either because of company-specific problems or a worldwide shortage of credit, maturities must actually be met by payment. For that, only cash will do the job.

Source:   Berkshire Hathaway Shareholder Letters

Borrowers then learn that credit is like oxygen. When either is abundant, its presence goes unnoticed. When either is missing, that’s all that is noticed. Even a short absence of credit can bring a company to its knees. In September 2008, in fact, its overnight disappearance in many sectors of the economy came dangerously close to bringing our entire country to its knees.

Source:   Berkshire Hathaway Shareholder Letters

The riskiness of an investment is not measured by beta (a Wall Street term encompassing volatility and often used in measuring risk) but rather by the probability – the reasoned probability – of that investment causing its owner a loss of purchasing-power over his contemplated holding period. Assets can fluctuate greatly in price and not be risky as long as they are reasonably certain to deliver increased purchasing power over their holding period.

Source:   Berkshire Hathaway Shareholder Letters

Stock prices will always be far more volatile than cash-equivalent holdings. Over the long term, however, currency-denominated instruments are riskier investments – far riskier investments – than widely-diversified stock portfolios that are bought over time and that are owned in a manner invoking only token fees and commissions. That lesson has not customarily been taught in business schools, where volatility is almost universally used as a proxy for risk. Though this pedagogic assumption makes for easy teaching, it is dead wrong: Volatility is far from synonymous with risk. Popular formulas that equate the two terms lead students, investors and CEOs astray.

Source:   Berkshire Hathaway Shareholder Letters

On Climate Change: This issue bears a similarity to Pascal’s Wager on the Existence of God. Pascal, it may be recalled, argued that if there were only a tiny probability that God truly existed, it made sense to behave as if He did because the rewards could be infinite whereas the lack of belief risked eternal misery. Likewise, if there is only a 1% chance the planet is heading toward a truly major disaster and delay means passing a point of no return, inaction now is foolhardy. Call this Noah’s Law: If an ark may be essential for survival, begin building it today, no matter how cloudless the skies appear.

Source:   Berkshire Hathaway Shareholder Letters

Acknowledging what you don’t know is the dawning of wisdom.

Source:   Poor Charlie's Almanack

Beta and Modern Portfolio Theory and the like – none of it makes any sense to me…how can professors spread this? I’ve been waiting for this craziness to end for decades. It’s been dented and it’s still out there.

Source:   Poor Charlie's Almanack

If you stop to think about it, a pari-mutuel system [like a race-track] is a market. Everybody goes there and bets, and the odds change based on what's bet. That's what happens in the stock market.

Source:   Poor Charlie's Almanack

The long term future of a company is at best “an educated guess”. Some of the best-educated guesses, derived from the most painstaking research, have turned out to be abysmally wrong.

Source:   The Intelligent Investor

The margin-of-safety idea becomes much more evident when we apply it to the field of undervalued or bargain securities. We have here, by definition, a favorable difference between price on the one hand and indicated or appraised value on the other. That difference is the safety margin. It is available for absorbing the effect of miscalculations or worse-than-average luck. The buyer of bargain issues places particular emphasis on the ability of the investment to withstand adverse developments. For in most cases he has no enthusiasm about the company’s prospects.

Source:   The Intelligent Investor

[Margin of Safety] guarantees only that he has a better chance for profit than loss – not that loss is impossible.

Source:   The Intelligent Investor

Mathematics is not just a "numbers game", it is a way of thinking…probability is a qualitative subject.

Source:   Fooled By Randomness

It is a fact that our brain tends to go for superficial clues when it comes to risk and probability, these clues being largely determined by what emotions they elicit or the ease [with which] they come to mind. In addition to such [a] problem with the perception of risk, its is also a scientific fact, and a shocking one, that both risk detection and risk avoidance are not mediated in the "thinking" part of the brain but largely in the emotional one (the "risk as feelings" theory). The consequences are not trivial: It means that rational thinking has little, very little, to do with risk avoidance. Much of what rational thinking seems to do is rationalize one's actions by fitting some logic to them.

Source:   Fooled By Randomness

From standpoint of an institution, the existence of a risk manager has less to do with actual risk reduction than it has to do with the impression of risk reduction.

Source:   Fooled By Randomness

…it is not natural for us to learn from history…It is a platitude that children learn only from their own mistakes; they will cease to touch a burning stove only when they are themselves burned; no possible warning by others can lead to developing the smallest part form of consciousness. Adults, too, suffer from such a condition...This congenital denigration of the experience of others is not limited to children or to people like myself; it affects business decision-makers and investors on grand scale.

Source:   Fooled By Randomness

Where statistics becomes complicated, and fails us, is when we have distributions that are not symmetric [and/or not stationary].

Source:   Fooled By Randomness

The science of econometrics consists of the application of statistics to samples taken at different periods of time, which we called time-series. It is based on studying the time series of economic variables, data, and other matters. In the beginning, when I knew close to nothing, I wondered whether time-series reflecting the activity of people now dead or retired should matter for predicting the future. Econometricians who knew a lot more than I did about these matters asked no such questions; this hinted that it was in all likelihood a stupid inquiry...I am now convinced that, perhaps, most of econometrics could be useless - much of what financial statisticians know would not be worth knowing.

Source:   Fooled By Randomness

In his 'Treatise on Human Nature', the Scots philosopher David Hume posed the issue [of induction] in the following way: "No amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute than conclusion".

Source:   Fooled By Randomness

The reason I feel that he [Karl Popper] is important to us traders is because to him the matter of knowledge and discovery is not so much in dealing with what we know, as in dealing with what we don't know…My extreme an obsessive Popperism is carried out as follows: I speculate in all of my activities on theories that represent some vision of the world, but with the following stipulation: No rare event should harm me. In fact, I would like all conceivable rare events to to help me.

Source:   Fooled By Randomness

Like [Pascal's Wager], I will therefore state the following argument: If the science of statistics can benefit me in anything, I will use it. If it poses a threat, then I will not. I want to take the best of what the past can give me without its dangers. Accordingly, I will use statistics and inductive methods to make aggressive bets, but I will not use them to manage my risks and exposure. Surprisingly, all the surviving traders I know seem to have done the same. They trade on ideas bases on some observation (that includes past history) but, like the Popperian scientists, they make sure that the costs of being wrong are limited (and their probability is not derived from past data).

Source:   Fooled By Randomness

…Investing can't be reduced to an algorithm and turned over to a computer. Even the best investors [or algorithms] don't get it right all the time. The reasons are simple. No rule always works. The environment isn't controllable and the circumstances rarely repeat exactly. Psychology plays a major role in markets and because it's highly variable, cause-and-effect relationships aren't reliable. An investment approach may work for a while, but eventually the actions it calls for will change the environment, meaning a new approach is needed. And if others emulate an approach, that will blunt its effectiveness. Investing, like economics, is more art than science. And that means it can get a little messy.

Source:   The Most Important Thing

Theory says high return is associated with high risk because the former exists to compensate for the latter. But pragmatic value investors feel just the opposite: They believe high return and low risk can be achieved simultaneously by buying things for less than they’re worth. In the same way, overpaying implies both low return and high risk.

Source:   The Most Important Thing

Ben Graham and David Dodd put it this way more than sixty years ago in the second edition of Security Analysis, the bible of value investors: “the relation between different kinds of investments and the risk of loss is entirely too indefinite, and too variable with changing conditions, to permit of sound mathematical formulation.”

Source:   The Most Important Thing

Where does that leave us? If the risk of loss can’t be measured, quantified or even observed—and if it’s consigned to subjectivity—how can it be dealt with? Skillful investors can get a sense for the risk present in a given situation. They make that judgment primarily based on (a) the stability and dependability of value and (b) the relationship between price and value. Other things will enter into their thinking, but most will be subsumed under these two.

Source:   The Most Important Thing

There have been many efforts of late to make risk assessment more scientific. Financial institutions routinely employ quantitative “risk managers” separate from their asset management teams and have adopted computer models such as “value at risk” to measure the risk in a portfolio. But the results produced by these people and their tools will be no better than the inputs they rely on and the judgments they make about how to process the inputs. In my opinion, they’ll never be as good as the best investors’ subjective judgments.

Source:   The Most Important Thing

And that brings me to the quotation from Elroy Dimson that led off this chapter: “Risk means more things can happen than will happen.” Now we move toward the metaphysical aspects of risk.

Source:   The Most Important Thing

Understanding uncertainty: The possibility of a variety of outcomes means we musn't think of the future in terms of a single result but rather as a range of possibilities. The best we can do is fashion a probability distribution that summarizes the possibilities and describes their relative likelihood. We must think about the full range, not just the ones that are most likely to materialize. Some of the greatest losses arise when investors ignore the improbable possibilities.

Source:   The Most Important Thing

Bruce [Greenwald] has put it admirably into words: “There’s a big difference between probability and outcome. Probable things fail to happen—and improbable things happen—all the time.” That’s one of the most important things you can know about investment risk.

Source:   The Most Important Thing

For the most part, I think it’s fair to say that investment performance is what happens when a set of developments—geopolitical, macro-economic, company-level, technical and psychological—collide with an extant portfolio. Many futures are possible, to paraphrase Dimson, but only one future occurs. The future you get may be beneficial to your portfolio or harmful, and that may be attributable to your foresight, prudence or luck.

Source:   The Most Important Thing

Whereas the theorist thinks return and risk are two separate things, albeit correlated, the value investor thinks of high risk and low prospective return as nothing but two sides of the same coin, both stemming primarily from high prices.

Source:   The Most Important Thing

Controlling the risk in your portfolio is a very important and worthwhile pursuit. The fruits, however, come only in the form of losses that don’t happen. Such what-if calculations are difficult in placid times.

Source:   The Most Important Thing

The longer I’m involved in investing, the more impressed I am by the power of the credit cycle. It takes only a small fluctuation in the economy to produce a large fluctuation in the availability of credit, with great impact on asset prices and back on the economy itself. The process is simple: 1) The economy moves into a period of prosperity. 2) Providers of capital thrive, increasing their capital base. 3) Because bad news is scarce, the risks entailed in lending and investing seem to have shrunk.  4) Risk averseness disappears. 5) Financial institutions move to expand their businesses—that is, to provide more capital. 6) They compete for market share by lowering demanded returns (e.g., cutting interest rates), lowering credit standards, providing more capital for a given transaction and easing covenants.   At the extreme, providers of capital finance borrowers and projects that aren’t worthy of being financed. As The Economist said earlier this year, “the worst loans are made at the best of times.”

Source:   The Most Important Thing

In Field of Dreams, Kevin Costner was told, “If you build it, they will come.” In the financial world, if you offer cheap money, they will borrow, buy and build—often without discipline, and with very negative consequences.

Source:   The Most Important Thing

Time and time again, the combination of pressure to conform and the desire to get rich causes people to drop their independence and skepticism, overcome their innate risk aversion and believe things that don’t make sense. However negative the force of greed might be, always spurring people to strive for more and more, the impact is even stronger when they compare themselves to others. This is one of the most harmful aspects of what we call human nature. People who might be perfectly happy with their lot in isolation become miserable when they see others do better. In the world of investing, most people find it terribly hard to sit by and watch while others make more money than they do.

Source:   The Most Important Thing

Investment results will be determined entirely by what happens in the future, and while we may know what will happen much of the time, when things are “normal,” we can’t know much about what will happen at those moments when knowing would make the biggest difference.

Source:   The Most Important Thing

When buyers compete to put large amounts of capital to work in a market, prices are bid up relative to value, prospective returns shrink, and risk rises. It’s only when buyers predominate relative to sellers that you can have highly overpriced assets. The warning signs shouldn’t be hard to spot.

Source:   The Most Important Thing

The lender who insists on margin for error and lends only to strong borrowers will experience few credit losses. But this lender’s high standards will cause him or her to forgo lending opportunities that will go to lenders who are less insistent on creditworthiness. The aggressive lender will look smarter than the prudent lender (and make more money) as long as the environment remains salutary. The prudent lender’s reward comes only in bad times, in the form of reduced credit losses. The lender who insists on margin for error won’t enjoy the highest highs but will also avoid the lowest lows. That’s what happens to those who emphasize defense.

Source:   The Most Important Thing

Of the two ways to perform as an investor—racking up exceptional gains and avoiding losses—I believe the latter is the more dependable.

Source:   The Most Important Thing

Worry about the possibility of loss. Worry that there’s something you don’t know. Worry that you can make high-quality decisions but still be hit by bad luck or surprise events. Investing scared will prevent hubris; will keep your guard up and your mental adrenaline flowing; will make you insist on adequate margin of safety; and will increase the chances that your portfolio is prepared for things going wrong. And if nothing does go wrong, surely the winners will take care of themselves.

Source:   The Most Important Thing

[Some of Marks's observations]:  1) Too much capital availability makes money flow to the wrong places. 2) When capital is in oversupply, investors compete for deals by accepting low returns and a slender margin for error. 3) Widespread disregard for risk creates great risk. 4) Inadequate due diligence leads to investment losses. 5) In heady times, capital is devoted to innovative investments, many of which fail the test of time. 6) Hidden fault lines running through portfolios can make the prices of seemingly unrelated assets move in tandem. 7) Psychological and technical factors can swamp fundamentals 8)  Markets change, invalidating models. 9) Leverage magnifies outcomes but doesn’t add value. 10) Excesses correct.

Source:   The Most Important Thing

Loss of confidence and resolve can cause investors to sell at the bottom, converting downward fluctuations into permanent losses and preventing them from participating fully in the subsequent recovery. This is the greatest error in investing—the most unfortunate aspect of pro-cyclical behavior—because of its permanence and because it tends to affect large portions of portfolios.

Source:   The Most Important Thing

Risk control and margin for error should be present in your portfolio at all times. But you must remember that they’re “hidden assets.” Most years in the markets are good years, but it’s only in the bad years—when the tide goes out—that the value of defense becomes evident. Thus, in the good years, defensive investors have to be content with the knowledge that their gains, although perhaps less than maximal, were achieved with risk protection in place … even though it turned out not to be needed.

Source:   The Most Important Thing

In a pure exchange, equilibrium has a clearly defined meaning: it is the price that clears the markets. When it applied to financial markets, equilibrium becomes more like a theological concept: it is the price that ought to clear the markets if market prices did not have any effect on the participants' attitudes and/or the fundamentals. But it is the nature of financial markets that they do have such effects. Consequently financial markets often develop boom/bust sequences and other far-from-equilibrium conditions.

Source:   The Alchemy of Finance

There seems to be a special affinity between reflexivity and credit. That is hardly surprising: credit depends on expectations; expectations involve bias; hence credit is one of the main avenues the permit bias to play a causal role in the course of events. But there is more to it. Credit seems to be associated with a particular kind of reflexive pattern that is known as boom and bust. The pattern is asymmetrical: the boom is drawn out and accelerates gradually; the bust is sudden and often catastrophic.

Source:   The Alchemy of Finance

Valuation is supposed to be a passive relationship in which the value reflects the underlying asset; but in this case [of credit] it involves a positive act: a loan is made. The act of lending may affect the collateral value: that is the connection that gives rise to a reflexive process.

Source:   The Alchemy of Finance

More money has probably been lost by investors holding a stock they really did not want until they could “at least come out even” than from any other single reason. If to these actual losses are added the profits that might have been made through the proper reinvestment of these funds if such reinvestment had been made when the mistake was first realized, the cost of self-indulgence becomes truly tremendous. Furthermore this dislike of taking a loss, even a small loss, is just as illogical as it is natural. If the real object of common stock investment is the making of a gain of a great many hundreds per cent over a period of years, the difference between, say, a 20 per cent loss or a 5 per cent profit becomes a comparatively insignificant matter. What matters is not whether a loss occasionally occurs. What does matter is whether worthwhile profits so often fail to materialize that the skill of the investor or his advisor in handling investments must be questioned.

Source:   Common Stocks and Uncommon Profits

The price of any particular stock at any particular moment is determined by the current financial-community appraisal of the particular company, of the industry it is in, and to some degree of the general level of stock prices. Determining whether at that moment the price of a stock is attractive, unattractive or somewhere in between depends for the most part on the degree these appraisals vary from reality. However, to the extent that the general level of stock prices affects the total picture, it also depends somewhat on correctly estimating coming changes in certain purely financial factors, of which interest rates are by far the most important.

Source:   Common Stocks and Uncommon Profits

Buffett is able to maintain this high level of knowledge about Berkshire’s businesses because he purposely limits his selection to companies that are within his area of financial and intellectual understanding. His logic is compelling. If you own a company (either outright or as a shareholder) in an industry you do not fully understand, you cannot possibly interpret developments accurately or make wise decisions.

Source:   The Warren Buffett Way

“Invest in your circle of competence,” Buffett counsels. “It’s not how big the circle is that counts; it’s how well you define the parameters.”

Source:   The Warren Buffett Way

“Severe change and exceptional returns usually don’t mix,” Buffett observes. Most people, unfortunately, invest as if the opposite were true. Investors tend to be attracted to fast-changing industries or companies that are in the midst of a corporate reorganization. For some unexplained reason, says Buffett, investors are so infatuated with what tomorrow may bring that they ignore today’s business reality.

Source:   The Warren Buffett Way

What’s wrong with conventional diversification? For one thing, it greatly increases the chances that you will buy something you don’t know enough about. “Know-something” investors, applying the Buffett tenets, would do better to focus their attention on just a few companies—five to 10, Buffett suggests. For the average investor, a legitimate case can be made for investing in 10 to 20 companies.

Source:   The Warren Buffett Way

"It is a mistake to think one limits one’s risk by spreading too much between enterprises which one knows little and has no reason for special confidence. . . . One’s knowledge and experience are definitely limited and there are seldom more than two or three enterprises at any given time in which I personally feel myself entitled to put full confidence." [said Keynes]

Source:   The Warren Buffett Way

Keynes prepared a full policy report for the Chest Fund, outlining his principles: 1. A careful selection of a few investments having regard to their cheapness in relation to their probable actual and potential intrinsic [emphasis his] value over a period of years ahead and in relation to alternative investments at the time; 2. A steadfast holding of these fairly large units through thick and thin, perhaps several years, until either they have fulfilled their promise or it is evident that they were purchased on a mistake; 3. A balanced [emphasis his] investment position, i.e., a variety of risks in spite of individual holdings being large, and if possible opposed risks.

Source:   The Warren Buffett Way

Buffett, Munger, Ruane, Simpson. It is clear the superinvestors of Buffettville have a common intellectual approach to investing. They are united in their belief that the way to reduce risk is to buy stocks only when the margin of safety (that is, the favorable discrepancy between the intrinsic value of the company and today’s market price) is high. They also believe that concentrating their portfolios around a limited number of these high-probability events not only reduces risk, but helps to generate returns far above the market rate of return.

Source:   The Warren Buffett Way

...loss aversion, and it is, in my opinion, the single most difficult hurdle that prevents most investors from successfully applying the Warren Buffett approach to investing.

Source:   The Warren Buffett Way

Buffett has a different definition of risk: the possibility of harm or injury. And that is a factor of the “intrinsic value risk” of a business, not the price behavior of the stock. The real risk, Buffett says, is whether after-tax returns from an investment “will give him [an investor] at least as much purchasing power as he had to begin with, plus a modest rate of interest on that initial stake.”

Source:   The Warren Buffett Way

Risk, for Buffett, is inextricably linked to an investor’s time horizon. This alone is the single greatest difference between how Warren Buffett thinks about risk and how modern portfolio theory frames risk. If you buy a stock today with the intention of selling it tomorrow, Buffett explains, then you have entered into a risky transaction. The odds are no better than the toss of a coin—you will lose about half the time. However, says Buffett, if you extend your time horizon out to several years, the probability of its being a risky transaction declines meaningfully, assuming of course that you have made a sensible purchase.

Source:   The Warren Buffett Way

Constantly thinking in expected-value terms requires discipline and is somewhat unnatural. But the leading thinkers and practitioners from somewhat varied fields have converged on the same formula: focus not on the frequency of correctness but on the magnitude of correctness.

Source:   More Than You Know

Risk has an unknown outcome, but we know what the underlying outcome distribution looks like. Uncertainty also implies an unknown outcome, but we don’t know what the underlying distribution looks like.

Source:   More Than You Know

In markets, a symbiotic relationship between positive and negative feedback generally prevails. If all speculators destabilized prices, they would buy high and sell low, on average. The market would quickly eliminate such speculators. Further, arbitrage—speculation that stabilizes prices—unquestionably plays a prime role in markets. But the evidence shows that positive feedback can dominate prices, if only for a short time. Imitation can cause investors to deviate from their stated fundamental investment approach and likely provides important clues into our understanding of risk. Next time you buy or sell a stock, think of the guppies.

Source:   More Than You Know

Here’s my main point: markets can still be rational when investors are individually irrational. Sufficient investor diversity is the essential feature in efficient price formation. Provided the decision rules of investors are diverse—even if they are suboptimal—errors tend to cancel out and markets arrive at appropriate prices. Similarly, if these decision rules lose diversity, markets become fragile and susceptible to inefficiency. So the issue is not whether individuals are irrational (they are) but whether they are irrational in the same way at the same time.

Source:   More Than You Know

Many models in standard finance theory assume that stock price changes are normally distributed around the well-known bell curve. A normal distribution is a powerful analytical tool, because you can specify the distribution with only two variables, the mean and standard deviation. The model, despite its elegance, has a problem: it doesn’t describe real world results very well. In particular, the model is remiss in capturing “fat tails”: infrequent but very large price changes. The failure of risk-management models to fully account for fat tails has led to some high-profile debacles, including the 1998 demise of the hedge fund Long Term Capital Management.

Source:   More Than You Know

Much of the real world is controlled as much by the “tails” of distributions as by means or averages: by the exceptional, not the mean; by the catastrophe, not the steady drip; by the very rich, not the “middle class.” We need to free ourselves from “average” thinking. —Philip Anderson, Nobel Prize recipient in physics, “Some Thoughts About Distribution in Economics”

Source:   More Than You Know

In a triumph of modeling convenience over empirical results, finance theory treats price changes as independent, identically distributed variables and generally assumes that the distribution of returns is normal, or lognormal. The virtue of these assumptions is that investors can use probability calculus to understand the distribution’s mean and variance and can therefore anticipate various percentage price changes with statistical accuracy. The good news is that these assumptions are reasonable for the most part. The bad news, as physicist Phil Anderson notes above, is that the tails of the distribution often control the world.

Source:   More Than You Know

The standard model for assessing risk, the capital-asset-pricing model, assumes a linear relationship between risk and reward. In contrast, nonlinearity is endogenous to self-organized critical systems like the stock market. Investors must bear in mind that finance theory stylizes real world data. That the academic and investment communities so frequently talk about events five or more standard deviations from the mean should be a sufficient indication that the widely used statistical measures are inappropriate for the markets.

Source:   More Than You Know

The risk-reducing formulas behind portfolio theory rely on a number of demanding and ultimately unfounded premises. First, they suggest that price changes are statistically independent from one another. . . . The second assumption is that price changes are distributed in a pattern that conforms to a standard bell curve.

Source:   More Than You Know

Do financial data neatly conform to such assumptions? Of course, they never do. —Benoit B. Mandelbrot, “A Multifractal Walk down Wall Street”

Source:   More Than You Know

In an important and fascinating book, Why Stock Markets Crash, geophysicist Didier Sornette argues that stock market distributions comprise two different populations, the body (which you can model with standard theory) and the tail (which relies on completely different mechanisms). Sornette’s analysis of market drawdowns convincingly dismisses the assumption that stock returns are independent, a key pillar of classical finance theory. His work provides fresh and thorough evidence of finance theory’s shortcomings.

Source:   More Than You Know

Complex adaptive systems include governments, many corporations, and capital markets. Efforts to assert top-down control of these systems generally lead to failure, as happened in the former Soviet Union. Thinking about the market as a complex adaptive system is in stark contrast to classical economic and finance theory, which depicts the world in Newtonian terms. Economists treat agents as if they are homogenous and build linear models—supply and demand, risk and reward, price and quantity. None of this, of course, much resembles the real world.

Source:   More Than You Know