Posts filed under “Mathematics”

Be Wary of Serial Correlation

MIT’s Andrew Lo:

The key concept here, developed by MIT professor and noted hedge-fund theorist Andrew Lo, is “serial correlation.” Simply put, serial correlation is the degree to which each month’s returns in a fund mirror the results of the month before. A fund that returns the exact same amount every month is perfectly serially correlated. Madoff’s returns were strikingly consistent month after month, year in and year out. That kind of performance—a nice, smooth line going up no matter what the market does—is a really good sign that you should look more closely.

The extraordinary thing that Lo does in the third chapter of his book Hedge Funds, published earlier this year, is to demonstrate mathematically that an excessive degree of serial correlation is a powerful indicator that the holdings of a fund aren’t being reported realistically. What Lo shows from the pattern of historical returns in hedge-fund databases is that when funds’ returns grow too consistent, it is a sign that the investments are either very hard to value accurately and the returns are just guesses, or, worse, that they’ve been manipulated in a way that smoothes them artificially. What Lo creates is a mathematical model for judging what “looks too good to be true.” Lo’s work turns a lot of the conventional thinking about what’s safe on its head. It shows that the evenness that investors have traditionally been taught indicates safety and reliability can actually be the best sign risk is being hidden or that the data are unreliable.


Madoff Dilemma: How Can You Spot A Wall Street Crook?
Mark Gimein
Big Money, Friday, December 12, 2008 – 3:57pm

Hedge Funds
Andrew W. Lo
Princeton University Press (May 18, 2008)

Category: Hedge Funds, Legal, Markets, Mathematics, Quantitative

Trading the Big Picture: A Conversation with Barry Ritholtz

To most traders and investors, Barry Ritholtz is the voice of The Big Picture, one of the more popular financial blogs on the Internet. Now hosted at, The Big Picture was one of the more prominent financial must-reads for traders and active investors during the second half of the Bush years. Some of the earliest concerns about the credit crisis and the housing bubble in the financial blogosphere were posted at The Big Picture – a blog that now boasts over a 29 million visitors and 39 million page views.

Barry Ritholtz is the man behind The Big Picture. He is CEO and Director of Equity Research at Fusion-IQ, an online quantitative analysis research firm. He was also recently the Chief Market Strategist for Maxim Group, a New York investment bank, managing more than $5 billion in assets. He is a frequent guest commentator in print, online and broadcast financial media including CNBC, Bloomberg, PBS and Fox Business.

His firm is also responsible for creating an online software tool, at Fusion-IQ, that uses his proprietary metrics to quantitatively rank more than 7,000 stocks and 400 industry groups. The Fusion metrics are backtested and used by both retail and institutional-level investors and traders.

I spoke with Barry Ritholtz by telephone the day after the Presidential election in November. We talked about ETF trading, contrarian trading and creating stories and narratives to help explain the cold, hard probabilities of quantitative analysis. What follows is an edited transcript of lively and insightful conversation with Mr. Big Picture, Barry Ritholtz:


David Penn: First, off I have to ask you about something I saw on The Big Picture this morning about exchange-traded fund (ETF) trading. ETF trading is something we have been very interested in, as well. You had a blog post about exchange-traded funds and leverage exchange-traded funds, particularly the new 3 to 1 ETFs

Barry Ritholtz: We do a ton of ETFs lately.

Penn: Do you? Let me just get your general overview on the rise of leveraged ETFs – including the new 3 to 1 leveraged funds. How effective do you think they are? Why should be traders be interested in them?

Ritholtz: ETFs do some really interesting things. We are bottoms up stock pickers, but in this environment, ETFs make sense. If you want any sort of instant exposure to a sector, a stock, a region, ETFs are just really, really simple, fast and painless. ETFs work well for that. The leveraged funds are really interesting.

Just for a little background: we came into this year (2008) very bearish. We had plenty of longs, but over the summer we were probably more cash than we’ve ever run, 50 to 60 percent cash in our managed accounts. Then as we went through August and into September, well, we have a couple of pretty firm rules about stock losses. We always manage risk by using stop losses. We have some other rules, but it’s long and complicated.

When a stock is working out for us, we try and raise the stop to a breakeven. If you have a big winner, we never want to give back 25 percent of the profits. And there are other mechanical ways of preventing yourself from riding what we like to call the “Cape Matterhorn” stock. Think of Apple in the 1990s; you had a run-up on the iMac introduction. It went from single digits to 100 plus, then back to single digits. This time, with the iPod and the iPhone, it hasn’t quite re-completed the round trip, butits given a ton back. There are plenty of people who ride stocks all the way up, and then don’t know what to do with them and of course, they ride them all the way back down. Ouch.

We hate doing that. So we came into the October lows with just an inordinate amount of cash and a lot of nervous clients. And when we made our bull call on October 10th – which may end up being just a cyclical trading rally, we don’t know and we won’t know for a couple of weeks — there was a real concern of, “I can’t believe you guys are buying here. You’re crazy.” [EDITOR: A similar buy call was made in real time on November 13th, and again, and again, no one complained]

So the approach we took was, let’s buy the two-for-one leverage SSOs (ProShares UltraS&P 500 exchange-traded fund), which are the S&P 500 X 2, and QLDs (ProShares UltraQQQ exchange-traded fund), which are the NASDAQ X 2. And at the same time, we maintained a 50 percent cash position.

Penn: An interesting approach.

Ritholtz: Yes. In a very strange turn of events, we had 100 percent market exposure and 50 percent cash, which if you stop and think about it, is a nice little trick to do.

We could have just gone 100 percent stock, but we never like to pick our points that way. The way that capital deployment worked, it gave us the upside exposure we wanted and yet, at the same time, maintained a modest amount of risk via our cash holdings. Since we don’t care about the actual market movements relative to an individual equity when it comes to stock losses, we had the same stops on the two-for-one leverage stock as if it were GE. It didn’t make any difference. Once it gave up a certain percentage and crossed certain key technical support lines, we were done, we get stopped out — trade over. But that hasn’t happened, so it really gave us this strange and interesting move, relative to what happened.

Penn: What has happened since?

Read More

Category: BP Cafe, Derivatives, Markets, Mathematics, Quantitative, Technical Analysis, Trading

Trading Markets Interview

I did a fairly comprehensive interview with the guys over at We discussed a lot of issues not usually covered in most interviews — quant analysis, probablity theory, uncertainty as the standard condition regarding the future. Some of you might find it kinda interesting: Trading the Big Picture: A Conversation with Barry Ritholtz David…Read More

Category: Credit, Derivatives, Markets, Mathematics, Quantitative, Technical Analysis, Trading

Stock Market Returns by Party

We’ve addressed this before, and came down firmly against these over-simplified arguments. However, I like the way Wolfram’s Mathematica allows you to control, for variables like inflation, policy lag, etc. In this Demonstration, you can compare what would happen if you left an investment in the stock market (represented by the Dow Jones Industrial Average),…Read More

Category: Digital Media, Mathematics, Politics

Prediction Markets Election Contest

> Over at the NYT’s economics blog, Economix, David Leonhardt is running a prediction market contest, looking at odds of various Intrade contests. Pick any 3 of the 20 questions to answer, and the winner gets showered with untold glory and fame. The contest has an interesting twist: Its based upon the betting at Intrade….Read More

Category: Economy, Markets, Mathematics, Politics, Psychology

Fractals: Hunting the Hidden Dimension

Nova discusses fractals, and the significance for various disciplines, such as Physics, mathematics and even markets:

Click for Video

In five parts:

They’re odd-looking shapes you may never have heard of, but they’re everywhere around you—the jagged repeating forms called fractals. If you know what to look for, you can find them in the clouds, in mountains, even inside the human body.
running time 11:36

In 1958, Benoit Mandelbrot begins using computers to explore vexing problems in math. They help him to understand repeating patterns in nature in an entirely new way. He coins the term fractal to describe them and develops the Mandelbrot set in 1980.
running time 9:51

Though many colleagues initially scorned Mandelbrot’s work, his mesmerizing fractal images launched a popular culture fad. More importantly, his book The Fractal Geometry of Nature explained how his ideas could be applied in the real world. Mandelbrot’s ideas inspire an ever-increasing number of applications, including the fractal antenna.
running time 10:40

Fractal patterns turn up everywhere in biology, from the irregular rhythm of the heart to basic eye function. The fractal nature of such physiological processes, which obey simple mathematical rules, offers hope of better diagnosis and treatment of problems as well as new insights into how such processes work.
running time 10:15

With carbon dioxide levels around the world rising, a team of American scientists travels to a rain forest in Costa Rica. They employ fractal geometry to analyze how much CO2 the rain forest can absorb.
running time 7:52

(Full transcript here)

Category: Mathematics, Quantitative, Science, Video

PBS Video: Taleb & Mandelbrot

Economist Nassim Nicholas Taleb and his mentor, mathematician Benoit Mandelbrot, speak with Paul Solman about chain reactions and predicting the financial crisis.

click for video



RAY SUAREZ: Finally tonight, we return to a subject on many minds these days: the financial crisis. Our economics correspondent, Paul Solman, checked back in with one particularly prominent voice in the investment world and his colleague, who guided his thinking.

Here is the pair’s sobering conversation on what may lie ahead.

PAUL SOLMAN, NewsHour Economics Correspondent: One of the world’s hottest investment advisers these days, Nassim Nicholas Taleb, author of "The Black Swan," who’s been warning of a crash for years, betting on one, and winning big.

He’s been ubiquitous in the financial media of late, from cable TV’s "Colbert Report" to the BBC’s "Newsnight," where he was infuriated by what he called "bogus accounting."

NASSIM NICHOLAS TALEB, Scholar and Author: The first thing I would get immediately, immediately, I would suspend something called value at risk, quantitative measures of risk used by banks, immediately.

PAUL SOLMAN: We sat down with Taleb and the man he calls his mentor, mathematician Benoit Mandelbrot, pioneer of fractal geometry and chaos theory. And even more than feeling vindicated, they’re both scared.

NASSIM NICHOLAS TALEB: I don’t know if we’re entering the most difficult period since — not since the Great Depression, since the American Revolution.

PAUL SOLMAN: The most serious situation we’ve been in since the American Revolution?


Top Theorists Examine Rippling Economic Turbulence   
PBS, October 21, 2008

Category: Markets, Mathematics, Quantitative, Video

Alpha Into Beta

Category: Markets, Mathematics

Actual Merrill CDO Sale: 5.47% on the Dollar

Category: Credit, Derivatives, Mathematics, Valuation

Visualizing Data

Category: Mathematics, Quantitative, Technical Analysis