Thursday, September 20, 2012


nice article from the world question center by Mr. Charles Seife...


Our very brains revolt at the idea of randomness. We have evolved as a species to become exquisite pattern-finders — long before the advent of science, we figured out that a salmon-colored sky heralds a dangerous storm, or that a baby's flushed face likely means a difficult night ahead. Our minds automatically try to place data in a framework that allows us to make sense of our observations and use them to understand events and predict them.

Randomness is so difficult to grasp because it works against our pattern-finding instincts. It tells us that sometimes there is no pattern to be found. As a result, randomness is fundamental limit to our intuition; it says that there are processes that we can't predict fully. It's a concept that we have a hard time accepting even though it is an essential part of the way the cosmos works. Without an understanding of randomness, we are stuck in a perfectly predictable universe that simply doesn't exist outside of our own heads.

I would argue that only once we understand three dicta — three laws of randomness — can we break out of our primitive insistence on predictability and appreciate the universe for what it is rather than what we want it to be.

The First Law of Randomness: There is such a thing as randomness.

We use all kinds of mechanisms to avoid confronting randomness. We talk about karma, in a cosmic equalization that ties seemingly unconnected events together. We believe in runs of luck, both good and ill, and that bad things happen in threes. We argue that we are influenced by the stars, by the phases of the moon, and by the motion of the planets in the heavens. When we get cancer, we automatically assume that something — or someone — is to blame.

But many events are not fully predictable or explicable. Disasters happen randomly, to good people as well as to bad ones, to star-crossed individuals as well as those who have a favorable planetary alignment. Sometimes you can make a good guess about the future, but randomness can confound even the most solid predictions — don't be surprised when you're outlived by the overweight, cigar-smoking, speed-fiend motorcyclist down the block.

What's more, random events can mimic non-random ones. Even the most sophisticated scientists can have difficulty telling the difference between a real effect and a random fluke. Randomness can make placebos seem like miracle cures, harmless compounds appear to be deadly poisons, and can even create subatomic particles out of nothing.

The Second Law of Randomness: Some events are impossible to predict.

If you walk into a Las Vegas casino and observe the crowd gathered around the craps table, you'll probably see someone who thinks he's on a lucky streak. Because he's won several rolls in a row, his brain tells him that he's going to keep winning, so he keeps gambling. You'll probably also see someone who's been losing. The loser's brain, like the winner's, tells him to keep gambling. Since he's been losing for so long, he thinks he's due for a stroke of luck; he won't walk away from the table for fear of missing out.

Contrary to what our brains are telling us, there's no mystical force that imbues a winner with a streak of luck, nor is there a cosmic sense of justice that ensures that a loser's luck will turn around. The universe doesn't care one whit whether you've been winning or losing; each roll of the dice is just like every other.

No matter how much effort you put into observing how the dice have been behaving or how meticulously you have been watching for people who seem to have luck on their side, you get absolutely no information about what the next roll of a fair die will be. The outcome of a die roll is entirely independent of its history. And, as a result, any scheme to gain some sort of advantage by observing the table will be doomed to fail. Events like these — independent, purely random events — defy any attempts to find a pattern because there is none to be found.

Randomness provides an absolute block against human ingenuity; it means that our logic, our science, our capacity for reason can only penetrate so far in predicting the behavior of cosmos. Whatever methods you try, whatever theory you create, whatever logic you use to predict the next roll of a fair die, there's always a 5/6 chance you are wrong. Always.

The Third Law of Randomness: Random events behave predictably in aggregate even if they're not predictable individually

Randomness is daunting; it sets limits where even the most sophisticated theories can not go, shielding elements of nature from even our most determined inquiries. Nevertheless, to say that something is random is not equivalent to saying that we can't understand it. Far from it.

Randomness follows its own set of rules — rules that make the behavior of a random process understandable and predictable.

These rules state that even though a single random event might be completely unpredictable, a collection of independent random events is extremely predictable — and the larger the number of events, the more predictable they become. The law of large numbers is a mathematical theorem that dictates that repeated, independent random events converge with pinpoint accuracy upon a predictable average behavior. Another powerful mathematical tool, the central limit theorem, tells you exactly how far off that average a given collection of events is likely to be. With these tools, no matter how chaotic, how strange a random behavior might be in the short run, we can turn that behavior into stable, accurate predictions in the long run.

The rules of randomness are so powerful that they have given physics some of its most sacrosanct and immutable laws. Though the atoms in a box full of gas are moving at random, their collective behavior is described by a simple set of deterministic equations. Even the laws of thermodynamics derive their power from the predictability of large numbers of random events; they are indisputable only because the rules of randomness are so absolute.

Paradoxically, the unpredictable behavior of random events has given us the predictions that we are most confident in.

Wednesday, September 19, 2012

Taleb's Anti-fragility

from the world question center...


Just as a package sent by mail can bear a stamp "fragile", "breakable" or "handle with care", consider the exact opposite: a package that has stamped on it "please mishandle" or "please handle carelessly". The contents of such package are not just unbreakable, impervious to shocks, but have something more than that , as they tend to benefit from shocks. This is beyond robustness.

So let us coin the appellation "antifragile" for anything that, on average, (i.e., in expectation) benefits from variability. Alas, I found no simple, noncompound word in any of the main language families that expresses the point of such fragility in reverse. To see how alien the concept to our minds, ask around what's the antonym of fragile. The likely answer will be: robust, unbreakable, solid, well-built, resilient, strong, something-proof (say waterproof, windproof, rustproof), etc. Wrong — and it is not just individuals, but branches of knowledge that are confused by it; this is a mistake made in every dictionary. Ask the same person the opposite of destruction, they will answer construction or creation. And ask for the opposite of concavity, they will answer convexity.

A verbal definition of convexity is: benefits more than it loses from variations; concavity is its opposite. This is key: when I tried to give a mathematical expression of fragility (using sums of path-dependent payoffs), I found that "fragile" could be described in terms of concavity to a source of variation (random or nonrandom), over a certain range of variations. So the opposite of that is convexity — tout simplement.

A grandmother's health is fragile, hence concave, with respect to variations in temperature, if you find it preferable to make her spend two hours in 70? F instead of an hour at 0? F and another at 140? F for the exact 70? F on average. (A concave function of a combination f(½ x1+½ x2) is higher than the combination ½ f(x1)+ ½ f(x2).

Further, one could be fragile to certain events but not others: A portfolio can be slightly concave to a small fall in the market but not to extremely large deviations (Black Swans).

Evolution is convex (up to a point) with respect to variations since the DNA benefits from disparity among the offspring. Organisms benefit, up to a point, from a spate of stressors. Trial and error is convex since errors cost little, gains can be large.

Now consider the Triad in the Table. Its elements are those for which I was able to find general concavities and convexities and catalogue accordingly.

The Triad

Mythology — Greek
Sword of
Damocles, Rock of Tantalus
Biological & Economic Systems
Degeneracy (functional redundancy, in the Edelman-Galy sense)
Directed Research
Opportunistic research
Stochastic Tinkering (convex bricolage)
Human Body
Mollification, atrophy, "aging", sarcopenia
Hormesis, Mithridatism
Political Systems
Statelings, vassals under a large empire
City-State; Decentralized
Income of Executives (bonuses)
Modern urban
Ancient settlements
Nomadic and hunter-gatherer tribes
Decision Making
Model-based probabilistic
decision making
Heuristic-based decision making
Convex heuristics
Tacit with convexity
Ways of Thinking
Medieval Europe
Ancient Mediterranean
Hates mistakes
Mistakes are just information
Loves mistakes
Real life, pathemata mathemata
Real life and library
Additive treatment (give medication)
Subtractive treatment (remove items from consumption, say carbs, etc.)
Short Optionality
Long Optionality
Decision Making
Acts of commission
Acts of omission ("missed opportunity")
Oral Tradition
Small Business
Venture Capital
Public Debt
Private debt with no bailout
Small but specialized
Small but not specialized
Monomodal payoff
Barbell polarized payoff
Banks, Hedge funds managed by economists
Hedge Funds (some)
Hedge Funds
Agency Problem
Principal Operated
Reputation (profession)
Academic, Corporate executive, Pope, Bishop, Politician
Postal employee, Truck driver, train conductor
Artist, Writer
Reputation (class)
Middle Class
Minimum wage persons
aristocracy, old money

The larger the corporation, the more concave to some squeezes (although on the surface companies they claim to benefit from economies of scale, the record shows mortality from disproportionate fragility to Black Swan events). Same with government projects: big government induces fragilities. So does overspecialization (think of the Irish potato famine). In general most top-down systems become fragile (as can be shown with a simple test of concavity to variations).

Worst of all, an optimized system becomes quickly concave to variations, by construction: think of the effect of absence of redundancies and spare parts. So about everything behind the mathematical economics revolution can be shown to fragilize.

Further we can look at the unknown, just like model error, in terms of antifragility (that is, payoff): is what you are missing from a model, or what you don't know in real life, going to help you more than hurt you? In other words are you antifragile to such uncertainty (physical or epistemic)? Is the utility of your payoff convex or concave? Pascal was first to express decisions in terms of these convex payoffs. And economics theories produce models that fragilize (except rare exceptions), which explains why using their models is vastly worse than doing nothing. For instance, financial models based on "risk measurements" of rare events are a joke. The smaller the probability, the more convex it becomes to computational error (and the more concave the payoff): an 25% error in the estimation of the standard deviation for a Gaussian can increase the expected shortfall from remote events by a billion (sic) times! (Missing this simple point has destroyed the banking system).


Jensen's Inequality as the Hidden Engine of History

Now the central point. By a simple mathematical property, one can show why, under a model of uncertainty, items on the right column will be likely to benefit in the long run, and thrive, more than shown on the surface, and items on the left are doomed to perish. Over the past decade managers of companies earned in, the aggregate, trillions while retirees lost trillions (the fact that executives get the upside not the downside gives them a convex payoff "free option"). And aggressive tinkering fares vastly better than directed research. How?

Jensen's inequality says the following: for a convex payoff, the expectation of an average will be higher than the average of expectations. For a concave one, the opposite (grandmother's health is worse if on average the temperature is 70 than in an average temperature of 70).

Squaring is a convex function. Take a die (six sides) and consider a payoff equal to the number it lands on. You expect 3½. The square of the expected payoff will be 12¼ (square 3½). Now assume we get the square of the numbers on the die, 15.1666, so, the average of a square payoff is higher than the square of the average payoff.

The implications can be striking as this second order effect explains so much of hidden things in history. In expectation, anything that loves Black Swans will be present in the future. Anything that fears it will be eventually gone — to the extent of its concavity.

Monday, September 17, 2012

From Mr. Hussman's latest commentary

Last week, we observed a syndrome of evidence that matches only a handful of market extremes in history, including August-December 1972, August 1987, April-July 1998, July 1999, and March 2000, and April-July 2007. Investors with a good sense of market history will recognize all of those instances as points from which subsequent outcomes were steeply negative, even if stocks held up or advanced moderately over the short-run. With regard to the potential for steeply negative outcomes, we find that when we look across history, conditions similar to the present have been “enriched” with steep declines – another way of saying that the negative tail of the distribution is very fat here.

For example, if we break our estimates of prospective market return/risk into five quintiles or “buckets”, present estimates are clearly in the most negative bucket. Historically, 31% of instances in that worst bucket have been followed by a market decline of at least 10% over the following 6 month period, while 41% of all 10% market declines (occurring within a 6-month period) have started from instances in that bucket. In other words, while the lowest quintile captures 20% of the historical data, that bucket captures 10% market corrections more than twice as often as one would expect if those 10% declines were randomly distributed across market conditions. Similarly, the periods in the lowest quintile of prospective return/risk capture 45% of all 15% market declines that have occurred within a 6-month window, 54% of all 20% market declines, 69% of all 30% declines, and 87% of all declines of 35% or more (what would commonly be considered “crashes”).

In short, saying that our estimates of prospective return/risk are negative does not indicate that the market will or must plunge. Rather, it says that the average outcome has been quite negative, and the likelihood of extreme “tail events” is vastly enriched compared with more typical conditions throughout history. In this environment, market exposure has typically been far more costly than it has been beneficial, and investment opportunities have generally emerged after a period of market losses.

Mr. Hussman even more negative

As noted last week, Mr. Hussman has a very unfavorable risk-reward view of the U.S. equity market.  Mr. Hussman has been negative for quite awhile now, but look at what he thinks now...

Friday, September 14, 2012

What worries Mr. John Hussman

So what do I worry about? I worry that investors forget how devastating a deep investment loss can be on a portfolio. I worry that the constant hope for central bank action has given investors a false sense of security that recessions and deep market downturns can be made obsolete. I worry that the depth of the recessions and downturns – when they occur – will be much deeper precisely because of the speculation, moral hazard, and misallocation of resources that monetary authorities have encouraged. I worry that both a global recession and severe market downturn are closer at hand than investors assume, partly despite, and partly because, they have so fully embraced the illusory salvation of monetary intervention.

me too...

Tuesday, September 11, 2012

Mr. Seth Klarman quotes

Some good advice and knowledge to absorb from

“Most institutional investors… feel compelled… to swing at almost every pitch and forgo batting selectivity for frequency.”

“So if the entire country became security analysts, memorized Benjamin Graham’s ‘Intelligent Investor’ and regularly attended Warren Buffett’s annual shareholder meetings, most people would, nevertheless, find themselves irresistibly drawn to hot initial public offerings, momentum strategies and investment fads. People would still find it tempting to day trade and perform technical analysis on stocks. A country of security analysts would still overreact. In short, even the best trained investors would make the same mistakes investors have been making forever, and for the same immutable reason – that they cannot help it.”

“I will be buying what other people are selling. I will be buying what is loathed and despised.”

“In capital markets, price is set by the most panicked seller at the end of a trading day. Value, which is determined by cash flows and assets, is not. In this environment, the chaos is so extreme, the panic selling so urgent, that there is almost no possibility that sellers are acting on superior information. Indeed, in situation after situation, it seems clear that fundamentals do not factor into their decision making at all.”

“In the aftermath of this financial crisis, I think everyone needs to look deep within themselves and ask how they want to live their lives. Do they want to live close to the edge, or do they want stability? In my view, people should have a year or two of living expenses in cash if possible, and they shouldn’t use leverage anywhere in their lives.

“Baupost build numerous new positions as the markets fell in 2008. While it is always tempting to try to time the market and wait for the bottom to be reached (as if it would be obvious when it arrived), such a strategy has proven over the years to be deeply flawed. Historically, little volume transacts at the bottom or on the way back up, and competition from other buyers will be much greater when the markets settle down and the economy begins to recover. Moreover, the price recovery from a bottom can be very swift. Therefore, an investor should put money to work amidst the throes of a bear market, appreciating that things will likely get worse before they get better.”

“Here’s how to know if you have the makeup to be an investor. How would you handle the following situation? Let’s say you own a Procter & Gamble in your portfolio and the stock price goes down by half. Do you like it better? If it falls in half, do you reinvest dividends? Do you take cash out of savings to buy more? If you have the confidence to do that, then you’re an investor. If you don’t, you’re not an investor, you’re a speculator, and you shouldn’t be in the stock market in the first place.”