Category: Statistical Thinking

TV Weather Predictions? Wait Till Friday

April 21, 2008

An inexact science for sure.

The Odds of Dying From...

March 22, 2008

An interesting chart listing the odds of dying. I could not help but think of lottery odds when I saw that chart.

By the Numbers

March 03, 2008

This bit of research reminds me of Michael Lewis' Moneyball except this time it is the NBA receiving a "by the numbers" statistical analysis. The lesson? Count, count, count.

Black Swan

February 03, 2008

So was the black swan the Giants win or the Patriots undefeated record until the Giants win?

Super Bowl Strategy

February 01, 2008

With Super Bowl Sunday festivities ready to kick off, investors looking for a sure bet would be wise to watch the commercials. Buying the stock of publicly traded companies that run advertisements on game day has historically been a recipe for success, say researchers at the University of Wisconsin-Eau Claire. Sure bet?

Houston’s G.M. Is a Revolutionary Spirit in a Risk-Averse Mind

January 29, 2008

Another numbers guy takes the lead.

Economics of Recruiting

A new way to predict where top prospects will end up. Interesting research.

Food for Psych Thought

January 25, 2008

Just how representative are the people who volunteer for psychology experiments? Interesting.

Fat Tails and Nonlinearity

January 06, 2008

Food for thought (PDF) from Legg Mason's Michael Mauboussin.

The Median Isn't the Message by Stephen Jay Gould

January 02, 2008

A conversation about a friend's cancer came up today. I immediately thought of a chapter in Stephen Jay Gould's book "Full House". A quick search brought up the relevant passage. Of course, that "way" of thinking applies to all aspects of life.

The Black Swan Review

January 01, 2008

A review of (part 1 & part 2) The Black Swan forwarded to me by one of the Turtles.

Jim Simons Keeps Pushing

December 01, 2007

Perhaps the greatest example for viewing the markets as numbers is Jim Simons.

College Football Polls Aren’t What You Think

November 17, 2007

An interesting read that gets one into "numbers".

Give Me Some Fear!

November 03, 2007

A nice piece from the author of Freakonomics. Thinking in real numbers is not a human desire, the fear numbers are too good to pass up!

Monty Hall Problem

October 10, 2007

I am not saying this example will make you a better investor, but it will get your probabilistic juices flowing.

On the Randomness, or Lack Thereof, of a Baseball Linescore

August 23, 2007

A nice piece from Stephen Dubner that reminds of the markets.

Jim Simons Letter to Investors Today

August 10, 2007

Interesting reading...

***

Dear Renaissance Investor,

As promised in my July letter, posted today on the RIEF website, I want to share some thoughts on August-to-date performance in order to provide perspective on a most unusual period.

RIEF results through July 31 were below expectations, but not extraordinarily so. I’ve previously stated that the low volatility Basic System, to which our predictions are added, was not in sync with the market during much of this period. Nonetheless, we remain confident that over time the Basic System will match the return of the S&P and, enhanced by our predictive signals, should exceed it. Since we do not attempt to track this or any other index there will be periods of positive and negative relative returns.

August (down 8.7% through today) is a different story. The culprit is not the Basic System but our predictive overlay. While we believe we have an excellent set of predictive signals, some of these are undoubtedly shared by a number of long/short hedge funds. For one reason or another many of these funds have not been doing well, and certain factors have caused them to liquidate positions. In addition to poor performance these factors may include losses in credit securities, excessive risk, margin calls and others. All of this may not influence the direction of the overall market, but it may certainly alter the relationships of stocks to each other in a dramatic way. Given the undoubted partial overlap of our portfolios, these liquidations have had a negative impact on RIEF.

Other examples of such liquidations are the meltdown of risk arbitrage positions in the October 1987 crash, the forced liquidation of junk bonds around 1990 and the collapse of European bonds in 1994. Some of these were in the midst of a bear market, some not.

Such events tend to occur extremely infrequently. We cannot predict the duration of the current environment, but usually such behavior causes first pain and then opportunity. While we may hedge out some market risk, our basic plan is to stay the course and, as conditions revert to the norm, we anticipate the possibility of an attractive opportunity for RIEF. Our firm remains strong, and although Medallion has experienced some losses in August, it is solidly profitable year-to-date.

We are confident in our approach, and we urge you to contact our staff should you have any questions.

Sincerely,
Jim Simons

Statistics and Gun Control Debate

April 26, 2007

WSJ writer Carl Bialik makes good points about the complete picture frequently going missing in the gun control debate.

Hedge Funds & Politics: Paul Tudor Jones Hedges the Presidential Election

John Carney writes:

Paul Tudor Jones II’s is hedging his political bets. He donated to Republican Rudy Giuliani’s presidential “exploratory committee” (apparently that’s political speak for the campaign before the campaign). And next month he’s holding a big fund raiser for Democratic nomination hopeful Barack Obama, the New York Observer’s Politicker blog notes...The event will be held at Jones' oceanfront Greenwich mansion, which reportedly sits on top of a 25-car garage. More than 500 guests are expected to attend. The Politicker implies that Jones may have dumped Giuliani in keeping with his reputation for getting out of losing investment positions. We’re not so sure. While we’re not exactly experts in presidential politics here at DealBreaker, it seems to us that this is not so much a strike against Rudy as much as Hillary. She’s supposed to be the candidate with all the pull on Wall Street (wife of Bill Clinton, connected to Citigroup's Robert Rubin) and her position as a senator from New York, should give her connections to nearby Greenwich, Connecticut’s hedge fund money. But Obama has been cleaning her clock when it comes to donations from the world of finance. And now he can add PTJII to the list.

Black Swans and Virginia Tech

April 24, 2007

A recent op-ed in the LA Times examines Black Swans and Virginia Tech (PDF). An excerpt:

Efforts to explain the Virginia Tech massacre perfectly illustrate one of the central points of an idiosyncratically brilliant new book by Nassim Nicholas Taleb, "The Black Swan: The Impact of the Highly Improbable." When completely caught out by some random event, we humans are wonderfully good at retrospectively predicting it. In reality, however, Cho was what Taleb calls a "black swan."

Nassim Taleb and the Black Swan: A Retrospective, by Dave “Surf” Goodboy

April 21, 2007

A first hand account about Nassim Taleb's new book from Dave Goodboy.

What Really Ruined Baseball

April 02, 2007

An article from the New York Times with implications beyond baseball:

April 2, 2007
Op-Ed Contributor
What Really Ruined Baseball
By J. C. BRADBURY

WITH an off-season that included Mark McGwire’s rejection by Hall of Fame voters, Barry Bonds’s continuing problems and accusations that Gary Matthews Jr. of the Angels had obtained human growth hormones, it’s hard not to think about the influence of performance-enhancing drugs this opening day.

Continue reading What Really Ruined Baseball »

Faux Experts

February 25, 2007

Following up on my post the other day about Nassim Taleb, I found a question/answer with him about his new book The Black Swan:

Q: What do you want people to take away from reading your book?

A: How not to be a fool for things that matter. You can take advantage of uncertainty if you know how to look it in the eye, and know the limits of what we understand. You should learn to accept fuzziness and know that we know very little in some domains, but that it can be so useful a guidance to reality. How to avoid taking seriously the "faux experts" (those who wear suits and act in a pompous way). How listening to the media, or studying economics, degrades your knowledge of the world.

His advice is straightforward and very on target, but how many people will really stop to reflect on his words?

Black Swan Glossary

February 23, 2007

The Black Swan Glossary (PDF) from Nassim Taleb. Good reading.

Tough Luck in the Rough

January 22, 2007

From a WSJ 'golf' article comes an excerpt about the long run:

So how should golfers treat luck, both good and bad, when it happens to them? Don't be paranoid or solipsistic. Gio Valiante, a mental-game consultant and author, says golfers "must separate what is controllable and what is not controllable." Weather and bounces, both good and bad, are definitely not. Dr. Valiante, who wrote the book "Fearless Golf," said golfers must "expect the best, but prepare for everything." When it seems that all the bounces are going your opponent's way, remind yourself that golf is a "fair game" and over many rounds of golf, the bounces do even out. For what most of us call luck, Dr. Valiante uses the more mathematical neutral term of probability. In other words, the golf gods aren't always against you. Really. But this time, pay up, pal.

Cambridge Appoints Professor of Risk; David Harding Effort

January 15, 2007

An interesting press release:


David Harding

A new Professorship designed to help improve people’s understanding of the mathematics of risk is being established at the University of Cambridge.

The new Winton Professor of the Public Understanding of Risk will seek to help individuals, institutions and government refine their decisions in risky situations.

Risk is a factor in all human activity and different people react to risks in very different ways. Questions requiring a scientific ability to assess the chances of something happening – or not happening – arise all the time. Here are some examples:

• Following the poisoning of the Russian ex-spy Alexander Litvinenko, traces of polonium-210 were found at various locations in London that he had visited. Statistically, how probable is it that someone who visited the same locations at a later stage would contract radiation poisoning?

• A recent study of transfusion patients given blood contaminated with the human form of mad cow disease has indicated that the 24 still alive are at “substantial” risk of contracting vCJD. What are the risks of contracting vCJD via a blood transfusion? How do they compare to the risks of getting the same condition by eating meat?

• An apparently healthy woman is judged to be at risk of breast cancer and is advised to undergo mastectomy. Should she do so?

• A person has to cross a main road to reach the shops. Should (s)he walk straight across the road, or use an available footbridge instead?

• How sensible would it be for me to invest in the stock market today? Might delaying improve my prospects greatly?

• A 29-year-old man decides to marry his girlfriend of three years. What is the chance that he will meet a more suitable partner at a later stage?

As these examples show, risks need to be considered in both the most ordinary of situations, and in high-pressure environments. Risk assessment is often based on analysis of data, but there is always a danger that statistics can be abused. Expert evidence in courts has been subjected to close scrutiny in recent high-profile cases such as the prosecution in the USA of OJ Simpson, and the cases of SIDS (sudden infant death syndrome) in the UK.

“The way to confront risk is via mathematics and statistics,” Professor Geoffrey Grimmett, head of the Department of Pure Mathematics and Mathematical Statistics, said. “This new Professorship will enable Cambridge to play an important role in clarifying the understanding of risk in many fields of human endeavour. It will strengthen our ability to reach out beyond Cambridge to government and the public alike.”

The new Winton Professorship has been created in perpetuity in the Statistical Laboratory of Cambridge University, thanks to a £3.3 million donation from The Winton Charitable Foundation. David Harding, a Cambridge alumnus and Managing Director of Winton Capital Management, a London-based hedge fund, is a Trustee of the Foundation.

“My time at Cambridge studying Natural Sciences showed me the importance of accuracy in empirical information and its interpretation,” he said. “This has been a key factor in my career in finance and is highly relevant to our awareness of the risks that affect us in our everyday lives. I am delighted to make a contribution to public debate and policy by helping create this new position at Cambridge.”

Professor Alison Richard, Vice-Chancellor of the University of Cambridge, said: “The Winton Charitable Foundation has been wonderfully generous in its support of the Cambridge 800th Anniversary Campaign. Endowed positions such as the Winton Professorship are of very special value to the University and I look forward to appointing the inaugural holder of this major new post.”

Mathematical Proof?

December 20, 2006

Feedback:

I could find no discussion of the mathematical theories which predict the success of trend following methods [in your book]. I believe that this omission is a deficiency in an otherwise excellent book. Of course, there is the possibility that I’m just stupid and can’t find what I’m looking for when it’s in front of my face. If this is the case, please forgive the above comments and direct me to the relevant part of the book. I have the “New Expanded Edition” [of Trend Following].

I will open this up to all readers for feedback.

Mark Shore White Paper on Skew

November 03, 2006

I had the opportunity to meet Mark Shore last spring in New York City at a presentation. His paper on 'Skew' (PDF) will be of interest to many readers.

Sabermetrician Bill James on Objectivity

November 02, 2006

I was forwarded this excerpt, which apparently first appeared on Victor Niederhoffer's site from a contributor. It is Sabermetrician Bill James speaking, from his 1981 Baseball Abstract, on the difference between sports writing and sabermetrics:

1. Sports writing draws on the available evidence, and forces conclusions by selecting and arranging that evidence so that it points in the direction desired. Sabermetrics introduces new evidence, previously unknown data derived from original source material.

2. Sportswriting designs its analysis to fit the situation being discussed; sabermetrics designs methods which would be applicable not only in the present case but in any other comparable situation. The sportswriter say this player is better than that one because this player had 20 more home runs, 10 more doubles, and 40 more walks and those things are more important than that players 60 extra base hits and 31 extra stolen bases, and besides, there is always defense and if all else fails team leadership. If player C is introduced into this discussion, he is a whole new article. Sabermetrics puts into place formulas, schematic designs, or theories of relationship which could compare not only this player to that one, but to any player who might be introduced into the discussion.

3. Sportswriters characteristically begin their analysis with a position on an issue; sabermetrics begins with the issue itself. The most over-used form in journalism is the diatribe, the endless impassioned and quasi-logical pitches for the cause of the day--Mike Norris for the Cy Young Award, Rickey Henderson for MVP, Gil Hodges for the Hall of Fame, everybody for lower salaries and let's all line up against the DH. Sports writing "analysis" is largely an adversary process, with the most successful sportswriter being the one who is the most effective advocate of his position. I personally, of course, have positions which I advocate occasionally, but sabermetrics by its nature is unemotional, non-committal. The sportswriter attempts to be a good lawyer; the sabermetrician, a fair judge.

James objective decision making process dovetails nicely with the objective decision making of his current boss trend following trader John W. Henry.

Maybe We Should Leave That Up to the Computer

July 18, 2006

From the NY Times, an interesting read (PDF). An excerpt:

Models have other advantages beyond their accuracy and consistency. They allow an organization to codify and centralize its hard-won knowledge in a concrete and easily transferable form, so it stays put when the experts move on. Models also can teach newcomers, in part by explaining the individual steps that lead to a given choice. They are also faster than people, are immune to fatigue and give the human experts more time to work on other tasks beyond the current scope of machines.

Lucky or Not?

June 26, 2006

From the Wall Street Jounral comes Russell Adams' article Is that team good -- or just lucky? An excerpt to consider:

Melky Cabrera, a highly touted 21-year-old outfielder for the New York Yankees, started off the season well, batting over .300 through early June. Now he is in a slump, hitting .189 in his last 10 games. For fans and the Yankees, the question is simple: How much of the rookie's impressive start was dumb luck? A lot of it, according to some baseball number-crunchers. Using new statistical methods, they calculated that the equivalent of one in four of Mr. Cabrera's early-season hits resulted from chance, not skill. Subtracting out good luck, his early season batting average should have been .231 -- nearly 80 points lower than what showed up in the box scores. Even in the numbers-obsessed world of sports, baseball has stood out for its efforts to track all aspects of the game. Now its fanatic record-keepers are on a quest to quantify something seemingly beyond measurement: the ethereal quality of luck. They're using insights into randomness that are shaking up other fields, from cancer research to weapons testing -- and that may even help you pick a good mutual fund.

This excerpt is useful food for thought when analyzing performance data of trend followers...especially when they are doing really well or really bad. The key is to think about how they typically trade.

9 Innings with Jeff Angus

May 13, 2006

As a former baseball catcher, I found this excerpt and associated PDF useful in thinking about trading success:

"Baseball metaphors run through business speak as easily as Willie Mays ran down fly balls. But too often, writes consultant and baseball columnist Jeff Angus in Management by Baseball (HarperCollins, May), business fails to live up to the American pastime. Fast Company (PDF) shared a bleacher with him at a spring-training game of his hometown Seattle Mariners."

In the PDF, this line caught my eye:

"It helps to think like a catcher, which is why so many become good managers. A catcher always has the whole play in front of him and can think critically about what he sees."

Busting Baseball Myths

April 22, 2006

A reader emailed me an article (PDF) tonight titled "Busting Baseball Myths: Scientist Throws Big Curveballs". It quickly reminded me of prior posts closely related:

1. Gerd Gigerenzer: Make Decisions Fast (Includes Video).

2. Simple Heuristics That Make Us Smart.

Not sure how this all relates to trading? It does. Give it some time to marinate.

Taleb Articles

February 16, 2006

There is a very good article (PDF) on Nassim Nicholas Taleb in the just out issue of Active Trader magazine. I don't subscribe, it just comes to me, but this one article was very good. The link above is, however, an abbreviated version of the print version. Taleb is another trader, like trend followers, chasing 'fat tails'.

More Taleb? Here is a Fortune article (PDF) on Taleb and his class syllabus (PDF).

Gambler's Fallacy

January 14, 2006

A good reminder (PDF) worth reading. An excerpt:

"Imagine an unbiased coin is flipped three times, and each time the coin lands on heads. If you had to bet $1000 on the next toss, what side would you choose? Heads, tails or no preference? Anyone calling tails is suffering from the gambler's fallacy - a belief randomness mean reverts. Of course, it doesn't. The coin has no memory, on each flip it is just as likely to come up heads or tails. How does this relate to the equity market? Well, year on year returns in equities are essentially a random process, just like the coin toss. So saying markets can't go down four years in a row is just like calling tails in the coin tossing example..."

I do know the article was written in 2003, but does that make a difference to the author's overall lesson?

European Trend Trader

May 11, 2005

Conducting interviews over the last 5 months has revealed "niches" among trend traders. What do I mean? My book Trend Following covers a distinct grouping of price-based trend following traders. There are, however, traders who trade trends using different entry and exit methods. Instead of relying on price, some rely on specific mathematically based patterns for their entries and exits.

Today I had a conference call with one such trader. Based he Europe, he manages over $1 billion USD in client money and has a track record exceeding 10 years (this is a different trader than the one I met with last Friday in New York City). The big picture lesson? Even if most trend traders are highly correlated, if you work hard and do the research, there exist uncharted territories in trend trading yet to be conquered.

But does this mean this trader's philosophy is entirely different than trend followers? No, not at all. It means he has found a space where he thinks his method of entry and exit are superior. He still, like trend followers, must use great risk management to control his downside. And at the end of the day, he too needs trending markets to make money.

Representing Uncertainty

May 04, 2005

In doing some research on the concept of 'uncertainty', this paragraph caught my eye:

"If there is one thing that defines and limits our efforts to better understand extreme and rare events it is uncertainty. Uncertainty arises from both an imperfect understanding of the rare events and processes we wish to study (e.g., terrorism, natural hazards), and the imperfect, out-of-date, and incomplete data we must work with in order to try and understand these events and processes."
Mark Harrower
University of Wisconsin-Madison

Along these lines consider the following white paper "Confronting Uncertainty: Intelligent Risk Management with Futures" from trader Robert M. Tamiso: View PDF.

Sharpe Ratio Thoughts

April 25, 2005

How should one look at trend following performance? Winton Capital, David Harding's successful trend following shop, offers insights from their recent white paper PDF.

What Are the Odds?

April 11, 2005

Consider:

"The true meaning of the word [odds] is ''a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection.'' In other words, pure happenstance. Yet by merely noticing a coincidence, we elevate it to something that transcends its definition as pure chance. We are discomforted by the idea of a random universe. Like Mel Gibson's character Graham Hess in M. Night Shyamalan's new movie ''Signs,'' we want to feel that our lives are governed by a grand plan. The need is especially strong in an age when paranoia runs rampant. ''Coincidence feels like a loss of control perhaps,'' says John Allen Paulos, a professor of mathematics at Temple University and the author of ''Innumeracy,'' the improbable best seller about how Americans don't understand numbers. Finding a reason or a pattern where none actually exists ''makes it less frightening,'' he says, because events get placed in the realm of the logical. ''Believing in fate, or even conspiracy, can sometimes be more comforting than facing the fact that sometimes things just happen.''...We are far too taken...with superfluous facts and findings that have no bearing on the statistics of coincidence. After our initial surprise...the real yardstick for measuring probability is ''How surprised should we be?'' How surprising is it, to use this example, that two 70-year-old men in the same town should die within two hours of each other? Certainly not common, but not unimaginable. But the fact that they were brothers would seem to make the odds more astronomical. This, however, is a superfluous fact. What is significant in their case is that two older men were riding bicycles along a busy highway in a snowstorm, which greatly increases the probability that they would be hit by trucks...Statisticians ...emphasize that when something striking happens, it only incidentally happens to us. When the numbers are large enough, and the distracting details are removed, the chance of anything is fairly high. Imagine a meadow, he says, and then imagine placing your finger on a blade of grass. The chance of choosing exactly that blade of grass would be one in a million or even higher, but because it is a certainty that you will choose a blade of grass, the odds of one particular one being chosen are no more or less than the one to either side...One relatively simple example of this is ''the birthday problem.'' There are as many as 366 days in a year (accounting for leap years), and so you would have to assemble 367 people in a room to absolutely guarantee that two of them have the same birthday. But how many people would you need in that room to guarantee a 50 percent chance of at least one birthday match? Intuitively, you assume that the answer should be a relatively large number. And in fact, most people's first guess is 183, half of 366. But the actual answer is 23. In Paulos's book, he explains the math this way: ''[T]he number of ways in which five dates can be chosen (allowing for repetitions) is (365 x 365 x 365 x 365 x 365). Of all these 3655 ways, however, only (365 x 364 x 363 x 362 x 361) are such that no two of the dates are the same; any of the 365 days can be chosen first, any of the remaining 364 can be chosen second and so on. Thus, by dividing this latter product (365 x 364 x 363 x 362 x 361) by 3655, we get the probability that five persons chosen at random will have no birthday in common. Now, if we subtract this probability from 1 (or from 100 percent if we're dealing with percentages), we get the complementary probability that at least two of the five people do have a birthday in common. A similar calculation using 23 rather than 5 yields 1/2, or 50 percent, as the probability that at least 2 of 23 people will have a common birthday.'' Got that?"
The Odds of That, New York Times
Lisa Belkin

The great traders "get" all this. Do you?

Mark Cuban "Gambling" Hedge Fund

December 02, 2004

Mark Cuban, the owner of the Dallas Mavericks professional basketball franchise, has proposed starting a hedge fund that makes money from "gambing".

Read:

1.) Mark Cuban's blog entry.
2.) CNN/Money press report.

Whether Cuban's project lifts off the ground or not, he should be saluted for his statistical thinking and his correct analysis that markets are inefficient. These beliefs (not the gambling fund as I don't know how the great trend followers would feel about such a venture) place him in good company with trend followers. I would be curious if Cuban is aware of trend following trading.

PI & Red Sox

November 13, 2004

Number of days between Red Sox World Series triumphs: 31,459.

The fabled mathematical concept, PI (of PI R SQUARED fame): 3.14159.

Source: ESPN.

Non-Correlation

September 21, 2004

Millburn Ridgefield Corporation offers on their site this view of correlation:

Including the Millburn Diversified Portfolio in a portfolio of traditional investments, such as U.S. stocks, U.S. bonds and international stocks may bring the substantial benefits of an attractive return, as well as added diversification. This diversification benefit is observable anecdotally in the adjacent table of annual returns (in which Millburn frequently had high returns in years where traditional assets performed poorly), and statistically in the nearly zero correlation of Millburn's returns with those of traditional assets."

Depending on your objective, trend following trading offers additional benefits beyond absolute returns.

Psyching-Out The Market

August 29, 2004

Kathryn Welling brings the great question forward:

"What struck me even at the time was that here were these supposedly very bright guys who insisted on applying a theory to the markets despite plentiful evidence that what the theory said couldn't happen in fact doesoccur with staggering regularity in the markets. Big fat tails swat investors in the fanny with fair frequency. So-called 'six sigma events' aren't really terribly rare, no matter what the equations tell you."
Kathryn M. Welling, Weeden & Co.

Woody Dorsey responds:

"Absolutely. What I wrote about in the book is that it is like the invisible hand comes along once in a while to spank the markets. The inference is that boy, you really should be on your guard because you know these events are going to happen. And when they do, those big fat tails provide the biggest and best opportunities to safely build capital; that's when you take advantage of market opportunities. That's the lesson. Yet [efficient market theorist and University of Chicago Professor] Eugene Fama himself says that the 1987 crash was an aberration--as was 1929. Insists they really didn't matter. But they mattered to a lot of people."
Woody Dorsey, Market Semiotics

Wise Random View

August 28, 2004

"Most things in life are not like steam engines, but people treat them as if they were. Life in general, and markets in particular, involve large random factors, have complicated stochastic structures, and regularly spring nasty surprises. Their behaviour over short timespans may have so little significance as to be nothing but noise. Extrapolation is impossible or meaningless. Yet try as we might, we continue to see patterns where none exist, misunderstand the role of randomness, seek explanations for chance phenomena, and believe that we know more about the future than we do."
Mark Wainwright
Plus Magazine

Bleed or Blowup?

August 27, 2004

In a recent paper Nassim Nicholas Taleb outlined:

"In some strategies and life situations, it is said, one gambles dollars to win a succession of pennies. In others one risks a succession of pennies to win dollars. While one would think that the second category would be more appealing to investors and economic agents, we have an overwhelming evidence of the popularity of the first. A popular illustration of such asymmetry in returns is evident in the story of the Long Term Capital Management hedge fund. The fund derived steady returns over a dozen quarters then lost all of them in addition to almost all its capital in a single observation - only for the main principals to restart a new, albeit milder, version of the strategy. Is there a systematic bias in favor of such return profiles?"
Nassim Nicholas Taleb

An Eerie Calm

July 26, 2004

The Economist: An eerie calm
Jul 22nd 2004

The fact that impliedie, expectedvolatility in financial markets is so low should give investors everywhere pause for thought

THERE are few beasts in the financial jungle more curious than the market in uncertainty. Traders buy and sell uncertainty as readily as if it were something tangible, like pork bellies or Treasury bonds. Strange though it may seem, it is no exaggeration to say that the price of just about every risky asset in the world depends in part on investors' perceptions about the price of uncertainty. It is precisely because investors appear so certain about the future that the prices of so many assets are now so high. The opposite holds too, of course. If investors became less certain, those prices would fall.

In financial markets, uncertainty goes under the name of volatilityhow much asset prices are moving around. One popular measure of stockmarket volatility, the Chicago Board Options Exchange's VIX index, has fallen to its lowest since 1996 (see chart). In August 2002, it soared to 45; this year it has mostly traded between 14 and 16. Interest-rate volatility has also fallen sharply, though not as far.

What most concerns traders and investors is not how much assets have moved in the past, but how much they are expected to do so. In the jargon, this is called implied volatility. It is the number that traders plug into the models they use to price options: the VIX, for example, is an index of implied volatility of options on America's S&P 500 stockmarket index.

Lately, investors in risky assets of all sorts have been selling options. Whether they think of it this way or not, they have been selling volatility too. The whole world is short volatility, says David Goldman, the head of fixed-income research at Banc of America Securities, with a flourish. As volatility has fallen, so investors have raked in profits on those risky assets.
The price of uncertainty

The market for traded uncertainty really came into being in 1973, with the publication of a now-famous paper by Myron Scholes and Fischer Black. Before then, pricing options had been something of a guess. The problem was putting a price on a contingent liabilitysomething that would be exercised only if it was in the buyer's interest to do so. The paper produced a neat solution, which has been developed over the years. All the seller needed to do was to put in a few variables, and the Black-Scholes model, via some ferocious maths, churned out an answer. Implied volatility is the most important of these inputs.

According to the latest survey by the Bank for International Settlements, at the end of last year there were roughly $50 trillion-worth of options outstanding in the world. Vast though this figure is, the true total is many times greater, because many assets have options embedded in them, even if their presence is not always plain. For this reason, understanding volatility is crucial to understanding movements in the prices of many securities.

Some of these options that are embedded in securities are more obvious than others. Take the market for mortgage-backed securities (MBSs), or bundles of mortgages, which in America is now bigger than the Treasury market. Sellers of American fixed-rate mortgages, which the buyer can repay at any time, have, in effect, sold the holder an option to redeem. The price of that embedded option is thus vital for putting a price on an MBS.

Similarly, anyone buying a firm's debt takes the risk that they will not be repaidand is thus, in essence, selling the firm an option to default. The extra yield above that on government bonds is the premium that investors demand for that risk: the greater the risk of default, the higher the spread. The same applies to government bonds, which is why emerging-market debt has historically traded at a discount to rich-country debt. Current tight spreads imply that investors think that companies and emerging-market governments are less likely than usual to default.

Investment banks have spent many millions of dollars trying to tie theory to practice. They started in the 1980s with MBSs and in recent years have tried to do the same with corporate bonds. Many investment banks and even the big rating agencies now use signals from the stockmarket as a guide to the riskiness of a company's debt. The implied volatility of options on a company's shares, for instance, can be viewed as the cost of insurance against the worsening of a firm's prospects, as measured by its share price.

When equity prices are falling and the cost of that insurance is high, spreads widen. But as equities have climbed since the dog days of autumn 2002, and implied volatility has fallen to a third of its level then, prices of corporate bonds and other risky assets have risen dramatically.

The question, of course, is whether the price of uncertainty, particularly in equity markets, will remain as low as it is now. Markets have become less volatile than they were between the spring of 2000 and the autumn of 2002. Moreover, firms in many countries, particularly America, are swimming in record profits, and the longer the global recovery continues, the more convinced investors become that the good times will continue. Both make for more certain share prices.

But the steep fall in implied volatility is nonetheless a bit odd. There are, after all, many things that could go wrong for financial markets: tensions are still bad in the Middle East; the oil price is again over $40; and the Federal Reserve is raising interest rates when American households are more indebted than they have ever been.

One reason why volatility is so low is that there are so many sellers of equity optionssellers, as it were, of insurance against falls in share prices. Their sales have driven down the price of implied volatility. In the absence of nasty surprises, selling options is a splendid way of making money, and buying them a wonderful way of losing it. This is why, in the absence of decent returns elsewhere, investment banks and fund managers of every hue, hedge funds not least, have been selling them with a will. It is, if you like, another consequence of the world's still-low interest rates.

It is also risky; sometimes, very risky. Many financial catastrophes have been caused by selling options. The most famous came in 1995, when a rising star at a British bank sold 34,000 options on Japan's Nikkei 225, driving implied volatility on the world's second-biggest stockmarket from 22% to 11%. But share prices plummeted after the Kobe earthquake, volatility soared, and the bank went bust. The man's name was Nick Leeson and the bank was called Barings.

Reversion to the Mean

June 15, 2004

James Simons, President of Renaissance Technologies, offered in a roundtable forum:

"I heard this story and I think it's true. Anyway, it's a pretty good story. It's about how the Air Force trains pilots. When a trainee made a good landing, he would be praised. When a trainee made a bad landing, he would be ridiculed. Well, it was perfectly clear to the general that the first approach was lousy and the second approach was good. He had statistics demonstrating that when you praised a pilot who made a perfect landing, his next landing was not likely to be as good. Whereas, if you berated a pilot who made a bad landing, his next landing was likely to be much better. However, if you think about it, it doesn't matter what you do, because landings are most likely to be average. If a pilot had an exceptional landing, his next landing was likely to be average. If he had a poor landing, his next landing was likely to be average, also. By slicing the data and only looking at what follows good landings and praise, you only see part of the picture. You must consider how data was selected before you can draw conclusions. This example is closer to home. We interview a lot of managers, because we do some asset allocations. Although I haven't compiled careful statistics on this, it frequently seems that a manager with a marvelous record does not perform as well after I invest with him. Why is that? Well, do managers who lost 35% in the last three years show you their records? No, those guys aren't showing anyone their records. You are seeing a sample of the best managers, a sample of "good landings." Going forward, some people do better and some people do worse, but reversion to the mean is probably a persistent phenomenon in both managing money and landing airplanes."

Trillion Dollar Bet

June 09, 2004

"The question that I don't yet know the answer to, and I suppose what the partners of Long Term Capital, I can suppose what their answer would be, but I don't yet know the balance between whether this was a random event or whether this was negligence on theirs and their creditors' parts. If a random bolt of lightning hits you when you're standing in the middle of the field, that feels like a random event. But if your business is to stand in random fields during lightning storms, then you should anticipate, perhaps a little more robustly, the risks you're taking on."
Trillion Dollar Bet (PBS Special)

Correlation and Trend Following

May 03, 2004

Ponder the statement:

"Statistics alone can never prove causality, but it can show you where to look."

True trend following traders, if trading similar markets, will typically have very similar winning months and very similar losing months. A good historical example is the summer of 1998 (when Long Term Capital Management went bust). During August and September 1998 most trend followers had winning months. Interestingly, July 1998 was a losing month for most trend followers. Comparing monthly performance numbers of trend followers is best done through correlation analysis. Correlation, however, does not prove causality. It tells us where to begin the investigation. So when looking at correlations among trend followers, especially very large monthly gains or losses, it makes sense to look for the other side of the trade to better understand "why".

100-Year Floods Happen All the Time

April 25, 2004

We have all heard the term "100-year flood" applied to the markets. The Long Term Capital Managements of the world predicated their trading on the flood happening only once every 100 years. Reality is quite different as Hunt Taylor reminds:

"I'm wondering when statisticians are going to figure out that the statistical probability of improbable losses are absolutely the worst predictors of the regularity with which they'll occur. I mean, the single worst descriptor of negative events is the hundred-year flood. Am I wrong? How many hundred-year floods have we lived through in this room? Statistically maybe we should have lived through one and we lived through seven now at this point."
Hunt Taylor
Director of Investments, Stern Investment Holdings

James Simons: Mathematics and Common Sense

April 18, 2004

James Simons reminds us all that complication in trading can cause problems:

"Years ago, a colleague came up with an extremely complicated model. Initially, it worked well, but then it began to falter. I said, "Can we understand more about this model? It's so complicated." He said, "Oh no, you can't understand it. I've added this and that and put it all together and I've maximized here and there and...who knows what it is?" I said, "That is not satisfactory. I know its rotten, because its losing money. Let's figure out what else it is." I gave him some experiments which would restrain the function to a small set of parameters and -- guess what -- it was a linear function. It had little curls here and twists there, but they didn't matter. It was a linear model. Linear predictive systems fared poorly during that period, so naturally this one was losing money. The danger with some of these methods is that you can produce something simulated and it may look pretty good, but there is an air of anxiety because you don't understand it. We dont complicate models to the point where we dont understand what they are."

Statistical Thinking: Key for Trading

April 12, 2004

H.G. Wells outlined many moons ago the keys:

"If we want to have an educated citizenship in a modern technological society, we need to teach them three things: reading, writing, and statistical thinking."

Statistical thinking is the ugly stepchild. To this day it is left out of basic equations of our day to day life. Good directions to explore.

Short-Term Trading: Roy Niederhoffer?

April 06, 2004

Some professional short-term traders have raised some serious money in the last two years. Roy Niederhoffer (brother of Victor) trades short-term trading systems. However, should there be caution? What makes him different in the long run than Long Term Capital Management or Victor Niederhoffer? Are other short term traders also reliant on standard deviation as their measure of risk?

Sharpe Ratio Criticism

April 03, 2004

David Harding of trend follower Winton Capital argues for more than simple acceptance of the Sharpe ratio as the measure for assessing "risky investments":

"...large positive returns increase the perception of risk as though they could as easily be negative, which for a dynamic investment strategy may not be the case. Large positive returns are penalised, and thus the removal of the highest returns from the distribution can increase the Sharpe ratio: a case of reductio ad absurdum for Sharpe ratio as a universal measure of quality!"

Large, unexpected events provide trend following returns. Does Sharpe properly account for that?

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