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Stat 434 Financial Time Series ---

J. Michael Steele

A statistics course
committed to honest data analysis,
focused on mastery of best-practice models,
and obsessed with the dynamics of financial markets

Course Blog

Important: What Follows is the Course Blog for 2008!

This will tell you what happened last year in the course, but there is a new site for 2009.

Considering 434 for Fall 2009?

What you find below is the course blog for Fall 2008. If you are just now thinking about taking 434 next fall, you might want to jump down to a discription of the course prerequisites, etc. After that, you might look at some of the 2008 e-Handouts or read at random (from the bottom) in the blog. In the not-to-distant future, I will archive the 2008 blog, and start everything afresh for fall 2009. If for some weird reason you want to do so, you can even llook at the 2007 blog or 2006 blog. Things do change --- though never as fast as one expects (or hopes) they might.

Heads-up. The course is limited to 40 and that is the capacity of the room, so this course cannot accommodate auditors. Anyone attending the day one or day two lectures should be registered or on the waiting list.

bamboo

Picking Up Your Final Projects?

The best time to pick up or discuss your final project is during my office hours, which for Spring 2009 are on Monday 3:00-5:00 and Wednesday 2:30-4:25.

It is a good idea to email me to make sure that I know when you are coming.

Surely, I will be in the JMHH 400 suit but I could be in the conference room or in a colleague's office.

Grading Epiphanies ...

I am working through your papers, and learning some new facts --- or potential facts. Here are some to consider:

Repeat --- Project Due Date: Noon Wednesday Dec. 17

Project Advice --- the End Game

Anyone who works on any project will face questions that were not faced before the serious work on the project began. This is natural and good.

Unfortunately, at this stage of the game, I am hesitant to provide tons more coaching. Naturally, if you are really stuck, I am happy to help, but if you are just facing some of the blizzard of alternatives that any analyst faces once the work has begun --- well, in that case, it really is most appropriate that you to make your best choice and use your report to explain why you decided what you did.

After all, you are a reasonable person. Why should your decision not be something upon which real people would wager real money? In fact, arguing for your ad hoc decisions a way to win "points" on your project.

Wise decisions are --- after all --- the real force behind what one gets paid!

"Stunning Fraud of Epic Proportions" (12/11/08)

Bernard L. Madoff, septuagenarian Wall Street asset manager, gave it all up at the office today by allegedly telling employees that it was all a "giant Ponzi scheme."

It is murky now, but there is talk of as much as $50B missing from clients' accounts. I can't see how auditors could fail to see even a few million missing from client accounts, so it may well be that Mr. Madoff just went off his meds for a couple of days and things are mostly OK.

Let's call that the PollyAnna Point of View. What else can I cling to?

If the $50B number holds up, it will be a world record. Robert Vesco netted less than $200M and he came close to toppling at least a couple of governments.

Over the next few days there will be some strange distortions due to asset freezes, etc. There will also be some very sad statements from famous NYC charities that were high on the sucker list.

Got a Bucket?

Contango Profits are the highest in a decade. Buy oil at spot, sell the March futures and deliver the oil to satisfy the contract. You'll make an annualized 38%. This is a form of madness. The bottom line is that the spot price of oil is at least a little bit goofy. (12/7/2008).

Great Graphic --- 2008 is Different

Greg Mankiw's Blog is almost always interesting, but on 12/7/2008 he has a stunning "augmented histogram" that shows just how remarkable asset returns in 2008 have been. Do take a look. In addition to the story the graph tells about this specific data, it illustrates a very powerful principle --- even the most humble graphic can be improved. It certainly is a delight to see the (usually horrible) histogram get this nice make-over. [Thanks are due to Blake McShane for passing along this great link.]

Presentations All Done!

This was a very well prepared sequence of presentations that showed knowledge, hard work, and honest thoughtfulness. I was impressed!

Moreover, I am sure that the final projects will live up to the high expectations that the presentations have created, so I will have lots of work (but lots of fun) reading your final reports.

Lost and Found:

One very nice tea thermos was left in class on Wednesday. It can be picked up from the Statistics Department information desk during business hours anytime for the next few days. After that, it will be sent to Wharton Lost and Found.

Not Entirely Redundant --- EDA & a Gallup Poll

Employment Poll

The punch line here the question: "Based on what you know or have seen, would you say that, in general, your company or employer is — 1) hiring new people and expanding the size of its workforce, 2) not changing the size of its work force, or 3) letting people go and reducing the size of its work force?” (source NYTs, 11/29/08)

This question is asked in repeated polls of a sliding panel --- an intelligent design. The Blue and the Purple lines taken together are perhaps a little redundant, but they are not entirely redundant. The residual sum gives the "not changing" value, and this is useful information.

Can you think of a better plot? Is it curious that the "not-changing" value is nearly constant? I'd have guessed that it would be as volatile as any other piece of the picture.

Sidebar: Promised Link on "Zero Cost" Portfolios

Naturally, they are not zero cost, or why would we hold anything else, since some of these do indeed have positive expected returns. The arithmetic of returns is a little tricky here. I've made one pass, perhaps you can do better. At least this puts some issues on the table.

Sidebar: 130/30 Strategies

It's been kicking around for ages that one might do better to be 30% short and 130% long. You can find a lot about this idea on the web. JAI has a useful empirical piece that is easily accessible.

Day 24: Project Proposals --- First Day of Presentations

For 26th November 2008

The presentations today were all excellent. They showed thoughtful preparation, energy, and originality. They set a high bar for day two and three!

The scheduling also went without a hitch, and we had a good crowd for the Wednesday afternoon before Thanksgiving. Wharton staff left at 2pm, but we kept plugging to 3pm and beyond.

"Will We See a January Effect This Year?"

Mark Hubert has a nice piece on this. His bottom line is that the January Effect (i.e. bigger small cap returns than big cap returns from 12/15 to 1/15) is more pronounce in years where the market has been strong going into December.

That is decidedly not this case this year, so you might expect to have a small or non-existent January Effect. Humbert's analysis is based on "correlations that would convince even skeptical statisticians." Humbert's suggestion would make for a good EDA project, but unfortunately it does not fit well with our time series mandate.

Strange Yield Curve (11/28/08)

The 5, 7, 10, and 20 year treasuries are now 4.17% 3.78% 2.60% and 2.98%. This means that if you buy the 10 year, and the yields don't change, you will ride "down" the yield curve to a bond that yields 128 bp more. This is very bad news. Approximating the duration to be 5, your bond price goes down 6.4%, thus eating up your entire three years' of "coupons." The ten year US Treasury has never looked so bad. The only scenario that makes this make sense is ... well, deflation may do it, but that's pretty hard to believe.

AbnormalReturns --- A Fine Meta Site

The Abnormal Returns Blog does an excellent job linking to insightful articles on the web. It is almost always worth a daily look --- or at least a weekend review.

Factoid on Mean Reversion in the Long Run

If you are searching for some reason why we might get back some of the money that we have lost this year, it is worth noting that the "twenty year variance is just 45% of what it would have been if annual returns were uncorrelated" (cited by Delong, page 7 footnote.) Unfortunately, this also means that the twenty year standard deviation is just 67% of what it would have been. This sounds like less of a bargain. Still, we do have a little mean reversion baked into the cake. It's also worth noting that DeLong is writing about real returns.

Will Quants Beat Non-Quants in 2009-2010?

There is a piece from Washington Asset Advisors that argues in favor of the technical vs fundamental view. Who knows if it is right? My own confirmation biases push me in the direction of agreement. After all, it's what I want to hear.

Pedro Aspe

I could constantly plug Knowledge@Wharton, but you know I don't. Still it has some great coverage of a recent presentations by Pedro Aspe. This article is worth a quick read, even as the time shortens for your proposals and projects!

Citi Saved --- At Least For a While.

As you ponder your papers, it is perhaps nice to note that the $300B agreement between the US Government and Citigroup was done in four pages. I made a good trade here, but I admit that I was gambling.

Quality Computational EDA : BooksThatMakeYouDumb

If you have good computational chops, you may look at the design pioneered at BooksThatMakeYouDumb. I think it is an interesting social search model that tells us something about the world. You may be able to do the EDA better. It would certainly be interesting to replicate in other languages/educational systems --- e.g. France. Naturally, you have to think harder than this author did about the nature of the sampling bias. For example, large state schools will tend to have (1) lower SAT scores and (2) a more diverse collection of mentioned books. Also, it goes without saying that the inference in the title "BooksThatMakeYouDumb" surely has the inference reversed, if indeed there is any inference to be made at all.

Day 23: Putting the Pieces Together

For 24th November 2008

Today we will have completed just under two dozen lectures, and this is a very modest number given our goal of dealing honestly with one of the central factors of economic life --- the returns on financial assets.

Our plan for the day is to (1) review the stylized facts that we have verified from our own analyses --- and add a few new twists (2) review our models with a focus on where they add insight and value, and finally (3) look at a few ways these can inform the design of interesting projects. In particular, we'll look at the interesting distinction between univariate, multivariate, and ordered univariate strategies. Variations on these methods can be applied to almost any basic project idea.

I'll also add a word or two about the use of confidence intervals and suggest a new technique --- bootstrapping ---which you can use to get confidence intervals (of a sort) for the return on a trading strategy. The method is not perfect, but it definitely has its charms.

I'll also ring the bell again about the importance of data cleaning, EDA, and presentation with thoughtful tables and graphs.

Generic Advice about Project Design (and Process Comments)

Certainly read the Final Project Spec Sheet. I'll review some of the main points in class. The one I would underscore here is that clear thinking is a key to having an excellent report. You want to make clear assertions and you want to make sure that what you assert is backed up by clear, thoughtful, and thorough research. Even a "simple" theme can lead to a very rich report if it is engaged carefully and completely.

Pre-proposal Two Pager --- Due Monday 11/24

Everyone should hand in their two-page pre-proposal sketch on Monday November 24. This will not be "graded" directly but it will help me be up-to-speed when Proposal Presentations begin on Wednesday.

I may not have made this timing perfectly clear, so if you really can't give me anything on Monday then please email me your two pager on Tuesday.

Sidebar: "It's Morning in America"

About 25 years ago, Ronald Reagan was running for his second term, and his campaign produced an ad that has become a classic. UTube makes this classic (and many other moments of teary nostalgia) just a click away.

It is soapy, and nationalistic, but it is also brilliant writing that evokes emotion and gets votes. I am sure that one day again there will be an incumbent president who can again run on a record of achievement and integrity. I just hope it doesn't take a quarter of a century.

Sidebar: Was Marx Right? (Posted 11/20/08)

No, I don't believe for a moment that democratic capitalism is busted, but after losing 13% in two days, I did think I might be cheered by listening to a few rounds of the International. I warmly recommend its definitive MP3 site. The International is there in all languages, but I prefer the Russian or the French just for historical reasons.

The best anti-Marxist argument I can think of right now is that people must trust our government a lot if they are willing to buy the 1 year note with less than a one percent yield.

Sidebar: Dollar Weakness and Stock Market Returns?

A while back there was an instructive piece in Business Week on the relationship of the strength (or weakness) of the dollar to the returns on US equities. The article looks at changes (or returns), not levels, so it avoids a the classic spurious regression slip. The use of monthly data and the shortness of the series make it hard to put the article's inferences into the domain of stylized facts, but I would expect that there are observations here that will stand the tests of time

Sidebar: Wikipedia on the VIX

The Wiki piece on the VIX is pretty good, maybe even very good. You might test how often the VIX really does correctly forecast the next month absolute change.You could think about this in concert with the little volatility paper by Goldstein and Taleb a look at their paper. Yahoo!, may the name usually be cursed, does offer nice VIX graphics. Still, what is the logic of the log scale here?

Sidebar: Bear Stearns Preferred

The common stock of Bear Stearns was virtually wiped out in the sale to JPM, but the preferred shareholder got a notably sweet deal. Their shares were converted to JPM Chase preferred shares with essentially the same terms as the original Bear Stearns shares. That was one hell of a fine boost to the credit quality.

Now (11/22/08) if CitiGroup is forced into some combination, it is a natural bet that the preferred shares may escape unscathed --- or even enhanced. Given that they now trade to yield 20% or more, they look sweet --- conditioned on getting paid either by CitiGroup or by some surviving entity.

The fear of course is that that preferred shares can be clobbered; most FNM par 25 preferred now trade about between one and two bucks. Even that is a mystery since the coupon payments have been omitted.

Note: The cash injection and asset back up today (11/24) may make this speculation mute, but the general principle is still worth keeping in mind.

Sidebar: No Juggling This Year?

Traditionally I have used the day before Thanksgiving as a day to do some "odd" things. One topic has been to see how good you would have to be to justify playing in the World Series of Poker. The bottom line is that after accounting for the decreasing utility of long-tail returns, you'd have to be better than probably anybody has ever been. If you include the asymmetric tax treatment for non-professionals, it is certainly a bad deal --- unless you get $10K of fun losing (which I hope you don't).

The other topic that has served us well on the day before Thanksgiving is to show how learning to juggle with three balls can be a useful metaphor for learning any complex task.

Also, three ball juggling can be very beautiful --- and magically complex. We won't "cover" it in class, but there is no better way to have four minutes of fun than by watching the Fugly Beatles set.

Finally, there is our traditional strutting turkey ---- Oh, what he does not know? Sort of reminds me of Bear Stearns's James Cayne going off to his famous bridge tournament.

turkey walking confidently

 

Day 22: Comparing Asset Returns in the Context of Risk

For 19th November 2008

The plan for today is to look at the notion of risk adjusted returns from soup to nuts. This is a very interesting topic in financial time series, and it has been developed far less systematically than one might have guessed. We'll consider all of the conventional measures, and add a few variations of our own. We'll also look at what one might learn about risks by consideration of post-mortem analyses of crises and crashes.

Sidebar: TradeSports Closes Its Doors

TradeSports.com was an extremely successful futures market for political and sports events. Since the contracts were on binary outcomes, the futures prices had an immediate interpretation as market estimates of probabilities. These futures markets were much loved and much followed, but the ludicrously named Port Security Bill made transactions with TradeSports so cumbersome that they have decided to shut down their business and refund all money in the client accounts. This is a sad day for libertarian investors who are willing to place a bet on their view of the likelihood of a political event.

Note: We will (probably?) continue to have the Iowa Election Markets, but these were always very thinly traded compared to TradeSports.

Note: InTrade (the non-US parent) of TradeSports seems still to be open, so this is an on-going story.

Sidebar: The Risks of Being in Charge of Risk Models

Things do have a way of periodically blowing up, and now banks have found the natural goat -- the guy in charge of the VaR models. (see story). Reminds me of some advice I once gave a class of Wharton undergrads...

Sidebar: Volatility? What Volatility Are You Talking About?

When I saw the title of the paper " We Don’t Quite Know What We Are Talking About When We Talk About Volatility" by Daniel G. Goldstein and Nassim Taleb, I was quite excited.

At last, I thought, someone is making the point in print that I have made repeatedly in class. Namely, each time we say "volatility" we point to some parameter in some model, but the model and the parameter can differ from utterance to utterance. This is silly of us, but we all do it.

Goldstein and Taleb get a whiff of this, but not the full scent by any means. Still, you should take a look at their paper. It is a quick read.

Sidebar: PDP a Momentum ETF

PDP is a PowerShare ETF launched in March 2007. The prospectus is one that would make Jessie James uneasy. Unfortunately this asset has not been around long enough to be amenable to much analysis, but the underlying theory of the asset is interesting. It is a momentum story based on a proprietary momentum index --- which would all seem insane --- except that the proprietary index is published independently of PowerShares. Still, the index provider does not seem hesitant to be a promoter of the ETF. Net-net, this does not look like a healthy development.

Sidebar: Nice EDA --- Two Regions Each with Ten Sectors

If you take the 10 sectors of the SP500 and the 10 sectors of the MSCM EAFE you get 10 pairs of numbers, one for each sector. You can then plot these pairs in two dimensions and then ponder the meaning of the 45 degree line. Lo and Behold! It tells you in which of the two regions the given sector is now doing best.

This gives a very interesting snapshot of current market "stages." Note: Points that are near the line are doing about as well in each region, so not much "weight" should be placed on these points. Still, each one of these points deserves a story.

Note: The graph below is for November 2007. Oh, how sweet those returns look to us today! They are almost all positive for Pete's Sakes.

Two Regions Ten Sectors

I would love to see the dynamic analog of this graph, even for just one sector. The graph I have in mind would plot (x_t, y_t) where, for example x_t is the period t return on the EAFE energy sector and y_t is the period t return on the US energy sector. We could look at 3 month trailing returns and plot a point for each week. It could be a very informative picture.

Sidebar: Stupid Forbes Article

There is a Forbes article exactly on today's topic, and it illustrates just how shallow magazine articles can be. Here we can see the shallowness so easily, the article can cause us no harm. What scares me is not this article, but all the ones that I read where I think that I have learned something new.

Sidebar: Yet Another Black Rock Insane Bandit Fund

The Black Rock Fund Equity Dividend Fund (class A) MDDVX , has a front end charge of 5.25% and a turnover ratio of 2%. If you like this asset, just check the SEC filling, get the holdings, and voi-la 98% replication. This is a dominated asset with 750M under management. They should be ashamed of themselves. Oh, by the way, they have 100bp expense ratio, and --- a Morningstar rating of 4 stars --- which pretty well tells you how worthless Morningstar ratings can be.

What a bizarre situation! Well, small turn over may be virtue in some people's view, but why should anyone pay and annual 100bp for the experience?

Sidebar: Michael Lewis on "The End of Wall Street"

Michael Lewis is famous for his book Liar's Poker which chronicled the goings on at Salomon Brothers during the "Wall Street excesses of the 80's" which were actually pretty tame by contemporary standards.

His current piece is provides a compelling view of the sub-prime development and how if you had a brain and intellectual integrity you could have been on the right side of the trade of the century.

It is one of the most riveting pieces of financial journalism that I have read in years.

Sidebar: RiskMetrics on Volatility

The November 2008 research letter from RiskMetrics is worth a look. It's naive in many ways, but it does start some interesting conversations.

Day 21: Cointegration and Statistical Arbitrage

For 17th November 2008

Final Project --- The Full Details

The project specification has evolved over more than five years of experience, so it is hard to imagine the there is any ambiguity that remains to be squeezed out. Still, I do want to go over it to make sure that everyone knows exactly what is expected --- especially at the level of academic integrity.

Do not forget that your final report is due at NOON on December 17. You must deliver a hard copy to my mailbox in JMHH Suite 400 and you must send an electronic copy to my email. Both forms of submission are required. Late reports are penalized at one letter grade per day. This is a huge penalty. Don't even think about it.

You should note on the hard copy and the electronic copy if you are willing to have your report posted on the web for the possible guidance of future 434 students. Without your authorization, your report will not be posted, even if it is the perfect model for a 434 final project report.

***Schedule for the Project Proposal Presentations***

Main Business --- Cointegration and its Application

The plan is to develop the theory of co-integrated series and the application of cointegration to statistical arbitrage. There are many of variations on this theme, but we will be particularly attentive to pairs trading. This class of strategies has bought more than one nice house in Connecticut, but its popularity has repeatedly waxed and waned.

The Puzzle that Started Cointegration --- Spurious Regression

We'll begin with one of my favorite simulations. Simulate two independent random walks, store the values in vectors x and y, regress y on x, and WHAM --- you find a highly significant alpha and beta almost every time. Since we know that x can not tell us anything useful about y, we know we have a spurious regression.

Next, we'll look at the way out of the trap --- testing that the residuals are an I(0) process. If the residuals are an I(0) process we are safe (or at least in no more danger than usual). If the residuals fail to be an I(0) process, then we almost certainly have a garbage regression. It is amazing how often you will see people perform such regressions, not knowing that they have fallen into a well known trap.

We'll look at some resources that add further intuition to this process, including the famous "Drunk and Her Dog" story.

Finally we'll look at some ideas from statistical arbitrage including the idea of a synthetic index and methods of pairs trading. I've started a resource page on pairs trading and I will add to it over time.

Sidebar: News Impact in the Classical Sense (Kobe, Katrina, and Crisis)

How much does news move the markets? This is the question that is addressed by what are called event studies, and there is a nice summary of some of these in a popular article by Robert Shiller, who is well-known for his book Irrational Exuberance.

Oddly, the Kobe scenario was one of "bad news travels slowly." The day one reactions were minor, but after ten days the Nikkei 225 had fallen by more than 8%.

One of Shiller's theses is that market impacts are sometimes the result of news cascades; that is, a drumbeat of follow-up news stories can have more financial impact than the initiating event. Since Katrina was post the publication of Schiller's essay, you might see if Katrina fits into his mold. This won't really make a whole project for the final, but it would be a nice investigation to share with the class.

This theory of news cascade also seems relevant to the financial crisis of 2008. Lehman hits the tank, AIG gets massive, bail out, GM hangs by a thread, etc. etc. It's hard for the market to rally if the world keeps presenting a cascade of bad event that are all related and all on a glide path that takes many months to run.

Sidebar: China Share Classes

There is a brief article on Red Cat Journal that discusses the various classes of Chinese equity shares. We may discuss these as part of our conversation on "how to frame your final project." There is also a follow-up piece at Red Cat that opens a conversation about the eventual convertibility of the share classes. (My thanks to "Phoebe" Fei Gao for these links.)

Sidebar: KMP vs KMR

Kinder Morgan is the largest pipeline management organization in the US. Investors can participate in Kinder Morgan either as limited partners in the MLP with symbol KMP or through another vehicle which is a kind of management company that trades under the symbol KMR.

There is a comment at Morningstar that argues that these assets should trade in "lock step." To me it seems interesting to look at the time series properties of the spread on these two assets. You'll want to think about what is really going on with the two, and you will need to keep in mind that it is particularly awkward to short KMR, i.e. it may be practically impossible. Still, if you get amused by MLPs this is where the fight begins.

Sidebar: Details on a Blackrock Bandit Fund

People who have been ripped off are understandably thin skinned, so if you have an uncle who has been conned by some retail Merrill Lynch account representative into buying Black Rock Equity Index Fund CIEBX --- or something similar --- you have to be gentle as you coach your uncle out of the jam.

Now would be a good time; the capital gains are not likely to so large that taxes will be a worry.

The objective of the CIEBX fund is "to match the performance of S&P 500 index" and--- provided that they mean the total return of the index holdings rather than just the index price return --- this is a noble goal. Unfortunately, they have a" deferred' front end load of 4.50%, a 0.75% 12b fee and 1.17% expense ratio.

In a world where you now pray for a 4% real return, buying this fund throws away about half of the real return you hope to learn. Buying it is just like giving away half of your future real earnings --- or half of your initial investment.

Buy 100K of this fund, and asymptotically you are guaranteed to get a negligible fraction of what you would get with an investment in an honest SP500 Index Fund such as Fidelity Spartan or Vanguard Admiral. This isn't fancy theory; it's arithmetic. Saving your Uncle from this mistake for just 100K will over time save enough to pay for someone's full Wharton education.

Why Do They Do This? It's NUTS!

What I don't understand about Merrill Lynch and Blackrock is why they don't care more about the reputation risk that this kind of larceny at the retail level creates even at the wholesale level. It is transparent that the CIEBX fund is a crass rip-off. Other products are harder to analyze, but, if they are willing to rip you off when you can check exactly how much you have been scammed, then you have expect that they are REALLY ripping you off with their more obscure products.

Do People Learn? Evidently Not

" In 2002, Merrill paid $100 million in fines after regulators found analysts at the firm had recommended stocks they knew to be no good. "(ref)

Still, in every township throughout the land, one can find the friendly well-meaning ML rep, often clueless to his complicity, plugging products that under every possible future scenario will leave his clients with less money than they could have had if they had taken the time to read the prospectus and compare the ML products with the corresponding products from Fidelity or Vanguard.

Sidebar: Details on TIPS

There is a piece from GE Asset Advisors that provides a good tutorial on TIPS. It covers the mechanics and discusses both the strategic and tactical uses of TIPS. In a world where there is the possibility of deflation as in 2009Q1, there are some interesting twists on TIPS. Incidentally, they are a favored asset of David Swensen.

Sidebar: The Once Noble CREF is No Longer a Hero

Funds like Black Rock Equity Index Fund CIEBX are rapacious in their greed and exploitation of the credulous, but I am almost as irked by CREF.

In the early days, CREF was a genuine leader in providing investment value. Accordingly, they won a place close to the heart of academia. Sadly, in the last ten years, CREF has exploited that trust, and it now charges fees that are indefensible.

The CREF Equity Index Fund expense ratio is 0.50%, and, while this pales in comparison to the Blackrock fees, it is still a stupid price to pay. You can get the same product from Vanguard or Fidelity for less than a third of this price.

The excess spread --- say 35bp to 43bp--- may not look like much, but at retirement time when you have just 400bp to draw down to live one each year, it is at least 8.75% of your income. That is one hell of a tax!

Project Due Date: Noon Wednesday Dec. 17

The UPenn Exam Schedule has our final scheduled for Wednesday Dec. 17 so t his date is the "fairest" day to have your projects due. It also maximizes the time you can invest in doing a great project. I'll also get them all graded and have the grades posted before I go of to Puerto Rico for a little winter holiday. Seems prefect!

Day 20: Rolling Statistics and Momentum Strategies

For 12th November 2008

It never pays to ignore what you know, so any forecast, strategy, VaR level, or performance measure needs to be constantly up-dated as new data arrives. The first part of our plan is to review the tools in S-Plus that make this easy. The main tool is aggregateSeries(). This is a very general tool that makes it convenient to do "rolling anything."

Moving Averages --- Simple Minded, but Not Silly

We'll also look at some of the most ancient tools of time series analysis, the exponential weighted average. This is an all-purpose tool that is often used in combination with other, more sophisticated, time series tools. One of the apparent difficulties in the use of moving averages (simple or exponential) is that one has to pick a "window" size. We'll discuss some ideas for dealing with this problem, including" Foster's Trick." This is something that it would be very worthwhile to explore in a final project.

We'll see how it is used in the MACD, which is reported in many graphical packages, including the free on-line chart service BigCharts.com

MACD and Other Price Level Favorites

MACD is goofy in some ways but it has fascinated me for a long time, because it so often looks like "it works." Unfortunately, formal tests with individual equities mostly come back with the verdict: "No extra cheese."

I keep looking for the context where MACD really does pay the rent. My sense is that it has a good chance of working well in currencies, and in style spreads --- say small cap value vs small cap growth. It might also be useful in making guesses about sector rotation. Exploration of one or more of these ideas might make a good project.

Momentum Strategies

Finally, we will look at a resource page on momentum strategies. It has a CitiGroup FX Advisors presentation, and summaries for a few leading academic papers on momentum. The CItiGroup piece is pretty lame by the standards of 434, but it is worth a brief look. If nothing else, it suggests that at least some of the competition is not to be feared.

Sidebar: MLPs

I started a little resource page on MLPs, or Master Limited Partnerships. These form a very interesting asset class with attractive non-standard features, including very fat (and pretty stable) dividends and favorable tax treatment. These benefits spring from the tax law view that an MLP is a "wasting asset," but this theory may not apply to many MLPs --- except as a handy tax law fiction.

Sidebar: Tops and Bottoms Identified by Sector Leaders?

A random web wag suggests that at the market tops the leading sector is consumer staples (say as reflected in XLP) and at market bottoms the leading sector is consumer discretionary (say as reflected in XLY). Naturally, this case is built on recent experience, and it does make modest sense. Is it something you'd like to bet on? I can't decide, but it is something that I'll keep in mind.

One of the things that I find interesting in this analysis is the use of the XLY/XLP ratio. There are lots of other contexts were such an idea my be just what one needs to stir the "missing non-linearity" it to the model.

There is a related theory that says that of all the goodies out there that might be counted on for reliable trending --- retail is the king. If you are looking for leading indicators, the retail index RLX may be a good shot.

Sidebar: Markets and Mindshare

The size of the world's bond market (55T?) and world's equity market (45T?) are comparable in a "Fermi sense." Historically, equities have clobbered bonds. Moreover, bonds are hardly risk free. For example, the bonds of the Weimar Republic became worthless, but the stocks did not. On a less dramatic scale, you can have a very rocky road with even a 30 year US Treasury --- a 1% rise in interest rates can cost you perhaps 25%, depending on the initial interest rate. So, why are there so many people, businesses, and governments who are happy to own bonds? How does this fit with our "counterparty theory" of strategic investing.

Sidebar: Stylistic Features of SP500 Returns

Wilhelmsson (2006) also deserves some class time. One nice feature of the paper is a break-down 1995-2000 and 2000-2005 of the fundamental features of the SP500 returns. These are very useful for calibration of one's intuition about returns --- and hence for "Fermi" calculations. This is his Table 3, and it is not his main message, of course. The main message is that it pays to deal with kurtosis (fat tails), but may not pay to deal with skewness (asymmetry about zero). One of the take-aways is that GARCH(1,1) driven by shocks that have the t-distribution is the best of breed given method of evaluation. We may not buy that method, but the conclusion may still hold up for us.

Sidebar: Be Short Vol and Expect Sad Days

Straddles, Nick Leeson, and the collapse of Barrings Ban

Sidebar: Fact or Artifact

There is a Seeking Alpha piece that reports on weekly returns of SP sectors versus the weekly returns on oil. They get that energy is positive (well, duh!) and everything else is negative --- with XLP being the most negative. Do you expect this relationship to hold up over time, or is it simply an artifact of the study period (which ended in October 2007).

Day 19: Comparing GARCH Family Members

For 9th November 2008

Now that we have a substantial family of GARCH models, how should we choose between them? The plan is to first consider some structural features, especially the connection to the Wold representation and our old bête noire --- stationarity.

One useful way to compare the many animals in the Garch Zoo is by looking at a plot called the "news impact curve." Given two models we first find appropriate values for the parameters of the models, say by fitting both to the same data. When then fix those coefficients and consider the the conditional variance as a function of the innovation epsilon_ t.

This function tells us how the two models will differ in the importance that they attach to a given shock. This measure is not perfect, since it speaks to just the impact of one shock. Still, it seems to be informative, and it is easy to implement (see e.g. S-Code Ex.)

The picture we get will give some intuition about which models "care" most about a negative shock versus a positive shock. Still, the pictures are not perfect, since it is not always easy to say which parameters values are "comparable" when one looks at radically different models. One way to make progress is to fit both models to the same data. Unfortunately, this begs another question; namely, the question of model specification.

Next, we consider non-normal drivers of the GARCH model. This is an important issue that makes the GARCH model much better than it would be otherwise. Still, the trick is old, going back to Bollerslev (1986).

Finally, we dig into a paper of Hansen and Lund which compares some 330 GARCH models. This is a heroic effort which we will be delighted to cover only from the summaries. Still, there is room to note a fundamental philosophical point. To compare one needs a criterion. How is one to choose among the potential criteria? My favorite is fitness for use, but this is not always feasible.

CAVEAT

I tend to "sell" the take-away from Hansen and Lund to be that "you don't need to look much further than GARCH(1,1), or perhaps EGARC(1,1)." I do believe this, but it is a little sophistic to argue this just from exercises like that done by Hansen and Lund. The problem is the criteria for judging the models. Hansen and Lund use a bund of them, but a eight inadequate measures are not all that much better than one. Also, the idea of ranking a zillion pretty similar models and then looking at the ranks --- well, that is clever, but it is also a bit sophistic.

Alternative Features of Merit

There is anther principle that I like. You could call it simulated verisimilitude. You fit the model, then simulate data from the model, then do EDA on your simulated series and your original data. If the EDA (and other logical) comparisons are not pretty close, then you have good reason to be unsatisfied with your model.

It is amazing to me how seldom this method is used by model builders in operations research, scheduling, logistics, transportation, etc. Those guys very often use models that have very little relation to the stylized facts of their business. In financial time series, we do at least have this part of the drill down pretty clearly.

Last Homework! This homework provides experience using a GARCH model to engage something that is of bottom line interest --- the relationship of risk and reward. As it is presented, it is reasonably straightforward. Nevertheless,t if you have time, you can use it to do a little exploring for your final project. It also provides a reminder of the very on-going importance of basic regression and EDA studies.

Approaching the End Game

On Monday the 17th the last homework comes in, then Wednesday the 19th and Monday the 24th will be "regular days." On Wednesday the 26th, the day before Thanksgiving, we will have our first round of "Final Project Proposals." The second and third rounds will be on the 1st and 3rd of December, our last days of class. The final projects themselves will be due on December 12 at noon.

Change

Sidebar: Chicago Becomes "Booth" for $300M

David Booth co-founded Dimensional Fund Advisors to provide a keyboard of low cost but delicately sliced index funds that could reflect phenomena such as those one sees in the three factor model and earlier academic work. Good execution and thin margins led to a stellar reputation and $120B under management. DFA has always maintained close contact with academia and they have a research page that everyone should visit from time to time.

Mr. Booth did well enough with this service to be able at age 61 to give the University of Chicago Business School a little something.

Sidebar: Roll of Subjective Judgment in Risk Models

The NY Times article "In Modeling Risk, The Human Factor was Left out" adds a bit to our discussion of VaR models, especially those models that ignore "known but unobserved risks" such as the historical "peso problem" or the more recent "agency problems" of CDOs.

Sidebar: The "Silly Bid" and Structured Products

There is a curious strategy that has emerged in the last few months. You take some reasonably thinly traded stock and just place a "silly" bid --- say one that is 10%-20% below the market. Even now your bid is unlikely to be hit, but in this market, it is possible. Given that you have chosen a generic stock --- not a wounded rhino --- you should be very happy with the trade. I like this "trick" with structured products like NMQ. At present levels, NMQ is a SP500 Index asset but it is held mainly in retail accounts and the Amex market makers don't pay much attention to it.

Day 18: The "Leverage Effect" and the GARCH ZOO

For 6th November 2008

The GARCH model takes a major step toward a realistic statistical view of the noise in asset return series. Still, it is not perfect. In particular, the plain vanilla GARCH model responds symmetrically to either a negative or a positive shock. Historically, it is the case that a large negative shock has a more substantial impact on subsequent volatility than does a positive shock. A GARCH model cannot capture this phenomenon.

Fisher Black (partner with Myron Scholes in the Black-Scholes formula) called this phenomenon the "leverage effect" and the name has stuck. Black gave an interpretation of this empirical phenomenon from the point of view of the firms debt to market capitalization ratio. We'll do a Fermi calculation to see if this interpretation holds up as sturdily as the name.

One point to note: Black's leverage story may seem to contradict the Modigliani-Miller Theorem. If it did, it would not particularly bother me. Still the problem is worth pondering. I'll argue the view that there is no contradiction because the Modigliani-Miller assertion is about value, and Black's leverage story is about volatility. Now volatility does effect value, but subtlety --- through volatility drag from our perspective, but surely not enough to make us regard the MMT and Fisher's leverage effect as contradictory.

Cultural Note: Franco Modigliani --- an Italian-American --- pronounced the "dig" in his name and won the Nobel prize in 1985. Amedeo Modigliani --- an Italian painter --- pronounced gli as "li" in the Italian fashion and lived a brief life that was textbook Bohemian.

We'll then look at the models that attempt to cope with the so-called leverage effect. Most of our attention will be given to Nelson's EGARCH model, or exponential GARCH model. This is the "next step" model that has rather reasonably stood the test of time. It is definitely useful by both academic and practitioners. It definitely has its uses, though it does not provide nearly as big an increment to our toolkit as GARCH itself.

After EGARCH there were many other models that attempted to deal with this or that stylistic fact that is not well modeled by GARCH. Naturally, one eventually faces a certain law of diminishing returns. Still, it pays to know about at least a few of these.

We'll also look at some relevant examples in S-Plus. It does indeed turn out that when you fit a model like EGARCH to the returns of an individual stock, you are very likely to get a significant value for the leverage parameter.

It's not easy to say what this really means to us in an investment context, but it is certainly worth thinking about.

Leverage Effect not a Leverage Effect

For year's I have argued that Black's interpretation of the "leverage effect" as a "leverage effect' didn't really make sense, and II figured that everybody knew this.

Turns out that there was still a paper to be written, so if you want (substantially) more than what comes with our Fermi calculations, you can look at an informative 2000 paper of Figelwski and Wang.

Sidebar: Risk and Reward

There is a piece on the risk-reward trade-off posted at CXO that is worth a quick look. Some parts of the piece are confusing, but it puts interesting questions into play. The introductory story should make sense to you, and, if you get interested the original paper is worth a look.

The big question is "Do you get compensated for taking incremental risks --- or is it the case that for any given asset incremental risk (as measured by "volatility") is an a priori bad thing?"

In the classical stocks versus bonds story, we see historically a very reassuring compensation for risk taking, but through time and within one asset class the story comes close to reversing itself. You'll get to explore this in HW9.

Also, from CXO there is a nice list of assertions relating volatility and excess return. This is a good list to think about as you ponder your final project, which we will start discussing today.

Day 17: ARCH and GARCH

For 3th November 2008

The ARIMA models underpin a large part of the theory of time series, but they have an Achilles heal when applied to financial time series --- the conditional variances of ARIMA models do not change as time changes.

For financial time series, this is in violent contradiction to reality.

One of the most fundamental stylistic facts of asset returns is that there is "volatility clumping" --- periods of high volatility tend to be followed by periods of high volatility, and periods of low volatility tend to be followed by to be followed by periods of low volatility.

The ARCH and GARCH models were introduced to remedy this situation, and they have led to models that are much more representative of financial reality. Our plan will be to develop these models as they evolved, first looking at why they are really needed. We'll also look at the tools in S-Plus for handling GARCH models, either in simulation or in fitting.

Finally, we'll discuss some original sources, notably a review article by Robert Engle called GARCH 101. The notation used in this piece is no longer the standard notation, and some bits are best taken with a grain of salt. In particular, given what we know now, Engle's discussion VaR "optimistic." Still it is definitely fun --- and instructive---- to take a look.

Another paper we might discuss briefly is Engle's paper with Andrew Patton "What Good is a Volatility Model?" Ironically, this paper has the "tell" that I have mentioned in class, namely it uses the Dow (OMG!) as its illustrative price series. I don't know what motivated this choice, and I find it a little less serious than I would have hoped.

A positive feature of the paper is that it gives a brief list of "stylized facts," a very important notion to which we will start paying more systematic attention.

Sidebar: TIPS Spread and Money Manager Survey

"Nor do the managers worry about runaway inflation. They see prices rising by 3.28% this year, but by a lesser 3.02% in 2009." --- from the Barrons Big Money Poll 11/3/08

"TIPS yields indicate investors are betting consumer prices will fall. Five-year TIPS yielded 0.31 percentage points more than Treasuries of similar maturity this week." --- Bloomberg 11/1/2008

So, we have a horse race. Do you believe the consensus of money managers or do you believe the TIPS/Treasury spread?

My own bet is that you'll do much better with a hold to maturity 5 year TIP than the corresponding treasury --- even if there is not much difference in the first two years. Stocks "should" beat both over a five year period, but that horse is not in this race.

Homer Holloween

Sidebar: TrimTabs, Money Flows, and "Bottoms"

It's November 1st today, and this makes it interesting to look at the Market Letter of October 1 Charles Biderman at TrimTabs --- the flagship research firm on money flows. This work is interesting to me, even though I have confessed to something close to a learning disability concerning flows "into or out of stocks."

Flows into futures (though symmetric) are less paradoxical --- and money market flows are (probably) not paradoxical at all. Golly, mutual fund flows always make perfect sense, even though "stock market flows" do not make sense to me --- except for the transitions of IPOs, repurchases, privatizations, and a few other special cases --- that go beyond "normal" purchases and sales.

I respect the firm and Biderman, so it is interesting how one of the worst months in history was so misread ex ante. This is especially curious since fund flows do seem to have been a big driver for the month.

"When public companies are net buyers while individuals are heavy net sellers, the market is making a bottom": this is an interesting feature of the TrimTabs Liquidity Theory.

Sidebar: The Great Gasparino Mystery (3:38pm Oct 30, CNBC)

[Approximate Dialog between Dylan Ratigan and Charles Gasparino --- as real time blogged]

Ratigan: Charlie, what have you got?
Gasparino: What have I got?
Ratigan: Yeah...so give us the story.
Gasparino: What have I got? What have I got? What have I got?
Lee: Charlie, just tell us!
Gasparino: What have I got?
Ratigan: Charlie, we've got limited time.
Gasparino: What have I got? What I got is shoot for the capitalism.
Ratigan: 'Shoot for the capitalism'? What?
Gasparino: What have I got?
Ratigan: Okay, not really sure what just happened there.

Charlie Gasparino is a "movie star" for market wonks --- professional and amateur alike. This time he seems to have taken an unfortunate slide toward the Nick Nolte side of celebrity things, but who really knows?

Rumors will surely fly. There is a blog with an (imperfect) UTube link. Judge for yourself. We'll follow the fallout. There are also earlier interviews with Charlie on better, yet still revealing, days.

Up-side Alternative Suggestion: Maybe a CNBC Lawyer told Charlie he could not go with "What I got." Then, an exasperated Charlie just mumbled up his air time. To me, this does not quite compute. Charlie is slick enough to say, "I had a story, but I am just now informed by "legal" that I have to put a lid on it. We'll sort it out and get back to you."

Follow-up: On Friday Oct 31 Charlie and Dylan had their 3:35 meeting and --- after doing some regular business ---they just made fun of the Thursday contre-temps and Charlie's YouTube notoriety. This doesn't quite wash.

Follow-up: Equity Help Desk has a plausible story, without rehab implications.

Sidebar: Mean Reversion vs Momentum

Essentially every quantitative strategy depends on a view that is either "trend following" --- that is a momentum strategy , or "trend reversal" --- that is mean reversion strategy.

Between the two, there is always a finely pitched battle. It seems to me that the momentum story has more reported successes. Still, there are situations where the mean reversion case can be made. One of these was mentioned in the Granger article covered last time.

As a variation on the strategy reviewed there, take any set of say 100 stocks. Now on each day, buy the 3 that are off the most at the close, and hold these stocks for 10 days. Now, compare this strategy to the comparable market buy-and-hold strategy. How do you do? Here, by the way, you might take your transaction cost to be 5 basis points on each leg of the trade. This is realistic if your trades are small enough to avoid market impact cost.

The biggest potential "bug" in such a study is that your real-world "buy on close" price may have some slippage from the "print" close that you find in the historical data.

Notation --- Possible Pedantry vs Certain Sloppiness

I mentioned in class an example of a lecturer at a distinguished university who took such "liberty with notation" (the charitable interpretation) as to simply boggle the mind. It seems only fair that I provide a link --- which I will soon make dead. Just go to page 5 and ask yourself, "How could the students not be hopelessly confused?" Incidentally, I don't wish to pick on these authors (well, maybe); rather I want to point out that good notation makes for good reasoning.

Actually, it is more certain that bad notation makes for bad reasoning.

Physicists, chemists, and astronomers, sometimes scrape along with dodgy notation --- but only because they are much smarter than we are --- and more accustomed to living with notational ambiguity.

In fact, even these princes of science have often confuse themselves unnecessarily for years. Rigor really is a great simplifier.

Finally, to be super charitable, I will later present a computation that I learned from the delinked notes. Yes, you can learn from even the most muddled sources.

I find this consoling. No matter how daft I may be --- or may become ---I am reasonably confident that I will not damaged your minds irreparably.

Sidebar: Purchase Price Parity and the Big Mac Index

The Economist this week has come out with one of its perennial favorite articles, the world survey of exchange rates and their comparison to PPP as reflected in the price of a Big Mac.

Sidebar: A More Positive Case for VaR and a Spin on Subjective Input

There is a WSJ piece (temporarily misplace) that sings high praise for the use of VaR at GS and its value in helping to steer them out of some of the subprime mess. They eventually get hammered by the systemic issues, but at least they had a moment of reprieve. Eventually I'll have an essay on VaR.

Day 16: Switching Regressions, Non-Linearity, Forecastability, and Cost-Benefits of Subjectivity --- and, oh, Tells!

For 29th October 2008

Our main goal is to review a classic discussion paper by Clive Grainger, "Forecasting Stock Market Prices: Lessons for Forecasters."

Grainger shared the 2003 Nobel Prize in economics and his contributions find few equals in the world of econometrics.

Granger's old paper has benefits for us even though at this point the it is rather dated. One benefit is that it can be 95% understood at the level of Stat 434. Second, and more persuasively, it suggests some potentially useful ideas that even now have not fully explored.

As a caveat, his introductory comments on martingales and the EMH (and a few other things) are way off the mark. For example, if asset prices were martingales as the introduction considers, then only risk-seeking gamblers would invest.That is just silly.

This part of t he paper can be fixed with just a small correction. For example, one can use a I mentioned alternative earlier. Specifically, the ratio of an asset price to the market price may be more feasibly viewed as a martingale --- or even a supermartingale which you recall is a "bad" game. This makes the assertion logical. Unfortunately, it remains untestable.

At other places in the paper, we have to be concerned about data quality, or stationarity, or data relevance. For example, one of the papers that Granger discusses uses market returns back to 1896. For me, this is just too far past the "use by date".

Similarly, at one place Granger looks at transaction costs of 0.5% or ever 1%. Nowadays, this is a silly level of transaction costs for the assets in question --- except in the remotely relevant situation of market impact costs. In more common (but still special) situations, you are even paid to trade; that is, you make money trading, even if you just break even on the trades. This sounds weird, but I will explain. It is a little bit like being a shill in a poker game. Sidebar: The Wiki piece on shills looks only at the negative side. There really is a positive side too!

Nevertheless less, if anyone is looking for advice about how to have better luck forecasting asset returns, this is a very sensible place to begin.

Note: Citation Searches

When you find an article that you like (or even one you don't like), you can find more recent articles that follow up on it by doing a citation search. This is typically a much more efficient way to find relevant research than just by looking up a topic. In particular, if you look up a topic that is too broad --- like forecasting --- almost no one can thread his way through the forest. Citation searches are a very powerful research trick.

Note: S-Plus Tools For Rolling Regressions

We may also discuss the tools that are available in S-Plus for dealing with dynamic regression. Rolling regressions and weighted rolling regressions are a staple in many of the Stat 434 final projects, but at this stage you can probably learn everything that you might need about these tools just by working through the code box example.

Note: Risk Free Rates

For a CAPM style modeling exercise, one needs "risk free rate." Exactly which rate one might choose is open to debate, but 30 day treasury yields are usually appropriate. When you put any rate into the regression you will naturally have to make sure you are comparing apples and apples --- i.e. daily stock returns and daily risk free returns. To convert treasury yields to daily yields, you can use the conventional 360 day year. For data resources you have several options.

Sidebar: The Old Bellwether Idea --- It's now Now the Apple Tell

For the longest time people would look to GM (LOL!) and later IBM as "bellwether" indicators of the market. That is, these were viewed as leading indicators of the whole market. Mr. Love-Him-Hate-Him Cramer put it out on 10/28/2008 that Apple is the new "bellwether." Is this baloney, or is it cheese?

BTW, "cheese" is a 434 term of art that stands for "excess returns." This friendly term has not been used much this year, perhaps as an apology for past year abuses --- or as an acknowledgement that there have not been many excess returns this year.

Sidebar: Uses of Subjective Information

In science and engineering there is a tradition of working hard to minimize subjective content of models and analyses --- but even there one has to admit that many design choices are based on subjective information. There is a phenomenon in economics called "physics envy" and this is one of sources of pressure for analysts to minimize subjective input into financial and economic models. The downsize is that this leads to more and more weight being place on historical observations. As we know from the discussion of the Peso Problem, such back-looking empirical estimates may ignore some serious economic facts.

This brings us to the thorny issue of subjective input in to models like those that are used in VaR calculations. It is clear to me that subjective input would have provided at least some improvement on the VaR models that have blown up over the last year. If one does advocate subjective input, it's a good idea to give a periodic review of the cognitive biases which can be as real --- and as dangerous --- as the "path-focused objective myopia" which one might hope to ameliorate with the inclusion of at least some explicit subjective inputs.

Sidebar: Regarding CAPM and Other Puzzle --- What Changes a Mind?

“Children do eventually renounce their faith in Santa Claus; once popular political leaders do fall into disfavor…Even scientists sometimes change their views….No one, certainly not the authors, would argue that new evidence or attacks on old evidence can never produce change. Our contention has simply been that generally there will be less change than would be demanded by logical or normative standards or that changes will occur more slowly than would result from an unbiased view of the accumulated evidence.” ---Nisbett and Ross (1980), quoted by Hong and Stein (2003).

Incidentally, this quote is consistent with the notion of confirmation bias which asserts that a person holding a view is more likely to be attentive to evidence that supports his view than evidence that does not. Confirmation bias is a feature of human psychology that has been demonstrated in a great variety of experiments.

Sidebar: Remembering: October 30, 1961

Tsar Bomba was detonated at 11:32 a.m. on October 30th, 1961 over Novaya Zemlya Island in the Arctic Sea. With a lead tamper, the bomb had a yield of 50-60 Megatons, more than ten times the explosive force of all of the explosives used in the Second World War --- including the atomic bombs of Hiroshima and Nagasaki. Tsar Bomba was a very clean bomb, as essentially all of the fallout would come to rest on the USSR. With a more "traditional" design using uranium tamper, the yield would have been expected to be100 megatons. The Tsar Bomba is the most powerful bomb to be detonated on Earth --- so far.

Vestigial Sidebar: Volatility Drag

We may also revisit the formula for volatility drag, though I think this is well-known to you now. The spin I do not want you t miss is that volatility drag may offer some explanation of why the "2x" leverage funds do not provide returns that are as large as one might have expected given the returns of the underlying asset.

Day 15: Time Series Regression and Applications to CAPM

For 27th October 2008

The plan mostly focuses on the natural extension of ordinary least squares regression (OLS) to financial time series. Still, there are new topics, such as the likelihood ratio test and the AIC criterion. We'll particularly look at AIC, AIC weights, and the way to use these to combine forecasts.

We'll look at the nuances of the model and its associated tests. We may also cover a MSFT/CAPM example that is bundled with Finmetrics, but you can just as well look at this by yourself.

One of the most famous models that fits into this context is the 1992 Fama-French Three Factor model. This is the model which for many (but not all) signaled the "death of the CAPM." Parallel Mark Twain's line, the rumors of the death of CAPM may have been greatly exaggerated. Still, the true believers are starting to face a sea of troubles that are almost as tough as the ones face by those who preferred had a hard time with heliocentrism, but comparably sure experiments are much harder to come by.

The Wikipedia article on Fama describes the three factor model, and it also has useful links, including one to the original FF92 paper and a good humored one to a Dartmouth humor magazine.

If you do look at the original lFF92 article you will see that there is a fair amount of technology there which we have not engaged. Still, with the tools we do have you can tell very similar stories. The basic tale is pretty robust. It's time to list it as one of our "stylistic facts."

Maximum Likelihood and the ML Ratio Test

Basically all the test that you have seen in all of the statistics courses that you have taken are obtained by on general method, and they are all what is called a maximum likelihood ratio test.

The computations behind these tests are a basic part of other statistics courses, but we still to well to review a bit of this theory. In particular, it gives us the chance to nail down the very fundamental notion of the likelihood. This is critical for maximum likelihood estimation, for the likelihood ratio test, and for other cool stuff like the AIC, which comes up next.

Akaike's Information Criterion and Model Averaging

The Akaike Information Criterion (or AIC) is perhaps the most widely applied criterion for model selection.

For my own account, I am not a huge fan of AIC. The main problem is that in many cases one assumes at least as much going in as one hopes to infer coming out. In pure model selection there may be some net gain in most cases, but, since there can be loss in some cases, it is not clear that one wins over all.

Still, the AIC is out there, and it mostly seems to point in the right direction. It's probably worth consideration in most contexts, provided that one does not get too carried away.

Model Averaging: A Practical Alternative to Model Selection

If you are interested in using your model as a forecast, you may be able to side-step the problem of model selection. Rather than simply chose model A or model B to make your forecasts, you can instead consider an appropriate average of the forecasts given by the two (or more models).

Foster's Trick For Model Averaging

There are many rules one can pose for averaging the forecasts given by a set of models. You could just take the simple average, or you could take a weighted average where the more accurate model is given a larger weight. A still more principled idea that I learned from Dean Foster is to use regression. Here one takes the forecasts of the models and regresses the observed returns against these forecasts. One can then use the regression coefficients as "weights" for the combined model. Here we use the quoted because the weights can be negative and need not add up to one, so this method is not strictly an averaging method.

Naturally this idea must be combined with good sense. The forecasts given by your original models are quite likely to be highly correlated, so this regression problem can be ill-conditioned. My advice would be to consider this as a exploratory tool. There is no reason at all why you cannot stir in your own judgment.

The "Best" Criterion --- Fitness for Use

The model that is best is the one that "works" best for you. Ironically, this criterion is not often discussed. I have written a bit about this, and eventually I will write more. The whole notion of a model is one that deserves a richer --- and more philosophical --- view that is common in statistics courses.

Sidebar: Surprises with Qualified and Non-qualified Dividends

The crash of Fall 2008 created some eye-popping dividend yields, but it also created some quirks that may surprise investors who chase those yields. The so-called qualified dividends are those on US tax paying corporations and these are taxed at a maximum federal rate of 15% but non-qualified dividends (such as those on REITs) are taxed at a maximal 35%. The surprise is that for the dividend to be qualified the corporation must pay federal corporate tax, and, with earnings in the tank, many firms will not pay taxes. Thus, those "juicy" dividends stand ready to be taxed at the higher rate --- if indeed they are paid at all.

Sidebar: "120/20 Good Buddy"

Among the strategies that now have the public ear are the 120-20 strategies ---- leverage up 20% on the long side and off-set this leverage by going short for an amount of 20%.

Naturally, such a strategy would be nuts --- unless you could pick winners for at least part of your up-position and pick mostly under-performers for your short position. As a retail investor, you would also face an 8% margin cost headwind on the 20% that you are leveraged and the headwind of any dividends to be paid on the downside.

Thus, for an individual investor replication of a 120-20 strategy is a non-starter.

As an institutional investor, your long position will cost LIBOR and a bit and your short position will pay LIBOR minus a bit, so for professionals the whole game becomes modestly feasible.

Thus, professionals have the opportunity to let you in on this game --- for a modest fee, of course. This is a good trick all by itself, but the 120/20 pitch has a ready listening. You can look at some of the recent pitches.

My own view is that these retail issues are not good deals, but I am open to arguments on the question. If you are looking for a final project, you might want to consider a project that plays off of these funds.

Sidebar: "Is RSP a Stinker?"

Just as a side note, you might want to think about a project that plays RSP versus MDY or VO. My best guess is that RSP is almost a dominated asset, or at least a stochastically dominated asset. My guess is that you will almost always be able to beat RSP with MDY (or at worst a blend of MDY and SPY).

Yet more strangely, I bet you can dominate MDY with VO. This needs to be checked, but if it pans out then one finds yet another place where investors could save a few tens of millions of bucks (per year)..

Sidebar: Fed Funds Rate Cut on Stage

fed funds

Everyone expects a move this week, but there isn't a lot of wiggle room left.

Day 14: VaR --- The Sad Story

For 22th October 2008

The first (and main) part of the plan today is to look first at the most widely used tool for expressing risk exposures:VaR, --- or Value at Risk.

As I said even before the 2007 course blog: "There is much wrong with the way VaR is used and calculated --- even in the most enlightened firms. Some implementations are close to (1) a hoax or (2) at least naively self-delusional. "

Still, VAR used almost universally. Moreover, the vast majority of implementers are sincere they have done their best.

The people I hold responsible for the destruction caused by VAR are those who said, "Everyone else has good Value at Risk measures. Either you guys come up with a system that works, or I'll get someone who can." In such an organizational situation, you are guaranteed to get bogus analyses --- all of which will agree very comfortably agree with all the other delusional models. This is sad, but very human --- the mechanism of social proof is as universal as any phenomenon one can imagine.

Again, humbly quoting myself from the 2007 blog, "If one could simply bet against run-of-the-mill VaR estimates, one would not need to look for other investments. This would be ... a veritable paradise of Black Swans, vastly more lucrative than those (too rare) Black Swans that stingy options traders occasionally provide."

Why, Oh Why, Is this So?

There are two virtually insurmountable problems with VaR as it is calculated in most firms. These are the "Peso Problem" and the "everything is correlated at the extremes problem. " There is also a less overtly dangerous but still unavoidable problem I call "Tukey's Biased Estimate of Variance."

The "Peso Problem" is a standard part of economic lore ---- but it is steadfastly ignored by essentially ALL VaR models.

The "correlation problem" has also been widely understood for a long time. It was one of the forces that led to the demise of LTCM. It was one of the forces in the Niederhoffer's first blow up after the Asian Crisis of 1994. My favorite example actually goes back to the great flood of 1927, and I'll tell that story in class.

Still, the" correlation problem" is ignored in 99.9% of VaR models.

Finally, how about Tukey's Estimate? I'll elaborate in class, but --- it's ignored. Why? Because it would force everyone to bring down their leverage. Well, in October 2008, we have the strong sense that bringing down the leverage would have been smart for every bank that did. Sad, but true.

John Tukey understood all of this, even before the ideas came into play in a financial context.

With a barrel-chested sotto voce rumble, he would say, "The variability that you have seen is always an under estimate of the true variability." In our context, where volatility and variability are cognates, Tukey is on one side, and the world's VaR models are on the other.

My money is on Tukey.

Still, many firms are getting better at VaR, and we just need to have evolution play its role. Though many individuals in many firms will kick and scream, the big firms with the best VaR models (and other risk controls) will be survivors. As the "subprime" story plays itself out, we are likely to find that many firms had VaR estimates that were pure garbage. It seems inevitable that some measure like VaR will always be with us --- and it seems that sometime again in the future it will greatly fail us.

Extreme Value Distributions --- Use at Extreme Risk

On the more technical side, we'll look at extreme value theory, which is one of the tools that theoreticians always seem to want to trot out when there is a discussion of big market moves. The mathematics of the extreme value distributions is interesting, but for several reasons extreme value theory doesn't deal with the reality of extreme market moves.

We'll discuss the Gumbel (or Fisher-Tippet) distribution in class. It comes out of a beautiful limit theorem, and it is the leading example of what are know as extreme value distributions. Sadly --- and in stark contrast to the Central Limit Theorems --- there is a major disconnect with any level of honest practice.

You will see from a homework problem that the convergence is excruciatingly slow even in the ideal case of normally distributed random variables. There are people who have advocated the use of this distribution in financial practice. It has even been used as part of the Tokyo building code. These applications are bogus, bogus, bogus.

Still, extreme value distributions are worth learning about. There probably are special contexts where they are applicable, and they have a undeniable charm. Also, they are part of the common language, and any time "extreme" events are discussed, they are likely to be drawn into the conversation. When this happens, be prepared to be skeptical.

As a sidebar, this also give us a chance to discuss the some core ideas of simulation, including the rejection method and the inverse probability transform method.

Risk-Adjusted Returns

FInally, we will look at some suggestions that have been made for comparing returns on a risk-adjusted basis. These are useful --- certainly better than simple raw returns --- but they still can lull us into forgetting the peso problem. The Wiki piece on the Sharpe Ratio gives the basic definition, though it is a little short on motivation. The piece also has links to a bunch of related ratios, some of which were new to me. Almost all of the final projects will need to deal with risk-adjusted returns in one way or another. At some point in life, everyone should read Bill Sharpe's Original Article.

Finally, here is a somewhat dated table of Sharpe Ratios from our friends at Merrill Lynch. This should be considered in light of the Bloomberg piece on their write-downs in Oct 2007 (i.e. ONE YEAR AGO)..

Sharpe Ratio Table

Sidebar: Related Material

You might want to look at the exposition of Taleb and Pilpel. It makes similar points to those made above, though I naturally prefer my own path. I'll collect further related material as time goes by, but I don't want every one to be depressed ---- just realistic.

Sidebar: RiskMetrics

RiskMetrics is a consulting firm that spun off from Deutsche Bank and which had its origins in VaR calculations, including daily estimated variance-covariance matrices of a large set of assets. This was in the early 90s. Once upon a time, they also provided teaching materials for VaR, but these have gone away (one only has the Cashed Index) .

RiskMetrics has had to do a considerable amount of self-reinvention to stay viable --- and VaR does not now seem to be a major part of their current product line. A previous Stat 434 page may have contributed to some changes at the RiskMetrics site.

Sidebar: Hyman Minsky as Channeled by George Cooper

Hyman Minsky

There is a recent book by George Cooper with the charming title The Origins of Financial Crises: Central Banks, Credit Bubbles, and the Efficient Market Fallacy. In a way it is an up-to-date and well written elaboration of a train of thought begun my Hyman Minsky, pictured above. I'll pass along any tidbits ... in the meanwhile you might look at the book review at FinFacts Ireland, where I pinched the Minsky pic.

Sidebar: Wal-Mart Sales of Safes Spike in Crisis Week

The CEO of Wal-Mart gets to see secrets of human behavior that most can never see. In a CNBC interview on 10/22/2008 Lee Scott observed that his store have seen a "run on safes" during the weeks of the October financial crisis.

Sidebar: Structured by Cows

From a report on CNBC: instant message exchange between two unidentified Standard & Poor's officials about a mortgage-backed security deal on 4/5/2007:

Official #1: Btw (by the way) that deal is ridiculous.

Official #2: I know right ...model def (definitely) does not capture half the risk.

Official #1: We should not be rating it.

Official #2: We rate every deal. It could be structured by cows and we would rate it.

News FASH: HW6 and Our Own Market Fatigue

Please prepare HW6 for Monday Oct 27 (not Oct 20 as originally scheduled).

The early appearance of the fall break, together with market fatigue, created a bump in the schedule that I did not properly anticipate. We need to cover some things before it makes sense to tackle HW6.

Still, taking a little break is not so bad, and perhaps it even helps out with your other midterms, etc.

Day 13: Stationarity and Unit Root Tests

For 22th October 2008

We've already discussed stationarity to a considerable extent. We didn't have any choice.

Stationarity is the assumption that gives us a link to the past. Without stationarity, we have (almost) no way to learn from what has gone before. It is natural then that economists and others would hunger for ways to test for stationarity.

We know from the "cycle construction" that this is impossible in general, but how about in the specific? For example, one may be willing just to test for stationarity while assuming an ARMA structure. An ARMA model may be stationary or non-stationary, so there is indeed something to do even in this confined context.

The fist and most famous of such domain-limited test is the Dicky-Fuller Test (1979).

DF is in essence a "t-test" but the corresponding tables for p-values just happens not to be the famous t-table. The relevant distribution theory actually depends on Stochastic Calculus, and we may chat about this if there is time. As a practical matter, one just uses S-Plus to find the relevant p-values.

The Unit Root code fragments explore the augmented Dickey-Fuller tests and comment on some examples described in Zivot and Wang. In the example for log-exchange rates and for stock prices we fail to reject the null hypothesis that there is a unit root. For stock prices this is certainly no surprise, but for exchange rates it may not have been expected. Such economic ideas as purchase price parity might have pointed toward stationarity.

Still, for PPP to come into play, one needs to deal with the separate inflations in the two countries. As the example of Brazil shows, one can have something close to PPP yet have exchange rates that are flamboyantly non-stationary. In general, emerging market exchange rates can be much more violent than one might imagine a priori, and one week moves of 5 to 10 percent are not uncommon. This plays havoc in the short term with emerging market asset returns, but "washes out in the long run" --- if we believe in that sort of thing.

More Caveat than Usual

As much as one wants to test for non-stationarity, our technology is not particularly compelling. I expand on this in a little"cultural" piece on unit root test.

Sidebar: Algorithms for the ARMA(1,1)

The ARMA(1,1) model cannot be fit by classical regressions because we don't observe the errors explicitly. One way around this problem is to use an iterative algorithm that uses successively smarter residuals to stand in for the errors. This is not the algorithm that is used in S-Plus, but it captures some of the features of the algorithm that S-Plus does use. We'll discuss the algorithm briefly.

Sidebar: Really Remarkable Commodity Prices

In class I commented on the chart below, and I made what I see in retrospect as a interesting --- but stupid--- mistake. I looked at the corn chart and said: "Golly, it's like a 95% loss from the top." This was dead wrong. Do you see why?

commodity prices

In real time, classmate Quishi Mao saw the fallacy of my statement. This chart is one of "percentage changes" so at the top the price of corn had gone from x to about 2x while at the bottom it was a bit more than x. Thus, the loss from the top price of corn was only 50%. Still, serious, but less so than the emotional message of the graph would seem to evoke.

Sidebar: Typical Yahoo! Error

If you look at MO (Altria) at Yahoo! you see that the P/E ratio is 4.97, which looks amazing for a company that has very predictable earnings (and decreasing litigation risk). Naturally it is too good. The folks at Yahoo! are not capable of providing software that deals with significant spin-offs, like that of Phillip Morris International (PM) from MO. It's easy to get a great P/E if you use one company's P and two companies Es.

Sidebar: NY Times Sector/Company Comparison Graphics

The NY TIme has an elegant way of presenting relative performance --- and doing dynamic incorporation of time.

Sidebar: VIX hits new record --- 82+

A year ago you would have heard vociferous arguments that this level of the VIX is simply impossible. Well, evidently it is not. Now folks will not even doubt that it could blow through 100, where it really starts to violate my sense of what I mean by implied volatility.

Sidebar: Structured Finance --- More Future than History

I mentioned in class a passage from Mohamed El-Erian's recent book “When Markets Collide." El-Erian is the co-CEO of PIMCO and former manager of the Harvard Management Company, i.e. Harvard Endowment. In his book he shared the advice he would give to his college-aged daughter about the most promising area for learning and a great career. The quote is on page 147, and I encourage you to read the whole argument --- even the whole book.

Incidentally, if you dig down into the Harvard link you will find a publicity blurb for their statistics department --- cool move brothers!

Day 12: Martingales, Probabilities, and EMH

For 15th October 2008

We will discuss the every useful notion of a martingale. Martingales were originally introduced to provide models for fair games, but they have evolved to become what many people regard as the most important notion in all of probability theory. The plan will only require a few intuitive observations about martingales before coming up with some wonderfully concrete results, such as the famous formula for the probability of ruin (i.e. losing all you money).

Martingales help on think a bit more precisely about the EMH or the ways one might measure the extent to which a money manager may have significantly out-performed the market --- or not.

Sidebar: The "Dropped Coverage" Tell

Here is a non-equilibrium speculation. It seems likely that the anointed nine banks will make subsequent purchases of lesser banks. After all, the new model says, "You must have a depositor base." Now, if the new Goldman Sachs bank wants to buy ABC bank, and if ABC bank is covered by a GS analyst, then you run into an awkward spot. So, perhaps we should set a Google alert for "dropped coverage." This would be something that probably would have to be done before any take-over. Caveat: We are in a time where the number of employed analysts is decreasing, so some coverage will be dropped just as a product of down-sizing.

News Flash : Bank of Sweden Prize

If you can't say something nice, it's best to say noting at all, so I have no comment about the 2008 Bank of Sweden Prize in Honor of Alfred Nobel.

On the other hand, the winners of the 2007 prize --- Leonid Hurwicz (University of Minnesota), Eric S. Maskin ( Institute for Advanced Study, Princeton), and Roger B. Myerson (University of Chicago) --- well, these are folks one can celebrate. The scientific background paper for the prize announcement should be interesting reading for many of the students in 434, especially those who know a bit about game theory or Bayesian models.

The models are too far afield for us to discuss in class, but, needless to say, expected utility is a huge diver of the work --- even though, in the Bayesian context it has a mildly Quixotic taint.

Sancho and his liege the knight errant Don Quixote may have the same utility for slaying a dragon but they can have different expected utilities --- based on different prior beliefs about the thing they see either being a real dragon or or simply being a windmill, as to most of us it would appear to be.

Going back to economics, understanding the potential for ambiguity in expected utilities is a good thing to understand. It may even suggest why some markets flourish and other dry up. In fact, this is a big part of the story told by the new Nobel Laureates.

Wisecrack du Jour:

"There is only one end of the world, and this is not it." --- Anonymous, but someone deserves credit.

No, this is not Armageddon --- at least if you are healthy and young. Still, it's no picnic, and the current market rout is as ugly as the ugliest. The New York Times (10/12/08) interactive graphic gives the full perspective.

"What is good for General Motors is good for America." --- Charlie Wilson, Chairman and CEO of GM speaking in 1955. On Friday the 10th, the market cap of GM fell below 2.5B --- about the size of a middling mid-cap. GM no longer calls the punches for the US economy and for this we can be thankful. GM has trailed its competitors for decades, and, one way or another, it will bite the dust.

Sidebar: The 200 Day MA of the SPY

Go over to bigcharts and take a look at the SPY along with its 200 day MA, the most classic of all technical tools. The strategy of being long the market only when it is above its 200 day MA has long been known to have historically out-performed pure buy-and-hold.

Nevertheless, this achievement is not given very much credit because most of the juice came from just one special period.It turns out that the special period came to be called the great depression.

Sidebar: Confidence --- of Consumers and of Others

Incidentally, the Wiki article on the great depression observes that concerning the causes of the great depression, "The only consensus viewpoint is that there was a large-scale lack of confidence."

bank run

The good news is that we now have structures in place (like the FDIC) that should keep consumer confidence from hitting the tank, as in the picture above of the run on the American Union Bank. We also have unemployment insurance, which keeps people consuming even if they suffer a job dislocation. The bad news is that we have also have a spaghetti bowl of linked derivatives that make everyone quite uncertain --- even about traditionally secure institutions, such as the Hartford and MetLife insurance companies.

There is an index of consumer confidence that is of high scientific quality, but it comes out only monthly, so it is always yesterdays news from the view of the financial markets. Gallop does its own consumer confidence poll. It comes out approximately every two days.

Incidentally, another recent survey suggests that young adults (19-29) are more pessimistic about the economy than other age groups. They aren't necessarily pessimistic about their own prospects, but they do think things were much rosier in the 1990's.

Sidebar: ProShares and Volatility Drag

ProShares (and its competitors) are designed to provide the holder with two times the daily returns on the benchmark asset. Because of volatility drag (the famous "mu minus half sigma squared" formula), such an instrument is guaranteed to provide less than the twice the return of the underlying over any longer period of time.

Sidebar: XOM and USO

While at bigcharts, take a look at the relationship between the price of oil and the price of Exxon-Mobil. To me, the three year chart for XOM and USO (the oil commodity ETF) is at least a little mysterious. When you compare XTO and USO, there is a more intuitive relationship.

Sidebar: Oct 10, 2008 VIX hits 70 and Dow Interday Swing is 1000+

What can you say? This is unprecedented. The thermometer may not be "broken" but the logic behind the thermometer is severely torqued. With sigma at 70, a minus 1.5 simga event means you could snap up the total market with just your lunch money.

If you must search for a silver lining, have a line from a recent Schwab report: "Following each move above 40 since 1990, the S&P 500 had consistently positive returns one month (8.7% average) and one quarter (11.3% average) later, although the performance was mixed in the very short term."

A Cramerian Bon Mot:

"It may be time to rent some stocks." --- MM on 10/10/2008 the last day of the worst week ever.

By the way, if even Bill Gross admits that he watches Cramer, then there is no reason for you (or me) to be embarrassed about watching. It's surely no worse than Lavern and Shirley --- though not as good as the Simpsons.

Well, OK, perhaps we should be a little embarrassed. That being said, have you ever played with the sound board?

Sidebar: Historical vs Implied Volatility (Oct '07)

Here is a plot of annualized realized volatility based on thirty day trailing data and the annualized implied volatility "based" on the 30-day at-the-money options. These track better than I thought they would. The WSJ source comments: "We're running a big fever --- the thermometer is not broken."

Historicall vs Implied Volatility

If we consider for a moment the art of honest graphics, one should note that this graph may suffer from what I call the "histogram cheat." Classically, this is the ruse where you overlay a density and an empirical histogram and observe that "it looks pretty good." For example, this device was trotted out in the Ljung-Box paper. An experienced analyst knows that such superpositions play tricks on our eyes.

In general it is much better to look at the spreads (i.e. the difference in the two curves) or at the multiplicative analog of spreads --- the ratio of the two curves. When put under such a microscope, you start to see that even this "surprisingly good fit" is actually pretty bad.

Day 11: Betting on an AR(1) and Introducing the EMH

For 8th October 2008

The first item on the plan is to develop the conditional Kelly Best sizing formula for the AR(1) model. We'll then do a Fermi calculation to gain some intuition about this formula.

The next item is to take a long look at Homework 5, where at last things start to get serious. This is a homework where you get to exercise some honest personal judgment. There are lots of choices to be made, and you get to make almost all of them. We have no class on Monday October 13 (due to Fall break) so Homework No. 5 will be due on Wednesday October 15. This gives you a big chunk of time to devote to the HW, if you are not otherwise occupied.

If you attempt the optional part of the assignment, you really do need to keep you eye on the "Fermi-type" reasoning. The general algebra may be "optimal" in some sense, but you will find that a back-of-the-envelope calculation will provide all the honest guidance that you need. This is especially useful --- for interviews, or if the algebra never "converges."

The second part of the agenda is to open the conversation about the Efficient Market Hypothesis (EMH). Everyone seems to know what this is all about until someone says --- "great, lets write this out as mathematics."

At that point almost everyone starts to become uneasy. The fact is that that there are some hard --- and debatable --- decisions must be made. Our first step will be to round up the "usual suspect." We'll then see what comes out in the wash. Incidentally, I have collected some sources on the EMH that may be useful to you, and you will surely have loads of material from your other courses.

One paper in this collection is Andy Lo's paper on the Adaptive Market Hypothesis. This paper gives a nice introduction to the EMH, the notion of informationally efficient markets, Samuelson's model, and a good many other things. To complement our discussion of utility, we'll look at his presentation of the Kahneman and Tversky (1979) example of risk seeking behavior and the break down of utility theory.

The resource pool on the EMH (and the now antique RWH) is virtually unbounded, but it is far from uniform. This is one case where the Wiki article is TOO LAME TO FIX; somebody will need to start it from scratch, and that is not usually how a good wiki piece evolves.

Finally, whenever we have a free moment, we should discuss the Nuveen Funds. These make interesting series for analysis, even though some of the time series are short (i.e. less than three years). These are not formally dominated assets, but they are pretty bad.

Please don't forget the previous note about the final project due dates.

Incidentally, if you want to prepare for an interview with Google or with a quantitative group on Wall Street, you might work through one of the collections of Fermi Problems. Moreover, if you are a SETI sort of person, you will be well amused by consideration of the Fermi Paradox .

Sidebar: Coaching on Writing

Many of you will end up being compensated to a large degree for (1) your personal presentations and (2) your written presentations. Thus, your future net worth depends to an amazing extent on your ability to maximize the effectiveness of both of these forms of presentation.

Here is a very big hint that works in both of these situations: You should assume that the person you are speaking to someone knows almost everything that you do. This means that you can --- and almost always should --- "jump to the chase. " Trust that your listener or reader can follow you, and trust that there is a ready listening for what you have to say that goes beyond the normal. ( Naturally there will be times when it is right to assume that your listener,or reader, is not quite up-to-speed. In such a case, you'll need to supply the missing background, or motivation, in a way that is efficient but not condescending.

Focus as much as you possibly can on what you have that is new, special, or out of the ordinary. When you write for a general audience of the craft is to make sure (without insulting the audience) that the" ordinary" is indeed collectively assumed.

In most cases (say in our class), this is not a problem.

Sidebar: October 2008 --- The VIX Goes Parabolic

VIX Oct 4

If you just gave me this chart without telling me that it was a chart of the VIX, I would not have a strong view about it being stationary or not. If force to make a call, I might even say it was non-stationary. On the other hand, if you tell me that is is the VIX (it is!), then I would say, "It is stationary!"

Is this science, or is it madness? I think it is science, though some allowance for madness seems prudent. The reason I think it is science is that we are right to have strong a priori beliefs about a good many economic phenomena. To believe that the VIX has gone non-stationary puts the options market into a scenario that I can't bring myself to accept. Naturally, we have to consider the possibility that I am just living in denial.

Sidebar: VIX as a Forecasting Tool

As we ponder the current state of the VIX, it seems like a good time to look at an amusing December 2006 paper from Credit Suisse on the use of the VIX as a forecasting tool for market returns. The two graphs on page two are both well conceived. Figure 3 is of the bread-and-butter kind that anyone would produce, though the authors have been smarter about the scale than many are. Figure 2 is more unusual, and I think it speaks quite usefully to a question that you are bound to ask yourself sooner or later. If you think about it, you'll see that a huge amount of computation that went into this one figure.

Over all, this paper does a good job of suggesting the kinds of analyses and the kinds of graphics that contribute to a good final project. As far as style is concerned, the paper is of the chatty, retail, sell-side kind that I encourage you to resist as much as you can. In 434, we favor the cut-to-the-chase style of internal by-side memoranda.

Sidebar:What are you going to believe, and why?

By the early 1990's, a mountain of observational studies supported the claim that beta carotene (stuff found in carrots and such) provides substantial protection against a wide range of cancers. When the results of one large clinical trial became available in 1996, the observational studies were set aside as perplexing curiosities, and the medical community embraced the view that supplements of beta carotene do not reduce cancer risks --- and may even increase them. When it comes to medicine, the randomized clinical trial is the gold standard.

Take a moment to read a brief NYTs article that reviews this history and then ask yourself what the message may be for students of financial markets.

Day 10: What to Do When Facing A Favorable Bet

For 6th October 2008

Naturally, we want to discuss the Homework 3 (being returned) and Homework 4 (coming in today).

The Plan for Day 10 then has us review the Law of Large Numbers, and apply it to the attractive but controversial notion of long-term growth rate of wealth. This rate will then lead us to the famous Kelly criterion for bet sizing. We will develop this in some detail.

For some richer context for the Kelly Criterion, you might want to browse my brief page of Kelly related links. I will add more to this page as time goes on, so you may want to revisit it when you start to think about your final projects.

Finally, we will see how the Kelly criterion relates to a classical paradox of utility theory, the famous St. Petersburg Paradox. As our discussion is unfortunately brief, you might want to look at comments on the Paradox by Shapley and by Aumann.

Shapely argues that it need not be the failure of risk neutrality that causes us to offer so little for the St. Petersburg gamble. Shapely says it can all be explained by counter party risk. This makes a lot of sense to us now considering, for example, how Ambac and MBIA looks like feeble backing for bond insurance.

Aumann argues that any unbounded utility function exposes one to paradox; for Aumann, utility must be bounded to make sense. These papers are brief, lucid, and written by central figures of modern economic thought. Where better could you spend a few minutes of your day?

Sidebar: Draft of The "Senate Bill"

Spend a harmless hour (or so) looking over the 451 page draft of the Senate "Emergency Economic Stabilization Act of 2008. " This Pork Barrel passed on Friday, so let's just hope the magic works. For entertainment, you might look at Section 503 (page 300, bottom). It's a real knee-slapper.

Sidebar: Coal Prices

The EIA has a site that tracks coal prices. Coal prices, like other commodity prices, may seem like they should be decently predictable. After all, both supply and demand are indeed decently predictable. Nevertheless, markets being markets, profitable prediction is no piece of cake. Hold that thought for a minute and take a moment to learn a bit about coal prices.

It's really amazing (to me!) how greatly the different types of coal diverge in prices as one varies BTU content and SO2 content. Just look at the spread on Illinois vs Powder River Basin prices! Finally, contemplate the observation that coal prices have been pretty stable, but coal stocks have taken a 50% nose dive.

By the old "it's all about expectations" mantra, this may be reasonable --- but maybe it is not!

Addendum: A 434 Alumnus points out that US supplies (as reported by EIA) are relatively stable, but there have been supply shocks to international supply due to new production coming on-line in Australia. He also notes that PRB coal is not exported and used almost exclusively for electricity production.

Sidebar: Quotes with an Economic Spin

I keep a web page of the quotes that amuse me. Since most of my reading is about contemporary economics, statistics, and finance, so are most of the quotes. You might take a look at these from time to time, just for the fun of it. Heck, they may even be educational.

Sidebar: When are the FINAL PROJECTS due?

Your final projects are due on Wednesday December 12 at HIGH NOON. Naturally, you can hand the project in earlier if you like. This date was determined by the 2008 University Schedule for Final Exams. Please note: This is a scant one week after the last day of class, so you really want to have a firm grip on your full project by the time of your "project proposals" on in the last week of class. Most of your proposals will be fine, but some people will need a "mid-course correction" and this is not so easy with just one week.

You will need to submit two copies of your project: One electronic copy is to be sent to me by email and one hard copy is my mail box in Suite 400 of JMHH. If the mail box seems insecure to you, you can slip your paper under my door (447 JMHH).

Pease see the policies page for information about the penalty for late projects, etc. This is very important.

Sidebar: Partner Issues?

Some people have had partners drop the course or otherwise go AWOL. If you are missing a partner, or want to explore a change, I suggest that you stay a little while after class today to meet like-minded others.

Day 9: ARIMA(p,d,q): Differencing, Estimating, Simulating

Posted for 1st October 2008

Our first step is to consider "differencing" as a tool for getting stationary time series from a non-stationary time series. This is a simple but useful trick. Also, when we look at continuous returns we are basically looking at the difference sequence of log price. This is one reason it is often (but not always) safe enough for us to assume stationarity of a return series. Price series themselves (or even log price series) are rarely stationary.

The main part of the plan is to go over the S-Plus tools for fitting ARIMA models and for Simulating ARIMA models. Important for us will be the use of arima.sim for simulating ARIMA series and arima.mle for fitting ARIMA series. Naturally, we'll also discuss the new homework HW4 as well as whatever else shows up.

Wisecrack du Jour

"I like two positions: Cash and the Fetal position." --- Jeff Macke, Fast Money, CNBC, (9/29/08)

Gray Monday, Sept. 29, 2008: Dow Drops 777 Points

Congress rejected the Economic Recovery Act and the markets responded with disappointment. The much-watched Dow-Jones Industrial Average was off "only" 6.98% while the Standard and Poors 500 Index dropped 8.81%. You might wonder which number best reflects economic reality. The answer is simple: the Dow is an out-dated, deeply flawed, index.

The Gray Wednesday of 2008 took place in a much different environment than the Black Tuesday of 1929 which rang the bell on what became the Great Depression. There a lots of reasons why "it is different this time." In response, one wag observed, "Yeah, Lehman Brothers survived the Crash of 1929."

A more reassuring difference is that the world's central banks are much more well-informed. Unfortunately, legislators don't seem to have made much intellectual progress. Another difference is that Gray Wednesday took place in the context of a reasonably priced equity market, thought perhaps not a cheap one when the 5% current inflation rate is considered. What is really different is that this is a credit (and credit derivative) driven sell-off.

The VIX has hit 48, which is not a record, but it is close. The bottom line is that --- up or down --- you can expect big time volatility.

Sidebar: Inflation and Stock Market Returns

I'm sure that many of you have a copy of Jeremy Siegel's Stocks for the Long Run. In the third edition (p. 196) there is an interesting chart that relates inflation and the real compound annual return on stocks. He takes the inflation rates, bins the years into five bins, and on the y-axis plots the average of the real returns for the years that fall into this bin. It's an instructive analysis, but relevant to our earlier discussion on graphics, I would much prefer to look at the plain vanilla scatter plot, perhaps with the points coded for decade.

Siegel's graph makes the clear inference that inflation over 4.4% is bad news for equity returns. The scatter plot is likely to be both less clear and more informative.

Sidebar: Listed Assets with Near Zero Beta

If you search for single assets that have near zero beta, you turn up some very odd birds. One that I find interesting is WESCO. It trades very thinly --- which is explained in part by being 80% owned by Berkshire Hathaway. WESCO is run by Charlie Munger, Warren Buffett's long-time sidekick. Munger is a great story teller and much can learned from the tales that he has told.

Sidebar: More Data or More Bayes?

What is the best way to think about what may be the likely returns to a long term holder of stocks? One model is to look back over all of the available data (say to 1880 in the US, or farther back in the UK) and look at the mean and variance as if annual returns were IID? Is this smart? Can one do better? Why do we believe what we believe? This is a huge discussion and it may lead nowhere, but it really is one of the issues that perplexes me most. It also relates nicely to many other discussions.

Cultural Sidebar: Lynch? But Not Peter or Merrill

Just to distract us from the agony of day-to-day developments, we'll take a moment to look at a statistical time series that is fortunately remote from us --- both in time and culture.. The series in question deals with a sad part of American history --- lynchings in the Southern States from the period of reconstruction (1870's and 1880's) until the depression (1930's). The key figure in the article has suggested to some that there was a relationship between cotton prices and the number of lynchings.

These series set some traps. It would be easy--- and wrong --- to trot out an analysis that ignores: (1) spurious regression in time series (a topic we take up later) (2) the notion of cointegration --- or the lack thereof (another future topic) or (3) the probably poor quality of the data --- not of cotton prices, but surely of lynchings --- the reported number of which were under the political control of the states.

Even given the scholarly source of the data, I view it as quite possible that the recorded number of lynchings could easily be off by a factor of two (especially on the low side) in any --- or even most --- of the given years. Lastly, the use of annual data makes the series very short. Given the humble efficiency of our methods, they are certainly too short for one to address honestly the issue of co-integration. Oddly enough, the whole puzzle does echo an interesting issue in behavioral finance --- namely the constant stalking horse of confirmation bias.

Day 8: MA(q) and ARMA(p,q)

Posted for the 29th September 2008

Our first task will be to survey your discoveries from HW3. If all goes as as usual, we will find that --- except in the luckiest of circumstances --- the daily returns for common stocks are not normally distributed. This is the first of the so-called stylized facts that we will discover about asset returns.

The non-normality of returns is often ignored by practitioners --- sometimes mindfully and often times thoughtlessly. We'll try to remain mindful of the non-normality of returns, but on many occasions we'll have to join the thoughtless herd and assume normality --- even when we know it is false.

How do we live with this situation? Well, first we admit that it is a goofy thing to do and then we just keep looking back over our shoulder to see if something has really gone haywire.

The rest of the plan focuses on the theoretical features of the general ARMA(p,,q) models, including the issues of general issues of stationarity, invertability, and identifiablity.

Sidebar: Test or No Test for Stationarity

One theoretical point (that we may or may not cover) is the construction of a stationary process that essentially proves the impossibility of testing for stationarity in the broad sense in which we have defined it. We will later discuss tests for stationarity in more narrow senses, and it will be up to you as a modeler to decide which description best reflects your world.

Sidebar: Tests vs QQ Plots

When we use a QQ plot to compare a sample with a theoretical distribution, we see the FULL TRUTH in our data, and when we us a test (like the JB test for normality) we really apply a microscope to some specific features of our data (e.g. skewness and kurtosis in the case of the JB test).

It is natural that the full truth is harder to "understand" than the partial truth of a p-value.

Also, throughout statistics, longer tailed distributions are more troublesome than distributions with normal-like tails. This inevitably shows up when we try to compare asset returns with t-distributions of various degrees of freedom. We can tell easily enough that a t-distribution is more appropriate than a normal distribution, but by the time we try to decide which t-distribution is "best" we may start to face more or the truth than is personally comfortable.

Sidebar: Phase Transition and a Vote for Momentum

There is a think piece from PIMCO that uses some metaphors from physics in the context of financial markets. Normally I dislike such metaphorizing --- but normally I do like the PIMCO pieces (especially those by Bill Gross and those by Mohamed El-Erian). One take-away from this article is that after passing through a "phase transition" the likelihood of momentum starts to exceed the likelihood of mean reversion. There do seem to be some historical examples to support that point of view, so it is worth contemplating, even if a satisfactory statistical confirmation is unlikely.

Sidebar: Ergodic? "I don't need no stinkin '' ergodic ... "

You might want to take a look at an amusing popular essay about ergodicity. It is fundamentally correct, but I can't honestly say what one would infer from the article, if one did not already know the formal meaning of ergodic. Still, it is consistent with our definition and it possibly adds some intuition.

There are several layers to this puzzle. John von Neumann once said: "We don't understand mathematics, we just get used to it." Well, the notion of "ergodic" is somewhat the same. We can master the definition, but mastery of the real notion just takes lots of "getting used to."

Incidentally, John von Neumann also had a role in the use of the word "entropy" in information theory. Claude Shannon asked him if he though the use of the term was appropriate, and von Neumann said "Go ahead and use it. Nobody knows what entropy means anyway."

Well, about von Neumann --- John Wheeler once said, "There are two kinds of people. Johnny and the rest of us."

Finally, the definition of ergodic in Z&W is not 100% up to snuff. Their definition and ours will coincide for Gaussian processes, but even our first brush with real asset data tells us that in our business we can't expect to see too many of those.

Sidebar: Too Much Company Stock in Employee 401(k)'s

The WSJ catches up on a point made in class last week: It's pretty stupid to hold your company's stock in your 401(k). If you get it at a discount, take it (maybe) but when you can trade out of the discounted stock --- do it! Just by working for a company you already have much more than a market weight in the company, to pour in more money rarely makes much sense. You should probably even underweight your company's industry.

The only exception I can imagine to this "rule" would be for C-Level executives who need to "fly the flag." These executives should look into the possibility of hedging the positions that they are essentially "forced to hold." Giving the "Caesar's wife" constraints such executives face, this may not be easy.

Day 7: The Full AR(p) model --- Features and Choices

Posted for 24th September 2008

The main part of the plan is to introduce the general AR(p) model. We'll discuss the historical contribution of Yule, his equations, and the ability to pick up periodic behavior, such as the 11 year cycle one finds in the famous sunspot data.

One issue of clear practical importance is that of choosing choosing an appropriate value of p. In general, this is a problem in what is called "model selection." We'll look at one natural approach based the so-called "partial autocorrelation function."

We'll also open an important conversation about "parsimony" in models. Is this a miracle, credo, or a practical and well-founded heuristic?

We'll also do some mathematics --- in part because it is honestly important for understanding the AR(p) model and in part because I want to remind everyone that --- however powerful simulation may be, it one needs lots of analytical insight to know what to simulate.

After warming up the old partial fractions, we'll find a useful criterion for stationarity in an AR(p) model. In theory this will be nice and explicit, but when turned back to practice we'll see that it is at least a bit schizophrenic.

Side Bar: Preferred Stocks and Volatility

Given the deal that was announced today involving Warren Buffett's purchase of 5 Billion dollars worth of Goldman Sachs preferred stock, it seems like a good time to look at what time series differences one might expect between the common stock and preferred stock returns. Historically, preferred shares have had very small volatilities in comparison with the common shares, but under current market conditions the preferreds are every bit as volatile as the common.

Day 6: Data Confronts the "Normality Assumption"

Posted for 22th September 2008

An important part of the plan is to go over the piece on using WRDS which also covers the importation of WRDS data into S-plus. We'll also discuss HW1 (going back), HW2 (coming in), and perhaps go over the newly assigned HW3.

Scheduling Note: It is a tradition in 434 to treat attendance the day before Thanksgiving as optional. I do hope and expect that some people will be around. We will have class, but those who are eager to get to Grand Ma's house can scuttle off without worrying about missing anything essential.

Sidebar: Pondering the Mysterious Role of Assumption in Models

We'll often simply assume that a series is stationary, though of course we won't be silly about this.

Most price series are clearly non-stationary, and there are even return series that we can't call stationary with a straight face. Nevertheless, except for isolated (but important!) periods, many (but not all) asset return series have behaved in a way that stationary enough for us to courageously push ahead and "assume" stationarity.

Later we will discuss some "tests of stationarity" but to tell the truth, these test are so limited in their power and applicability that they do not fully deserve the name. They are more technically known as "unit root tests" and they help one to discover when a random process "looks" like a random walk --- a vigorously non-stationary process.

The issue of Normality

Normality of the log-price change and independence of log-price changes are assumed in the development of the Black-Scholes model, a model --- and subsequent theory --- that is of rhapsodic beauty.

It is even a useful theory --- when carefully applied.

Still, as we experiment together, we will find that there is seldom much empirical encouragement for us to assume normality of returns (or differences of log-Price).

We'll start addressing the normality part of this set-up with help from the Jarque-Bera and Shapiro–Wilk tests of normality. For a purely seat-of-the-pants practical approach, one still does well by eyeballing the qqplots.

While we are at it, I should underscore that It is important that everyone in the class start sharpening their understanding of the theoretical side of our work --- even as we keep marching along with the practical side. It really is nonsense to suggest that one has a "practical" understanding without a "theoretical" understanding. We'll see lots of examples of the foolishness that can result when one loses track of what he is talking about.

In particular, make sure that your definitions are rock-solid.

For example, write down the definition of independence of two random variables.

Hint: if you use the word "correlation" you have a big gap in your knowledge. What is required is a very simple formula --- nothing else is genuinely true or complete. To be concrete, anything else is simply wrong. It may have mitigating virtues, but it is still wrong.

My concern is this --- if your understanding of the fundamental notion of "independence" is shaky, then the more subtle notion of "martingale" which we well use shortly must be incomprehensible. Without understanding the ideal of a martingale one is almost barred from a fully sensible adult conversation about market efficiency, gambling systems, and lots of other great stuff.

Suffice it to say ---- understand the definition of independence as deeply as you can.

Sidebar: JB in the Wiki --- Some Instructive "Slips"

If you are logically fastidious there are some irksome errors in the Wikipedia description of the JB test. These offer us a useful opportunity to illustrate some important distinctions. Everyone will understand them --- and afterwards they will be part of a small club that does understand them. It's worth the price of admission. Basically, this is the club where "you know when and where you need a hat."

Incidentally the Wikipedia article on Shapiro-Wilk is valid, though it is a too obscure to be directly useful to us. Nevertheless, there is an intuitive description of the SW test that we will discuss in class.

JFF Sidebar: Which Bill has the Shortest Life Time?

Or, how much currency is in circulation? Is most of this in the US or outside the US? All of these, must-know trivia questions are answered by the US Treasury.

Weekend Questions Regarding HW2.

Posted 20th September 2008

I've had a flurry of emails asking "this and that" about HW2.

The bottom line is that you should try a few k's and try a few T's and look as thoughtfully at what you get. There is no reason to be super fancy. Just try to be logical and --- as far as possible --- methodical. All of our exercises will call for you to make decisions about certain details. You should just go ahead and make the decision. If the decision is an important one, you should mention this in your write up and explain the reasons for your choice.

Naturally, if you what to go beyond the basics, I encourage you to do so. Even if you want to try something super fancy, by all means go ahead and do it. You have my permission from here until the end of time.

In general, when you have a homework in 434, think of it as being like a project for a manager of a quant group. You always want to do what has been requested, and then if you have time and energy go ahead and engage the other possibilities that occur to you. We will always go over the assignment in class, and it it great to have people who have done different things.

Addendum: On Monday we'll learn a bit more about the Graphics tools in S-plus. In the meanwhile you may want to look at a little micro note on graphics that I wrote.

Day Five: Ljung-Box, S-Plus Code, and the Wold Decomposition

Posted for 17th September 2008

Some comments are certainly in order on the truly astounding transformations that are taking place in the financial markets. There are lots of ways in which we are not in Kansas any more and it would be foolish to ignore these astounding events --- however much we "love" stationarity.

After catching our breath, we can return to the timeless core of the plan. We lock in the notion of an autocorrelation test and specifically to look at the Ljung-Box test --- the technically superior version of the more logical Box-Pierce test.

The original paper Ljung-Box (1979) requires more background than you are likely to have at this point, but you can still benefit from taking a quick look. Figure 1 (page 299) especially tells a good tale. It contrasts Chi-squared approximations of the Ljung-Box and Box-Pierce statistics, and we see from the plot that Ljung-Box is the winner. Even though from the point of view of pure logic, the now out-dated Box-Pierce statistic is dandy, we have to concede that from the point of view of the Chi-squared approximation, the Ljung-Box statistic carries the day.

We'll explore the Ljung-Box statistic with help from the S-Plus Finmetrics tools that are bundled into the so-called "acf test" which covers among other things our favorite Ljung-Box test. Specifically, we'll check out the code example, and play with it a bit.

We will also develop (in the context of the AR(1) model) an elegant theoretical tool called the Wold representation. Along the way we will also introduce the lag operator and some more finmetrics tools.

Finally, we'll also go over the new homework and deal with any logistical issues.

Hey, if we have a moment, we may have some fun with the translation functions of Google. Remember those little flags?

Addendum: You may want to check out the piece on Spike about the current financial situation.

Day Four: Autocorrelation Functions and Simulation Tools

Posted for 15th September 2008

The first order of business is to discuss the incoming homework, which I trust went well for everyone. There may also be some logistical issues of partnership formation, etc.

We'll then introduce the notion of an autocorrelation function, which is our front- line tool for looking for dependence in a time series. After pondering the general definition (valid for any stationary series), we will work out an explicit formula for the theoretical autocorrelation function for the AR(1) model. This calculation will also make it stunningly clear why rho must have absolute value less than 1 for our model to make sense.

We'll then look at the S-Plus function for computing the autocorrelation function. This will provide an opportunity to discuss the nature of S-Plus objects and to look at the relevant extractors.

We'll also discuss an example application of the Finmetrics tool arima.sim which can be used to make quick simulations of a large number of models. As promised, the new homework has been posted, but we'll go over it next class time.

As I mentioned in class there are numerous S-Plus tutorials on the web. The hard part it to find one that is really tailored to the needs of our class. For the non-time series basics, I think one does well to look at the tutorial of Konstantinos Fokianos of the University of Cyprus.

Homework Question

Posted 13th September 2008

Some people have asked about the form of delivery of the HW. Please just hand in one copy per team. This should be a hard copy with both team members name clearly at the top. It should also be stapled neatly. No stapler? Get a good one! It's a fine investment that lasts a lifetime --- not like a stupid cell phone.

Three Thursday Notes

Posted 11th September 2008

There are some people who for one reason or another are now without a partner. If you are such a person, please do complete HW1 on your own, but rest assured that on Monday you will have the chance to find a partner.

On more minor business, on Wednesday someone left a pair of sunglasses in the class and on Monday someone left a cell phone in class. These can be retrieved from the Statistics department reception desk (ask for Adam).

Finally, for the fun --- what a hell of a market today! If you scan financial history for similar days, they will be few but interesting. This is a strange but feasible way to engage new (perhaps goofy) kind of security analysis.

Day Three: More on AR: Simulation and ML Estimation

Posted 10th September 2008

We'll cover the day 3 plan, attend to any question on the Homework No. 1 Assignment, worked a bit with S-Plus, including the examples of functions and loops in a baby AR simulation.

Our main theoretical task will be to introduce the notion of a Markov process and to note that AR(1) is the leading example. We'll also review the notion of maximum likelihood estimation and use that principle to obtain explicit formulas for estimates of the AR(1) parameters. The only "tricky" part of the process is that we really only get estimates that are approximately the MLE.

Important Note: Everyone will eventually need a Wharton account or a "class account". If you are a non-Wharton student, you can get a class account from the class account link.

It will be worth pondering what may look like the extreme weirdness (and wildness) of the US market on the just passed Monday and Tuesday. There are talking heads (maybe wishful thinkers) that have said that such patterns are "typical of the bottoming process." You might do a little snooping to see if this slice of conventional wisdom holds historical water.

In general, we'll ponder for the first time but not the last ---"Why do we believe what we believe?"

Day Two: A First Model --- Modest but Clear

Posted for 7th September 2008

The first task will be to continue with the development of the AR(1) model, including estimates of the parameters. The AR(1) is a modest model but it has two nice claims to fame. First, it is a model that contains the "strawman" of a pure noise model that underlies many financial results, including the Black-Scholes model. Moreover, depending on the sign of ρ, the AR(1) points us to the fundamental distinction of "mean reversion" versus "trend following."

We'll also use the AR(1) model to deepen our discussion of stationarity. In particular, we will have a nice concrete illustration of the "volatility" versus the "conditional volatility."

The third task is to develop further some further S skills, including the use of loops, conditionals, and functions.

Please note that HW No. 1 is posted in the e-Handouts, and it is due on Monday September 15. You will also find the more detailed bullet points for today's class in the e-Handouts.

Anticipating Day One

Posted 28th August 2008

There will be three main objectives, beyond going over the logistics of the class. First, we'll go over the procedural details regarding homework, teams, and the final projects.

Second, there is at less a little nibbling at our first model --- AR(1), the simplest auto-regressive model and the simplest alternative to pure random noise. Over the course of the term, we'll develop considerable expertise with this model, but the main purpose the fist exposure is to help you calibrate the level of mathematics we will be using --- not too high, but not too low

Finally, we'll have a real-time introduction to S-plus which is our main software tool. Before next Monday you are expected to have installed S-Plus Finmetrics on you PC and to have given it a test drive. You also need to complete the student questionnaire and bring it to class.

Note: There are many S-Plus tutorials on the web. My advice is not to bother with them for the moment. We'll develop the tools that we need as we need them, and there are many S-plus tools that we will never need. Moreover, we will work almost exclusively from the command line, and many of the web tutorials are for lower-level courses that rely on the graphical interface which would only stir in confusion.

Still Shopping? What You Need to Know

If you are still course shopping, I may be able to save you some time.

First, everyone in the course absolutely must have access to a Windows PC on which they can install software. The reason for this is that we will be using the software S-Plus with Finmetrics, and this software does not run on Macs or Unix. Also, the software cannot be placed on public machines. If you are thinking about maybe scraping along without proprietary access to a windows box, I strongly encourage you not to try. From experience, I know this requirement is a deal killer.

Second, I should underscore that this is a course about financial time series. There are lots of applications of time series, and you might think that this course could help you with engineering or medicine or some other worthwhile activity. Unfortunately, that is not the way this course works. Most of our techniques and almost all of our efforts focus on just what is special about financial time series.

Certainly, from time to time, I will mention some of the ways that time series are used outside of financial contexts, but those will just be small parenthetical remarks. The course is about the models and empirical realities of asset returns. If asset returns are not deeply and absolutely interesting to you, then you will miss out on the real fun of the class. Taking the class would be like dancing without liking the music --- possible, but not a good use of one's time.

More Details about the Academic Prerequisites?

We will be writing some programs and dealing with some serious software tools, so it helps if you like such work. We won't be doing a ton of mathematics, but if you can't remember calculus, this is not the course for you. You will also have to have some acquaintance with linear algebra (matrix and vector concepts, matrix multiplication, matrix inversion, notion of matrix rank, etc).

From the beginning we will be using expectations, variances, co-variances, probability distributions, confidence intervals, and multiple regression, so you should have had some solid exposure to all of these. Still, I do not expect that all these tools have been completely mastered. Throughout the course a serious effort will be given to deepening your understanding of the fundamentals. This is a never ending process.

Just how much mathematics, statistics, and "computer sense" you need --- well, it's almost impossible to say.

Strength in one place can make up for weakness in another. In the end, what maters most is whether you look forward to trying your hand at discovering whatever something about the ways that asset prices evolve over time.

Almost without exception, personal motivation, honest curiosity, and dogged commitment will rule the day. These work best when combined with an informed interest in financial markets and a solid self-confidence in your own abilities and knowledge.

What About that First Day?

It's not one you should skip. On of the main tasks will be to sketch out a "mind map" that will provide the big picture for the whole course. We'll also be handling a lot of logistics, such as text requirements and software access. We'll also begin work with S-Plus, our main software tool.

About the Text --- Zivot and Wang Again?

In the Fall of 2008 we will again use the text by Zivot and Wang. I came to this decision, only after much soul searching. We are really only going to use about a fourth of its many pages, but there is no (legal) way that I could think of getting you just those pages that we need. It is not required that you have copy of the book, but life will definitely be easier for those who have comfortable access to a copy. Perhaps getting on copy per team would be a good compromise.

I wish that the book were (1) smaller (2) more focused on what we use (3) more "opinionated" about what works --- or doesn't (4) more generous with coaching about S-Plus (5) more sincere in its engagement of real financial issues. It is sadly a "computer manual" and a bit of a cookbook.

Still, it is a beginning, and one needs a place to start. Eventually, I will write my own text for 434, but there is no chance that a workable version will be available any time soon, even 2010 is a long shot. So, we will have to make do.

 

 

e-Handouts

2008 e-Handouts

Final Project Specifications

Presentation Schedule

Day 23 Bullet Points

Day 22 Bullet Points

Day 21 Bullet Points

Day 20 Bullet Points

Day 19 Bullet Points

HW9 Due Monday Nov 17

Day 18 Bullet Points

Day 17 Bullet Points

HW8 Due Monday Nov 10

Day 16 Bullet Points

Day 15 Bullet Points

HW7 Due Monday Nov 3

Day 14 Bullet Points

Day 13 Bullet Points

Day 12 Bullet Points

HW6 Due Monday Oct 27

Day 11 Bullet Points

HW5 Due Wednesday 10/15

Day 10 Bullet Points

Day 9 Bullet Points

Day 8 Bullet Points

HW4 Due Monday 10/6

Day 7 Bullet Points

Day 6 Bullet Points

HW3 Due Monday 9/29

Day 5 Bullet Points

Day 4 Bullet Points

HW2 Due Monday 9/22

Day 3 Bullet Points

HW1 Due Monday 9/15

Day 2 Bullet Points

Student Questionnaire

Mind Map of 434 (static version)

Day 1 Bullet Points

Resource Pool

434 Blog for 2007

Risk Free Rates

Index to some Resources

Black-Scholes and Facts

Trade Books for Context

Dow Flaws --- Cost to Fix

Burton Malkiel on EMH

Andy Low on AMH (and EMH)

Kelly Criterion Resources

Risk Mgt. and VaR

Historical Review VaR

R. Engle Garch 101

R. Engle (AER June '04)

GARCH and the Zoo

Model Selection

Portfolio Construction

Efficient Market Hypotheses

Wiki on EMH

Nuveen

 

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