Posts filed under “Mathematics”
Terrific l o n g article in the Sunday Times Magazine by Joe Nocera, titled Risk Mismanagement. Its all about how Wall Street developed and still uses VaR — Value at Risk.
The application of VaR remains hotly debated today. Did it contribute to the credit crisis — or was it ignored/misapplied/distorted, and THATS what was a key factor.
Risk managers use VaR to quantify their firm’s risk positions to their board. In the late 1990s, as the use of derivatives was exploding, the Securities and Exchange Commission ruled that firms had to include a quantitative disclosure of market risks in their financial statements for the convenience of investors, and VaR became the main tool for doing so. Around the same time, an important international rule-making body, the Basel Committee on Banking Supervision, went even further to validate VaR by saying that firms and banks could rely on their own internal VaR calculations to set their capital requirements. So long as their VaR was reasonably low, the amount of money they had to set aside to cover risks that might go bad could also be low.
Given the calamity that has since occurred, there has been a great deal of talk, even in quant circles, that this widespread institutional reliance on VaR was a terrible mistake. At the very least, the risks that VaR measured did not include the biggest risk of all: the possibility of a financial meltdown. “Risk modeling didn’t help as much as it should have,” says Aaron Brown, a former risk manager at Morgan Stanley who now works at AQR, a big quant-oriented hedge fund. A risk consultant named Marc Groz says, “VaR is a very limited tool.” David Einhorn, who founded Greenlight Capital, a prominent hedge fund, wrote not long ago that VaR was “relatively useless as a risk-management tool and potentially catastrophic when its use creates a false sense of security among senior managers and watchdogs. This is like an air bag that works all the time, except when you have a car accident.” Nassim Nicholas Taleb, the best-selling author of “The Black Swan,” has crusaded against VaR for more than a decade. He calls it, flatly, “a fraud.” . . .
What will cause you to lose billions instead of millions? Something rare, something you’ve never considered a possibility. Taleb calls these events “fat tails” or “black swans,” and he is convinced that they take place far more frequently than most human beings are willing to contemplate. Groz has his own way of illustrating the problem: he showed me a slide he made of a curve with the letters “T.B.D.” at the extreme ends of the curve. I thought the letters stood for “To Be Determined,” but that wasn’t what Groz meant. “T.B.D. stands for ‘There Be Dragons,’ ” he told me.
Best line in the article: “When Wall Street stopped looking for dragons, nothing was going to save it.”
I particularly loved the graphics and illustrations that were part of it:
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…Read More
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 ritholtz.com, 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?
I did a fairly comprehensive interview with the guys over at TradingMarkets.com. 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
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
> 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
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
THE MANDELBROT SET
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
ON THE DEFENSE
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
FRACTALS IN THE BODY
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
NATURE’S FRACTAL NATURE
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
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