The Big Picture | Mathematics

Volatility Spike, parts III and IV

Saturday, March 29, 2008 | 10:00 AM

in Markets | Mathematics | Psychology/Sentiment | Technical Analysis

On Thursday, we noted the increase in volatility via a Financial Post column. Today's chart porn comes via the NYT & Barron's.

First up, the NYT, with this gorgeous info-graphic on volatility -- note the peak in 2002, which marked the bottom of the Bear markets (Oct 2002/March 2003):

Chart courtesy of NYT

~~~

Second, have a look at Dick Arms column in Barron's. Dick believes the recent volatility surge is a Bullish sign.

I have a lot of respect for Dick, as his methodology is statistically based and empirically driven.

Even if you disagree with him, you can at least respect his methodology, which has zero cheerleading content in it.

Chart courtesy of Barron's

Previously:

Buy Volatility (January 14, 2006)
http://bigpicture.typepad.com/comments/2006/01/buy_volatility.html

Sources:
For Stocks, It’s the Wild West, East ...
FLOYD NORRIS
NYT, March 29, 2008
http://www.nytimes.com/2008/03/29/business/29charts.html

Whiplashed? That's a Bullish Sign
Now Is the Time to Buy, Not Sell
RICHARD W. ARMS
Barron's, MARCH 31, 2008
http://online.barrons.com/article/SB120676003110074029.html

~~~

Subprime Debt Values in a Recession

Monday, February 11, 2008 | 05:27 PM

in Credit | Derivatives | Mathematics | Real Estate

Amusing picture, via John Hussman:

Fun With Data Analysis: The Art of the Plausible

Sunday, January 27, 2008 | 10:50 AM

in Apprenticed Investor | Data Analysis | Markets | Mathematics | Quantitative

Barron's Mike Santoli looks at one of our favorite pet peeves: The use and abuse of data. His column this week, The Limits of History, notes that this has become especially prevalent of late:

"People who try to handicap the markets for a living practice the art of the plausible. Many trudge from conference room to lunch table to banquet hall lugging PowerPoint decks full of unobjectionable statistical touchstones for commission-wielding clients. At times of investor confusion and market dissonance, such as now, their art is often reduced to carving a slice out of economic history that ratifies their existing outlook."

Mike then proceeds to look at a "dog's breakfast of the kinds of historical analogies making the rounds." What is especially amusing about his list is the number of "Every time X happens, Y has occurred" that collectively produce all manners of mutually exclusive results. Since "X" occurred we will definitely have/avoid a recession; Stocks are undervalued/overvalued; Markets must rally/fall.

What is an investor to do? Whenever you are confronted with an "incontrovertible proof" based on historical data, prior to taking any action, I suggest asking yourself this short list of questions:

• Do we have enough historical examples? Is the data sample statistically significant?

• Causation or Correlation? Does "X" cause "Y" to occur? Or, are we presented with two things that may have the same underlying causes? Is there even interaction between X & Y?

• Coincidence? How possible is it that these two items are utterly unrelated (i.e., proof-we-are-clueless Superbowl indicator).

• Look for differentiating elements in different time periods: What factors are similar? What factors are different?

• Compare interest rates, inflation, dividend yield, P/E contraction or expansion, sentiment, overall market trend, business cycles -- across different eras. Might that account for potentially different outcomes?

• Any recent market environmental changes (regulation shift, financial innovation, etc.) have an impact? What might these specific changes do to the data? Consider Decimalization, ETFs, online trading, change in dividend tax, etc.

• Subjective versus Objective measures: Are the factors under discussion hard numerical data, squishy or somewhere in between? Percentage of stocks over 200 day moving average is objective; I find some chart pattern readings subjective. Earnings at time have been rather subjective; official inflation measures somewhere in the middle.

• Consider things in terms of probabilities, not outcomes: Assume a causative factor resulted in a specific event (X --> Y) 7 out of 9 times. The most you can say is that when "X" occurred in the past, it has resulted in "Y" approximately 78% of the time.

• There is a difference between historical occurrence and future likelihood. In the example above, this does not necessarily even mean that since "X" has just occurred, there is a 78% that "Y" will happen. Consider: was the first X/Y occurrence really a 100% or zero? Did the second one become 100% or 50%, then next a 66% or 33%?

• Contextualize data: Sometimes a single data point -- even a mean or median -- only tells half a story. Any data point can be trending or reversing. Going higher, lower, topping, bottoming. Each of these may have differing implications for what comes next. Inflation is high, but coming down. Gold is high -- and going up. It helps to think of data not as a still photograph, but as a frame in an ongoing film.

I'm sure there are more -- that short list is off the top of my head.

Any others? Please make your suggestions below. If we get enough good ones, I'll try to massage this into a more formal column.

Source:
The Limits of History
Mike Santoli
Barron's, MONDAY, JANUARY 28, 2008
http://online.barrons.com/article/SB120130827516518451.html

8 Big Numbers

Friday, January 11, 2008 | 10:00 AM

in Data Analysis | Fixed Income/Interest Rates | Markets | Mathematics

Andrew Burkly of Brown Brothers Harriman & Co puts out a list of significant numbers each January. Its a clever way to think about various aspects of the market and the economy -- by the numbers.

These are his "8 Big Numbers" for 2008.

The S&P 500 Index needs to close above its March 2000 peak of 1552, as well as break its 2007 trading range of 1575 – 1370 to keep the structural bull market intact. An upside break of the range would indicate that the volatile trading of 2007 was merely a high-level consolidation. One indication that the bull market is back in gear would be the number ofcommon stocks hitting net new 52-week highs climbing back into the 500 range.

Domestic equity funds witnessed outflows in 2007 totaling $54 billion suggesting that investor sentiment is far from euphoric. Finally, the average gain during year 4 of the presidential election cycle has been 8.9% since 1928.

Meanwhile in 2008, 3.6% is a key level to watch for the 10-year Treasury yield, the commodity bull market moves into its 6th year, and the S&P 500 Energy Sector looks for its fourth sector performance crown in five years - a winning percentage of .800.

1. “1552” The March 2000 peak in the S&P 500 Index
2. “1575-1370” – The 2007 trading range in the S&P 500
3. “500” The number of stocks hitting net new 52-week highs in a healthy market
4. “-54” Outflows ($billions) from domestic funds in 2007 (through Nov.)
5. “4 2008 is year 4 of the presidential election cycle
6. “3.6%” A significant support level for the 10-year Treasury yield
7. “6” 2008 marks the 6th year of the commodity bull market
8. “.800” Energy going for its fourth sector performance crown in five years

Good stuff. Thanks, Andrew . . .

Baseball Stats and Freakonomics Wannabes . . .

Saturday, December 22, 2007 | 08:31 AM

in Data Analysis | Mathematics | Quantitative

Much of investing relates to mathematics and the application of statistics. Markets are statistical data generating machines, and that data can be sliced and diced in a myriad of ways. We always pay close attention whenever we see an interesting application -- or misapplication -- of quantitative data that may be instructive or applicable to investing.

So I was particularly intrigued by a study in today's NYTime's OP-ED page that purported to look at the impact of steroids on the performance of Baseball players, based on the Mitchell Report. They asked the question: "In a complex team sport like baseball, do the drugs make a difference sufficient to be detected in the players’ performance records?"

Their conclusion? The authors of More Juice, Less Punch found that Steroids, Human Growth Hormone and the like do not have a net benefit to major league players. Based on their review of pre- and post- steroidal usage, the overall impact on players stats was de minimus.

I remain unconvinced.

Ever since Freakonomics became a runaway economics best seller, there seems to be increasing attempts by "rogue economists" and others to discover the hidden, counter-intuitive side of everything. This column seems to be of that genre. They would have been better served if they were channeling the statistical approach of Moneyball, instead.

When you come across broad attempts to explain complex systems, your inner mathematician should always be concerned that the methodology employed is sound, any initial assumptions made are justified, and the analytical steps taken are well supported.

In the present case, I suspect they are not. Consider the following statistical and analytical issues:

1. The authors of the Times Op-Ed looked at 48 batters and 23 pitchers named in the Mitchell Report; This may be too small a sample to draw any valid conclusion.

2. For pitchers, they studied ERA. Is the main impact pitching advantage of Juice the impact on ERA? That stat is a function of many things -- intelligence, pitch selection, opposing batter research, etc. -- not just physical power.

The authors ignored many other stats that might be more telling as to the impact of 'roids: Consider strike outs, average pitch speed, average number of pitches thrown per game, total games pitched. These data points would have been quite instructive as to the impact of performance enhancing drugs (PED) on issues such as strength and durability, even injury recovery.

3. For Hitters, they examined batting averages, home runs and slugging percentages. The same durability issues were overlooked -- games played and missed, total at bats, swings with ball contact, distance traveled of hit balls, etc.

And what about speed -- why not consider stolen bases? We know lots of runners and cyclers have been accused of using PEDs -- isn't this a valid data point to consider?

4. Dates: What were the Before & After dates? It appears that by drawing the line at the date of accusation, lots of PED usage will have taken place in the BEFORE data set. If the performance gains of the AFTER group, began in actuality during the BEFORE, the entire statistical conclusion becomes indeterminate.

5. No control group: All players begin to show statistical deterioration as they age, get worn down, injured, etc. How can we tell what their stats would have been looked had they not been juiced?

Rather than comparing pre-accusation and post-accusation stats, perhaps a better comparison would have been to look at the group of players who used PEDs versus those who didn't as their careers wound down. How do the two groups compare in their mid 30s? Late 30s? Early 40s?

Note that even this grouping may be flawed, because of the self-selection factor of those who chose to use the drugs in the first place (more injury prone, weaker, slower, etc).

6. False Accusations: Are any of the players accused in the Mitchell Report not guilty of using PEDs? I have no idea, but its a valid possibility. How might their false positives impact the author's conclusions regarding stats?

I don't know what the total impact of Steroids and Human Growth Hormone were on baseball player's performance -- but based upon the above, neither do Professors Jonathan Cole and Stephan Stigler.

~~~

One last thought: Why hasn't Baseball Commissioner Bud Selig resigned or been fired?

Shouldn't he -- like Merrill Lynch's O'Neal and Citigroup's Prince -- fall on his sword? This happened on his watch, and he apparently was asleep at the wheel. For this gross incompetency, Selig should be tossed aside like a used syringe.

Source:

More Juice, Less Punch
JONATHAN R. COLE and STEPHEN M. STIGLER
NYT, December 22, 2007
http://www.nytimes.com/2007/12/22/opinion/22cole.html

INDEPENDENT INVESTIGATION INTO THE ILLEGAL USE OF STEROIDS AND OTHER
PERFORMANCE ENHANCING SUBSTANCES BY PLAYERS IN MAJOR LEAGUE BASEBALL
GEORGE J. MITCHELL
DLA PIPER US LLP, December 13, 2007
http://assets.espn.go.com/media/pdf/071213/mitchell_report.pdf

S&P500 ex-Risk ?

Tuesday, November 06, 2007 | 06:48 AM

Here's an issue I have been mulling over, without a satisfactory answer:

There have been many investment thesis (thesii?) over the past few years about the market which supported the bullish side of the ledger: Earnings were high, stocks were cheap, risk was moderate, the Fed model favored stocks over bonds.

Regardless of whether you found these arguments persuasive or not, global markets have gone higher. While the U.S. indices may have lagged the rest of the world's bourses, they too, have powered higher.

Here's the odd factor: It turns out that many of the arguments made in favor of U.S. domestic growth have been based on an assumption that turned out to be false. To wit: The Financials, the largest sector in the S&P500, had legitimate, sustainable, normalized risk-based earnings.

That basic premise turned out to be wrong.

Picture a race car driver, going way too fast in the first half of a track. He puts up record breaking lap times, only to crash and burn in the last turn. His driving coach would say his risk-adjusted speeds were irresponsible.

That's how I perceive what has been going on with the Financial sector. It wasn't Fraud, but rather a reckless disregard for Risk that led to outsized returns on many big cap stocks in the group.

Merrill Lynch (MER) just wrote down $8 billion dollars, erasing 5 years of profits. Citigroup (C) dinged $11 billion. Washington Mutual, (WAMU) Countrywide Financial (CFC), Bear Stearns, GMAC -- there seems to be an ongoing parade of mea culpas that are erasing not just quarters of profits, but years of earnings. And there are likely to be many more of these, as tier 3 assets get priced appropriately. (UPDATE: Morgan Stanley (MS) now rumored to take a $3-6B writedown)

What's truly astounding is that we may only be seeing the tip of the iceberg. Its possible that the big brokers and banks have $1 trillion in toxic debt on their books to be written down. That would equal decades -- not years -- of profits to be wiped out.

To paraphrase the WSJ, "the financial crisis is becoming Shakespearean comedy."

So here's the odd question that I have been wrestling with: Given what we now know about how the true nature of the S&P500 earnings in this group, what did the past few years of data actually look like? Now that the big Banks have erased nearly all of their earnings of the past few years, what should that data have looked like from 2003-2007 with most of the Fins as a goose egg?

I would like to see historical data adjusted for the S&P500 for the Financial sector's losses. Specifically, if we back out the earnings that turned out to be based on a reckless disregard for risk, what does the following data look like?

• What were year-over-year Earnings?

• How cheap were stocks really?

• What were the actual risk adjusted returns?

• Were stocks as undervalued as the Fed model suggested?

Consider our race car driver from before. If he fails to finish the lap, his time gets voided. Any Financial compan's earnings are a function of measured risk versus potential reward. If earnings turn out to be based on far greater risk than assumed, and subsequent losses offset them -- i.e., they are not sustainable -- they too have been voided.

Question for our mathematics wizard readers: Can we figure out an easy way to take the historical data, and adjust these reckless risk-based earnings, now that they have been wiped out?

I don't know the answer to these questions -- but they certainly are food for thought . . .

Sources:
Markets fear banks have $1 trillion in toxic debt
Sean O’Grady
The Independent, 06 November 2007
http://news.independent.co.uk/business/news/article3132507.ece

Why Street Bankers Get Away With Repeating Old Mistakes
DENNIS K. BERMAN
WSJ, November 6, 2007; Page C1
http://online.wsj.com/article/SB119431284681383384.html

Fears intensify for prolonged turmoil
FT Reporters
November 5 2007 21:27 |
http://www.ft.com/cms/s/0/4cd5c262-8bd6-11dc-af4d-0000779fd2ac.html

The NYT, Magazine Cover Indicator, and Mean Reversion

Sunday, August 19, 2007 | 08:36 AM

in Data Analysis | Financial Press | Mathematics | Psychology/Sentiment

Would someone please explain to the nice folks over at the NYT, or the economics department at the U.C.L.A, the concept of mean reversion, contrary indicators, and (ahem) how the national businmess press operates? (We have discussed the magazine cover indicator previously, so those unfamiliar with it can read any of those posts at their leisure).

The ongoing innumeracy and logical fallacies that exists in this country continues to astound. Case in point: What the NYT called "the curse of the business press." (No Applause, Please).

Here's the relevant excerpt:

"Chief executives who are heralded as “best manager” or “best performing” or who receive some other kind of elaborate praise from business writers almost always see their company’s stock performance suffer afterwards, according to a working paper by two assistant professors of economics at the University of California, Ulrike Malmendier of Berkeley and Geoffrey Alan Tate of U.C.L.A.

“The stock market returns of award-winning C.E.O.s’ companies lagged those of their unheralded peers by about 4 percent per year over the three years following an award,” Larry Yu writes in Sloan Management Review in summarizing the research.

What causes the decline? The academics speculate that recognition in the press could lead to the executive’s becoming distracted. “Winning an award doubles the odds of the C.E.O. penning a book, and winning as many as five awards makes a C.E.O. four times as likely to sit on five or more outside boards.”

Or it could be that as Ms. Malmendier notes, journalists are simply very good at picking people who are going to underperform."

No, no and no.

Are these folks really that logically challenged?

There are a few simple answers: First, this is yet another classic case of confusing correlation with causation. Just because two thing occur proximate to each other in time is not a sufficient basis alone for assuming that one caused the other.

Second, Investors, Reporters and Professors need to ask themselves a simple question: "Why have these CEOs appeared on magazine covers?" Its more likely than not that they have done something that caught the attention of the investing public and eventually the media. And its also very likely that their stocks HAVE ALREADY had a great run up -- far above the average 12% we see for the SPX over the very long term.

Speaking generally (yes, of course there are a few exceptions), there's a more logical reason. What is a more likely explanation for the so-called "curse of the business press. is actually a simple case of mean reversion. By the time the mainstream press discovers the next star CEO, their stock has already put in best part of the run.

Source:
No Applause, Please
What’s Offline
PAUL B. BROWN
NYT, August 18, 2007
http://www.nytimes.com/2007/08/18/business/media/18offline.html