WHAT YOU FIND BELOW is the course blog for the Spring Term of 2007, so if you are looking for information about the up-coming Spring 2008 course you need to go to the new web page.
The Spring 2007 blog pasted below can be used to give you some idea of how the previous course went, but the content will change substatially in the Spring of 2008.
To put things in a general context, Stat 956 is not a generic "time series" course --- it is a course that looks at financial time series.
For example , we spend a lot of time on Garch models and co-integration, but hardly anytime on spectral methods. We'll also look at some of the implications of financial theory, and we will have some fun by looking at some 'goofy' financial assets.
Naturally, the 2007 blog reads in reverse chronological order --- the course stats at the bottom and ends at the top.
Bill Gross's May/June 2007 Outlook.
[May 1] Those of you who thought about the Gini index may want to learn about the related Herfindahl index. There is a piece by Standard and Poor's that examines this index over the period of the TMT bubble and bust. This analysis finds more concentration than Gini finds, but this difference can probably be attributed to a focus on the SP sectors rather than on individual firms. This analysis provides a reminder that any "concentration" story depends on the units of aggregation --- firm, industry, sector, etc.
[Apr 29] I look forward to getting your reports! I have received four already and read them with great interest. All have been excellent and informative.
On a related, but lesser, note --- Claymore has a ETF based on the Zacks Rotation Index. For 60bp expenses, the fund XRO lets you participate in a pig-in-a-poke rotation strategy that Zacks has back tested, and finds nice excess returns --- in their back test. The ETF has been running for a bit more than seven months now and has returned 23% versus the markets 12% for the same period. Future returns may vary, and I suspect they will, but for the moment XRO has a day in the sun. If you would like to work with me on reverse engineering this, it should be easy enough, though some new regression ideas might be needed. Incidentally, the volume is pretty thin, so this product has not yet been a bit hit for Claymore.
[Apr 28] First, a quote from a Mellon Bank press release: "In deciding whether to favor growth or value stocks, the Mellon Equity model analyzes interest rate spreads, the term structure of interest rates, and several valuation and profitability indicators for baskets of stocks of both investment styles. We are now able to identify the combinations of variables that are favorable or unfavorable to growth and value stocks."
If this is true --- and if "favorable" means what everyone is expected to believe it means, we can replicate the Mellon analysis, and --- incidentally --- pick up a nice piece of cheese, if they are right. Telling whether growth or value will out-perform is a very nice thing indeed.
Sadly, the Mellon quote is from February 2004 and it called for Growth to out-perform. Well, we know that Value prevailed in 2004, 2005, and 2006. Now, in April of 2007 I am personally prepared to say that the model has caught up and we can expect Growth to prevail for the rest of 2007. Hey, if I am wrong, at least I have done less damage than Mellon.
[Apr 24} For a small tidbit while you are taking a break from the serious work of your project, you might look at a scraped page of Vanguard content on portfolio allocations. It is useful for building one's intuition.
What it gives are the performance statistics of stock/bond allocations over a typical long horizon (1926-Now). The feature that I found most instructive was that the "worst year" which for the ultra-"conservative" 80% bonds/20% stocks was in 1974. People seem to forget what a brutal year 1974 was for investors. When you figure in the horrible inflation, it really ranks up there with the worst of all years. Journalists blamed this on the "waste" of the Vietnam war, but that argument seems too simple to me to hold water. It would be nice to know the real story, and hard-working economist have naturally engaged this. So far, Nelson (2005) looks like the best shot, but further references (or views) are appreciated!
Incidentally, it would be very interesting (and possibly publishable) to do an analogous analysis using a more interesting portfolio allocation scheme, such as Swensen's. You'll need nice graphics (and logic) to handle the multi-asset story.
BTW, what strikes me from the Vanguard page are the bad events that are not likely to recur. Central banking really has improved (I think!). In particular, repeats of the debacle of the Great Depression or the Stagflation of the 70's really do seem to be highly unlikely given the policies that are now in place around the world.
The "catastrophe on the horizon" --- if there is one --- is not likely to be like these. This should be viewed as progress even if we don't know what might next go bump in the night. My own guess is that we are more likely to be lulled in to more 1998-2000 style bubbles, if for no other reason that so many people had such a great time at the party.
As economic events, modest bubbles in liquid assets really are not much trouble at all --- just hiccups in the efficient allocation of capital. Note to self: Japan 1989-2006 was more than just the end of a "normal" bubble --- it was a monster bubble that had many layers of institutionalized nonsense that have still not sorted themselves out, though they are getting closer.
Finally, a non-academic economist of my acquaintance has the view that "all recessions are inventory recessions." If he is right --- and to some extent he must be --- we are very lucky to be living now when almost all big corporations exercise pretty sensible inventory controls. This means that if we have a negative quarter (inventory backed up, pipeline filled) these corporations don't keep turning out stuff that eventually must be dumped. The humble supply chain deserves a lot of credit for the stable world we find today. This is part of the story of Bernanke's great moderation which is one of the most useful "big picture" themes one might ponder.
[Apr 21] McKinsey "Corp Fin" has a piece on "beta post the TMT bubble" that makes some interesting points about distortions to beta that were created by the bubble. For example, the correlation between the utility sector and the market went from 0.6 to 0.2. The article does not claim this, but you might notice that for portfolio theory slaves this means that you have to increase your utility exposure, and lo-and-behold we did end up with an "echo" bubble in utility stocks 2002-2006. The same was true with the REITs, though other issues were also in play. Now, looking forward we see that the correlations of utilities and REITs are returning to traditional levels, so portfolio theory slaves need to sell them off --- and indeed right now we have a faint echo crash where utilities and REITs modestly down as the rest of the market rallies. Or at least that is my theory. If you have another, let me know.
[Apr 18] My main source for the discussion of sector momentum was Moskowitz and Grinblatt (1999),There is also a quick read from Arrowstreet Capital that comments on sector momentum in global markets. An understating that is evolving now is that all sorts of stable relationships were jiggled around by the 1998-2003 TMT bubble and bust (see the note for April 21), so it is not surprising that there is a 2006 paper that observes diminished momentum in the post-TMT bubble cycle.
[Apr 15] One of the market indicators that has a following is the put/call ratio, the ratio of SP500 puts to SP500 calls. There was an introductory piece on Seeking Alpha on Feb 7, 2007 that looked like the indicator had gone haywire, but lo-and-behold we did have a mini-crash on Feb 27. As a project, you might look into the predictive power of the put/call ratio. This is one of those situations where "registration" and "elasticity" become issues. It strikes me that some idea parallel to that of a "hazard rate" will be more appropriate than any plain vanilla fixed interval forecast. This would be new and valuable.
[Apr 7] On Monday we'll go over some lessons from the mini-projects, consider issues for the final project, and begin a discussion of the paper Can We Learn to Beat the Best Stock by Borodin, El-Yaniv, and Gogan. This is a clear paper that reviews what is sometimes called "universal portfolio theory." This is an area that has been pursued by information theorist and computer scientists, but pretty much ignored (or poo-pooed) by academic finance.
We may also discuss a paper from a Duke group that uses regression and neural nets in the context of emerging markets. For the study period (1991-2001) there were eye-popping returns (both up and down) in the emerging markets, so even the plain vanilla empirics make this a heart-racing page-turner. It would be amusing to up-date this analysis using bagging or other machine learning tricks.
Here is a short list of items which I hope that will be examined in the final projects:
[Apr 6] There is a Forbes piece on Gus Sauter and the Vanguard Strategic Equity (or Structured Equity) approach to capturing alpha. It is a quick read, and though nothing particularly detailed comes out, you do see from it how leading quant managers think about their business --- or at least how they frame it when talking to the public. I found the small comments on sector and capitalization rotation interesting. These are too macro for Sauter, and his internal research finds no alpha. Still, there are others who take views like "the period where energy out-performs a long" --- suggesting, of course, that despite its nice run for the last couple of years, energy may continue to out perform for several more years. How might you test this? Can you think of useful features of merit to compute, or graphical displays that would let us see what might support or refute this assertion?
[Apr 4] We'll discuss some of the projects, Ganesha's mice, why nonlinearly in a model may be essential if you hope for cheese, simple ways to stir in credible non-linearity, the class of ordered univariate strategies, the decile story, Dean's bizarre "factor" view of the small cap effect, Vanguard "structured equity" view of reliable alpha, the observation (indirect) that the Vanguard product really does just add noise to its benchmark, the religious view of the market weight portfolio, the practical interpretation of the market weight portfolio, comments on some university endowment histories (Stanford, Yale, Harvard), Dean's "threshold endowment" criterion for early years investments --- and its analogy to successful entrepreneurs, how farmers are big-time gamblers --- with Kelly that often nips at 2 (so they eventually go broke with probability one), why historical returns to commodities may not reflect future returns, asset allocation by country, and stuff like that.
[Apr 2] One topic we'll address is covariance estimation, the underlying assumptions, and its relation to portfolio theory. To make it real, we'll also look into to the history of some financial crises, especially the 1997 East Asia Crisis. Naturally this all points to one of our central agonies: When can we usefully assume stationarity. Almost everyone ducks this question, so we only have to make a most modest contribution to end up with the biggest contribution.
We'll also look a several other topics that engage the "cross sectional" features of time series. One of these is "within sector dispersion." This is discussed a bit below, and I think it is a very interesting time series object that may have predictive juice. There are lots of ways this idea can be spun, and it has many things to like: (1) robust, (2) understudied, (3) non-linear, (4) benchmark linked. These are all features that I like to see in any variable that might contribute to the cheese hunt.
[Apr 1] "It is interesting to note that it took the efficient frontier four years to recognize the devastating 1929 crash and go from 100% equity to 0% equity. Ironically, that happened just prior to the biggest cyclical bull market of the last century (1933-36)." This quote is from a web note that makes the point that the well regarded "efficient frontier" easily starts to look like the much discredited "market timing." [Up-date: See April 21 regarding beta distortions and portfolio consequences.]
[Apr 1] Alliance-Bernstein has an instructive two-part piece on the issue of timing of "value" versus "growth" as the style with the higher return. Their methodology focuses on comparison of the median active growth manager and median active value manager, and one of the bottom lines is that a 50-50 split between these two manages to "out perform" the SP500 57% of the time.
If you read the discussion carefully, you may spot some problems. One is that their selection of active manages may well have serious survivorship biases. The other is that "percent of time beating" is not something you can eat. In other words, I would be more interested in the comparisons of the compound returns rather than the frequency of "wins." I do find the use of "median" active manager to be an interesting notion, and I suspect that one can do more with this type of analysis after thinking past the knee-jerk criticisms.
[Apr 1] There is a Vanguard piece for institutional investors that has an very clever time series that is new to me. It's in Figure three which looks at the spread in the returns between the 25% and 75% percentile performers within a given industry sector, then these within sector spreads are weighted (I assume) by the sector market cap. The point is to get a measure over time of "cross sectional volatility" --- the extent to which the better returning firms are doing vis-a-vis the worse performing firms (all nicely robusitified via quartiles).
There is a lot of data massaging to get the full market picture, but you could do this for a given sector reasonably easily. This is another kind of time series (like the Gini measure) where you have a chance for forecasting since there is no direct connection to cheese.
[Mar 31] Abel Rodriguez and Edward Tower have an instructive paper that meets indexing head-on. They work within one family and study Vanguard's active vs Vanguard's index funds. Both the facts and the methodology are instructive. I was particularly intrigued by Exhibit 3 which plots short-term alpha versus portfolio R^2. They find that a managed fund that tracks the index closely is less likely it is to have positive "alpha." In fact, is is more likely to have negative alpha. There are natural "agency" arguments whose stories support this qualitative picture. It's a quick and informative read. You might consider some of their methodology for your final project.
[Mar 31] "Structured Equity" is a word that sounds a lot like "structured products" but it's a substantially different (though related) animal. The term "structured equity" (as used by Vanguard's Institutional Client Group, and many others) connotes an equity product that tracks a benchmark with in a wide but bounded range (say 2.5%) and which seeks through quantitative means to have positive tracking error the great preponderance of the time.
You could call this, reasonable cheese at a reasonable price. Formal "structured equity" has been around for a bit less than ten years, though informally "structured equity" has been around almost forever. This is a semi-active investment strategy, so it nibbles away at the notion of market efficiency. It is also a moving target, since strategies that are found to work are commonly believed to become less effective over time.
Vanguard has a nice background piece on structured equity.This piece is also a model of how one can believably "pitch" statistical ideas. It sticks closely to the basic theme "why should one consider structured equity" but it never overstates the case. At the end of the pitch, an institutional investor is almost inevitably asking himself, "How do I get a piece of this?" (Incidentally, Vanguard does offer retail analogs under the name of Strategic Equity and Strategic Equity Small Cap.)
For more perspective, there is a useful GS equity strategy report by Bob Litterman that focuses on his view that there is increasing interest by institutional investors in active and semi-active strategies, including GTAA (Global tactical asset allocation), hedge funds (w or wo baskets), structured equity, and enhance equity.
Technical Note: In these articles you will hear about the information ratio, which is given by the formula: Mean(Asset - Benchmark) / Sigma (Asset - Benchmark). This measure introduce by Treynor and Black (by another name) differs from the Sharpe ratio by forgetting about the riskless asset and focusing on returns relative to a risky benchmark. For structured equity, this is an especially natural measure since there is a canonical benchmark for each product. You might ask if there is an analog for the information ratio to the Sharpe ratio "theorem" on leveraged portfolios.
[Mar 27] The class will skip and dance around various tidbits, mostly reflecting on the financial cost and benefits of self-confidence, the behavioral notion of "recency" and the fact that the journalistically most appealing "explanation" is seldom right. I'm sure to mention the great tale of the Beardstown Ladies. Oh yes, there will be some honest statistics stirred into the pot, including the notion of a Gini index and a research question which might lead to a useful publication: Has the SP500 portfolio become more --- or less --- concentrated over time?" This is a generic line of inquiry with lots of stories that one can spin. Can you spell Knowledge@Wharton?
We discussed earlier the currently flat yield curve and the folk lore that an inverted yield curve presages a recession. There is a Forbes article that reviews the standard "evidence" and which offers a tiny and (probably specious) variation. I much prefer the "global yield" curve argument that we went over in class. This view is also supported by recent speeches by Kroszner and Bernanke (next paragraph) which also suggest projects!
We'll also follow up what I see to be the logical benefits of bagging. I'll give several arguments. There are also many research questions that are connected to the basic issue: When, where, and why does bagging "work"?
Flat Yield Curve: Observations and Projects. There is a wonderfully instructive June 2006 Speech by Fed Governor Randall S. Kroszner which gives a stunning summary of the reasons why the yield curve is so flat now. If his reasons hold up (as I bet they will), we can expect the yield curve to stay flat for a pretty long time. The paper also has footnotes with links to some interesting academic papers, including an some what older article by Bernanke on the same (or roughly same) topic.
Other News: "The combined assets of the nation's mutual funds increased by $152.8 billion, or 1.5 percent, to $10.567 trillion in January [2007]. Stock funds posted an inflow of $28.35 billion in January, compared with an inflow of $10.08 billion in December." --- according to a Forbes e-letter. Also, Henry Blodget (Yale, same year as Adi, banned from Wall Street for bad behavior) has a redeeming column on Slate where he explains how Cramer stepped over the line ... perhaps into oblivion, though that cat has nine lives.
{Mar 26] Well, the Zhang paper did not really hold up under the hot lights of interrogation, but we can't feel too bad. After all, 70/30 bets are not to be found laying on the pavement, and we had to take a look. Sadly, we did not get any real sense of the benefits of bagging, but to me the idea looks like it should work somewhere. The benefit of bagging is that it acknowledges the "data uncertainty" when we make our estimates, not just when we judge our estimates. Now if models were all Gaussian and our likelihoods were all honest, there would be no benefit to bagging. But our observations are not Gaussian and our likelihoods are not honest.
[Mar 25] On Monday we'll start poking at the Zhang paper that I mentioned earlier. There are some "tells" (poker term) that the paper may be naive, e.g. You will never see a serious finance paper that uses returns computed from Yahoo! prices or which even mentions the DOW which is an absurdly flawed index.
Still, Zhang makes great claims, and the paper gives us a chance to get machine learning into the game. It also promises lots of cheese, so we really must take a look, even if we are a priori skeptical.
[Mar 25] Here is one in the domain of "what am I missing?". The guys at Rydex (well-known bandits) have an ETF called FXE that tracks the Euro. This seems to be a fund that promises "give me x and in a year I will give you (1+r)x minus 40 bp where r is the change in Euro/Dollar." There is no mention of interest paid on the Euro holding, and if that is the case, this is an off-the-charts rip-off. So amazing, that I have probably just misunderstood something; I'll get the prospectus shortly and figure this out. Alternatively, you can sort this out as your mini-project.
In the meanwhile, consider shorting FXE and buying futures to hedge out the change in the Euro. Give yourself your local interest rate on the return from the short position (assuming, of course, that you are an institutional investor!), pay (indirectly) the implied interest on the futures contract, and earn for yourself the spread in the interest rates PLUS the 40bp that Rydex drains out of the ETF. Given the leverage of currency futures, this looks like a monster.
What am I missing? Is it perhaps impossible to borrow the shares? If so, what kind of ETF is this mutt? Even if there is interest paid on the Euro holding, there is cheese here.
[Mar 25] I did some simple simulations with two uncorrelated assets to see if I could get Swensen-like benefits from rebalancing. I was generous in that I took the second return series to be a random ordering of the first series, so we get nearly zero correlation but otherwise identical features (same means, variance, quantiles --- the whole distributional banana).
In this idealized situation, I picked up a decent 1.30% annual bonus with daily rebalancing and a more modest but useful 0.80% bonus with monthly rebalancing.
I did not charge myself transaction costs. You might recall that our back-of-the envelope calculations in class put such costs at about 0.30% per year for a portfolio of Yale's dimensions. We got this using razor-thin bid/ask spreads (and zero market impact drag) but I do think the overall number is reasonable. After all, a good fraction of the time you can use "new endowment money" or "regular endowment withdrawals" to handle the rebalancing.
There is a feature of my simulation that may underestimate the value of rebalancing. My base series did not have any built-in mean reversion. If you are exploring the rebalancing phenomenon for your mini project, you might want to look at AR(1) series with modestly negative rho. We know that equity returns are not well modeled as AR(1)s, but such a simulation still helps to "put a box" around the most we can expect from rebalancing. What other boxes can you imagine? Suppose you overlay a three-year mean reversion of returns with a slowly moving shift in mean. This would echo a behavior that some folks believe exists in stocks (though a lack of plausible stationarity dampens my enthusiasm for analyses that force me back to '27).
Incidentally, as we engage the rebalancing issue is is a good idea not to fall head-long into the problems that I mentioned in "project 5, March 18." I've come close to a logical blunder with my own simulation, but I think I skirted the tank. This is a situation where the simulated story and the empirical story can diverge substantially. That is why I loved my "no stinkin' models" approach --- which unfortunately does not pan out. The problem with simulation is that we tend to back into the "one-period world" with no real time series element to the model. Direct empirical checking, avoids this --- though future returns may vary.
[Mar 25] A random internet wag notes: "Economists agree that, in the long run, rents rise at about the same rate as [nominal] GDP per capita."
This assertion is actually pretty cool. It has been my informal experience that rents do go up faster than inflation (the natural alternative to GDP growth). Also, my sense is that in recession rents are flat to down, even though there can be CPI-U inflation. How about a time series regression model where you model "rent returns" versus factors, such as nominal GDP change, area population changes, etc.?
You'll probably need to work with yearly data here, so it's a bit more in the domain of economic modeling than the domain of financial time series, but we are flexible here. I haven't looked into data resources, so getting appropriate data would be part of your challenge. It might be easier to focus on commercial real estate.
[Mar 24] The one-minute-manager view of an inverted yield curve asserts that "an inverted yield curve foretells a recession." Historically this has been true to a modest extent --- many recessions were preceded by inversions and a decent fraction of inversions were followed by recessions. What's new is that whatever the strength of this relationship may have been in the past, the "effect" appears to be less now.
There is a sensible explanation of this change. Just like the term "short rate" is more ambiguous now because we live in a more globally integrated financial system, the notion of an "inverted yield curve" is also less meaningful now than it was earlier. It is much more useful to look at a GDP weighted version of the yield curve, where at each maturity you weight a country's bond yield by its fraction of global GDP. A rough cut suggests that this global yield curve tells us more about the likelihood of a global recession than any individual country's yield curve. This suggestion (see comments by Ken Fisher) seems not been extensively studied, though as noted below, there is some recent academic literature on the global yield curve. An exploration of the global yield curve (and its forecasting uses) could make a nice project --- mini, final, or super-maxi.
For a fancy model of the global yield curve, see Diebold, Li, Yeu (2006). This paper has many useful references and some "tricks" like the Fama-Bliss method for calculating zero coupon rates. You won't need any of this for a mini project or even a final project, but it's nice to know what is out there. For the project, you can just think about the 10 year vs 3 month spreads as a surrogate for yield curve slope.]
[Mar 22] We'll soon start looking at some of the tools from machine learning, and we will consider a paper by Z. Zhang that finds eye-popping cheese from some "boosting" and "bagging" applied to neural net models. Needless to say, future returns may vary, but the claims are so mouth watering that they must be examined however skeptical we may choose to be a priori.
On a more mellow ---yet still interesting ---note, I have been reading the most recent book by Ken Fisher, a guy who deserves some credit as a self-made billionaire who also writes a regular feature in Forbes. Fisher has several observations that suggest good projects. One of the most concrete of these is that "SP500 minus top hundred holdings" has a return series that very closely mimics the return of "small caps" (say the Russell 2000, though we hate that particular bench mark, for good reasons). If it holds up, this tells us something very interesting about the whole notion of "small caps". IMHO, you can get a paper published by checking this out carefully in a modest variety of markets (e.g. US, UK, Japan, and Eruoland).
[Mar 20] I've created a resource and analysis page on rebalancing. It contains some links that were previously on this page, but it also goes further. I'm starting to see through the trees and it's going to be a lot of fun sorting this our together. Please do look at the new page.
[Mar 20] It has been understood for five years (or longer!) that the Russell 200 Index has structural flaws that subject it to arbitrage frictions. Moreover, this drag has been augmented with further bad ideas: "Beginning in September of 2004, Russell began adding initial public offerings (IPOs) to its indexes on a quarterly basis provided the firm meets the minimum capitalization requirements for inclusion. Eligible IPOs must have gone public within the three months prior to their inclusion." OMG, do you really want exposure to a slightly seasoned IPO just because of its capitalization? This is like something from a "bad idea genes" skit.
[Mar 19] In class today, we'll complete our discussion of the weighted majority rule, and then we will look at what it may suggest about portfolios. Some of the other connections are to Bayesian model averaging and one of "my" inventions --- the ordered univariate strategy. We'll also discuss the notion of "model risk" --- as opposed to estimation risk. We'll also discuss the mini-project (due April 2) and the final project (due April 30). Please do read the entry for March 18 for project ideas, as well as older blog entries.
[Mar 18] Rolling right along with suggestions for your second mini-project and for the final project: how about some portfolio ideas? I'll list a couple below.
Project Idea 1. Barclays iPath has a new ETN (exchange traded note) that captures the return on the GSCI (Goldman Sachs Commodity Index) plus the return on the T-bills that would be used to hold a futures position on the GSCI futures. The ETN has symbol GSG and it trades like an ETF. The expense ratio for GSG is 0.75 which is not cheap, but it is reasonable given the asset class.
Now, how might one study (or use) this new asset? Ziv Bodie did work that suggest that a 60-40 portfolio of SP500 and CCGI would have "equity-like" returns with only 1/3 of the volatility. This is a very attractive suggestion if it really checks out. (Thanks to Ibrahim Erkan we now have the reference Ziv Bodie “Commodity Futures as a Hedge against Inflation,” The Journal of Portfolio Management Spring 1983, Vol. 9 Issue 3 pp. 12-17; I've requested the article. It's not available on line.)
Now, to complicate the mess, the GSG "portfolio" has to "roll" from futures contract to futures contract, so the holder ends up paying a kind of implied interest on the underlying asset. This interest can be high, so the realized returns from GSG may turn out to be a lot worse than the naively calculated returns on GSCI. For background, you might want to read what a SeekingAlpha wag recently wrote as he dropped GSG from his model portfolio because of "contango" concerns.
Side Project. The notorious Victor Niederhoffer has said in writing that the asymptotic value of GSG is zero. I hate to agree, but there is a chance that he is right --- in theory at least. You might save some investors a few billion if you could explain this clearly to the world.
I'd start with the idea that you are "paying interest" to hold something that is I(0) in PRICE.. There is logic to this view, and if it is true, then Niederhoffer is right --- just as a matter of mathematics. Ironically, this does not mean that you can't hold GSG in a periodically reweighted portfolio and still benefit. It also does not mean that you can rationally short GSG. Life may be beautiful, but it is also complicated.
Project Idea 2. Charles Munger, Warren Buffett's long-time business partner, is CEO of a holding company with an unusual feature --- it has zero beta. The firm is Wesco Financial Corp (WSC). Partially an specialty insurance company, Wesco also has a furniture rental business and a steel warehousing business --- classic Buffett stuff.
Consider a portfolio with p% of SPY and (1-p)% of WSC. What are its empirical risk and return characteristics? Are there other zero beta companies worth thinking about? Other zero beta, or negative correlation, assets?
Project Idea 3. Wesco is a strange asset, and a reasonable person might not want to rely on it to balance out a whole portfolio. Here is a more restrained suggestion than either relying upon GSG or WSC: Consider p% of SPY and (1-p)% of VDE, which is Vanguard's "Energy" ETF. You can use another investable surrogate for energy if you like, but the idea is that when energy is doing exceptionally well, then SPY may be doing poorly, so being "overweight in energy" may smooth out volatility without costing much in expected return. To be sure, SPY is about 6% energy already, so we might want to look at using VDE to move the overall energy weight to 10%, 15% or even 20%. As usual, you might want to look at all of the statistical features of the return series associated with the portfolio.
Project Idea 4. David Swensen, the very successful manager of the Yale endowment, says that in a typical year Yale will add 1.6% to the total return on its liquid portfolio by doing daily rebalancing to its assets so they are always at constant target levels. This statement needs some interpretation since half of Yale's investments are illiquid, but I think he means that he rebalances everything that can be inexpensively rebalanced. Even so, this is an amazing claim --- 160bp is HUGE.
So, explore this in some classic situations. Suppose you are a classic 60% stock (SPY) and 40% bond (AGG) investor. If you do daily rebalancing, weekly rebalancing, or monthly rebalancing, does the process add any return. How does the return to rebalancing depend on the historical period? Keep in mind that this is a kind of mean reversion story. It would be great to understand all of the features of this story --- one can expect change in volatility as well as in mean. In fact, via our old "mu minus half sigma squared criterion", volatility smoothing would be enough. The story will probably be most compelling with just two basic asset classes, but the pay-off may be better with larger numbers of assets.
BTW, the Portfolio that Swensen recommends in one of his books is 30% US Equity, 15% Developed Market Equity, 5% Emerging Market Equity, 20% Real Estate, 15% TIPS, and 15% US Treasury Bonds. It would be nice to see what daily, weekly, or monthly rebalancing will do for such a portfolio over a period of say 10 years. You can check this out either with ETF returns or Vanguard index fund returns. Inquiring minds want to know.
You will read a lot of nonsense about rebalancing on the web and elsewhere. This is a case where we have some local experience, but I am convinced that the story is not a simple "risk story" but a genuine "return story." Nevertheless, the "source" of the extra return is still a bit of a mystery to me. Mean reversion seems to be required on some time scale, and for most time scales there is more evidence for momentum than for reversion. This is a genuine puzzle.
There are connections with several different themes, and there are genuine mysteries to be explained. Mean reversion may go part of the way, but what we need is a "scale squishy" way to study reversion.
There is a pony buried in here some where. The pony may end up related to "ordered univairate" strategies, about which we will hear more later.
Project Idea 5. You know I love Vanguard, but one of their research pieces on rebalancing is pretty lame . Read it and write a paper explaining why it is out to lunch. BTW, although this project sounds "negative" it's not --- rebuttals have a lot of value. If we never take foolishness to task, we will be ruled by media nitwits.
BTW, the fact that Vanguard publishes such a piece suggests that even the wonderful Vanguard is subject to pressure to make a "profit" --- though in some formal way Vanguard is not a "for profit" but rather a "mutual" in the old sense of "mutual" insurance companies. This is a long story that I will never get time to tell you, but you can learn about on the web. To cut that story short, look at the "piece" and think about rebalancing EMPRICALLY. It should be clear that a simulation (as done in the piece) is a priori idiotic --- But, hey, let's prove it, not just claim it. I certainly could be wrong, and I would be delighted to learn that I am.
[Mar 15] We know that CEFs have weird behavior, but is is possible that they are simply dominated assets? In terms of our favorite "mu minus half sigma squared criterion" they may indeed be dominated. There are several ways to form projects on this theme, and you can get a good start by looking at Jeffrey Pontiff, "Excess Volatility and Closed-End Funds," The American Economic Review, March 2003, pp. 155-169. which argues that the prices of closed end funds are about 64 percent more volatile than the assets they hold. By the compounding criterion this suggests that CEFs (on average) are pretty close to dominated, if not formally dominated (according to my definition).
BTW, I think I "invented" this notion of "asset domination," but of course it is infinitely natural. If you find another source for the concept or the term, please do let me know.
Still, volatility is not all bad if you believe that trading is a properly compensated profession. When you tie excess volatility to mean reversion toward some equilibrium fraction of the NAV, you have the stuff that dreams of cheese are made of. As you ponder this, you might want to look at the survey of CEF strategies by Reichert and Timmons. This paper has many flaws, but it still may be worth a quick read to help you generate idea. At a minimum, it has useful references.
[Mar 14] Yesterday was a 2% "Dip Day" which is a reminder of the kind of volatility clumping that was mentioned in the blog item for March 7. I'll briefly discuss some of the so-called "leverage effect" models. This is definitely a situation where "so-called" is well deserved since leverage in the usual sense of the word is a an unlikely contributor to the phenomenon. For a project, I would encourage people to consider Gibbs models for the 2% dip days. This would be quite new and would find a pretty clear audience.
We'll also start looking at items from the Scary Sequence Project. There is a ton of stuff here; don't be frightened. We'll start with a look at the survey paper by Avrim Blum on On-Line Algorithms in Machine Learning. This is a very friendly development of the "weighted expert" algorithm which is an extremely fecund trick. The theory is lovely, and for us the issue is to see if it is practical as well.
[Mar 11] Well, the break is almost over, but I personally would not mind another week --- that would be just about perfect, particularly given the lost hour due to "day light savings." As you contemplate projects, one series that interests me, is the TIAA Real Estate Fund (price series) . This fund has an almost unique legal structure and if you take a look you will find that it is amazingly smooth compared to listed REITs or even the REIT indices. My rough sense of the data is that the smoothness makes for predictability, which may be exploited to a certain extent. There may be extra cheese here, though not too much given the limited liquidity. One way to "play" would be to go long until the REIT index has a big draw down (say 20%) and then step out of the TIAA fund for six months to a year. The idea is to get a solid fraction of the the REIT return while avoiding the big drops. It's like playing poker where when you lose a big hand your friends let you have your money back. In class I will go over the structural features of the fund that create this odd behavior. There are several kinds of projects that you can craft from this unusual series. The big theme here is,"where you see something that it too smooth something interesting is going on."[Post Note 6/07 Alex Bernstein examined the "sell on big dip" strategy for the TIAA Real Estate fund and found no excess cheese. Alex did note that this is still an "orthogonal asset" and that every one who can qualify for a little piece should take it.}
On Monday we will also discuss the final project. We'll have some more homeworks, but there is no reason that you can't start kicking around ideas for the final project. There is a lot of flexibility, and I am happy to work with you to refine a project that maximizes your personal utility.
[Mar 7] Volatility apparently follows volatility, especially after a big down-side move. There are many variations on the basic GARCH model that attempt to address this so-called (by Fischer Black) Leverage Effect. As a pure EDA approach to seeing the phenomenon, I like the following picture: There are Big Gaps in the return series without any (2%) dips, but then after one of these dips, one finds a mighty big chunk of big dips in the following 12 months.
A good project would be to explore this phenomenon. You can first benchmark what we see in the inset just with an appropriate coin flip model. Maybe the market dip-days are NOT more clumped than one would find with a p/q coin? If it is more extreme (and it probably is), can you calibrate a dependent coin with a Gibbs distribution that captures this phenomenon? (We'll discuss Gibbs measures later in the term, but you can get started anytime with the coin flip model.)
[Mar 6] I hope everyone is enjoying the Spring break. If you want a little light reading, there is a piece on optimal rebalancing that you might find amusing. The one line summary: regress portfolio returns against a quadratic function of rebalancing frequency, assume your fit reflects something real, and do one line of calculus to maximize the quadratic.
The trick has some appeal, and it is new to me. Nevertheless, aren't there a lot of ways this could blow up? For example, aren't frequency and frequency-squared pretty colinear? Won't this make the quadratic fit pretty ill determined? It would be a good project to look at the robustness of this paper. You'd have a solid shot at getting a publication out of it. At a minimum, you'd learn a bit more about colinearity problems. The paper does have other problems, such as using 72 years of data, but the colinearity issue seems to be particularly well-focused (i.e. easy to sell).
By the way, congratulations to everyone who was long Yen. You've had a great week, and you may end up with a fantastic month if the carry trade continues to unwind. Still, it may be a bumpy ride.
Small point for entertainment. MDSRX is a plain vanilla SP500 index fund. It has about $1B in assets, which is not so remarkable except that it has a an expense ratio of 0.60%, compared with the no-load Vanguard SP500 Admiral Shares with an expense ratio of 0.09%. The extra one-half percent may not seem like much but in a world that may only offer 2.5% compounded real returns it is just like giving away one fifth of your assets.
Stranger yet, to me, is that so much money can collect in a dominated asset. Many people must be very lazy, or ignorant, or compliant, but strange things happen. For example, it was in the portfolio of John Roberts at the time when he was nominated to the Supreme Court. So sad.
[Feb 27] The Shanghai Stock Exchange had a mini-crash overnight which has had spillage in Europe and now (as of 1pm) in the US. It will be interesting to see how this impacts the VIX; perhaps some people will be reminded that you deserve a decent premium for writing an option. It will also be interesting to see how BEP responds, it should go down less than SPX and there may even be a small positive "convexity" effect since better option premiums will make for more BEP income.
[Feb 27] Yup, the VIX was up 29% by 2:30pm, and BEP was off in proportional to the SP500 (while logic would have said "by less" since the calls they are short are now deeper out of the money, less in the money, etc.) By day's end "VIX shot up more than 70 percent to a high of 19.01 before subsiding somewhat to 17.97, still a gain of 61.2 percent. This overshadowed its 31.16 percent gain on Sept. 17, 2001, the first trading day following the Sept. 11, 2001 attacks. The previous record gain on the VIX was 51.72 percent on Nov. 15, 1991."
[Feb 27] Less exciting, but more relevant to last week's classes, is the newly reported decline in the House Price Index. We had a hint of this in Jonathan's comment about the Boston index.
[Feb 27] Bloomberg's Quant Corner has a nice piece on Engle and ARCH/GARCH. Did you know that Engle is also a champion figure skater? Not so common for an economist. Engle is also working on a book on forecasting correlation, which does sound interesting.
[Feb 24] Some people have posed questions about the current status of the EMH. I found one sources that seems balanced, accessible, and reasonably up-to-date. The survey by James Davis is also useful, especially as an introduction and context provider for the FF/3F model.
[Feb 22] Source file for Jonathan Reiss's Presentation, and the source data on House Price Index (see also Feb 16).
[Feb 20] You will want to download finmetrics and to download S-Plus. If you don't already have the SSNs and the LAC, please get then from me in class on Wed 21 or on Monday 26. For the first mini-project, R should be all you need --- only Garch is bogus.
[Feb 16 ] As I mentioned in class, on Wednesday (Feb 21), Jonathan Reiss will be giving a presentation. Jonathan will cover several topics, and in particular he will discuss housing price futures. The House Price Indexes are amazingly smooth, and now that there is a futures market for these indexes, there is a lot of room for interesting time series work. If you get curious about how the index is actually defined, Standard-and-Poors has useful coverage of the methodology of the Case-Schiller index. There are several kinds of projects one can do with the House Price Indexes.
For more general culture, You may also want to read Jonathan's Op-Ed Piece from Barrons (July 31, 06): Hedging Your Hedge-Fund Bet. You can get it by going to AnalyticalSynthesis and clicking on current projects.
While they won't be part of the Wednesday class, we will eventually discuss the return time series for Equity Linked Notes. These are very interesting instruments that offer equity participation and protection of the principle. Lehman Brothers has a useful (but fluffy) piece on ELNs. For an example, you can also look at the SEC filing for the Haliburton ELKS (symbol EHC). There is also a useful (but flawed) consumer protection piece on ELNs. Finally, the AMEX has lists of the ELNs that are traded on the AMEX. The AMEX site provides a link to the offering prospectus which gives the detailed definition of the structured product.
[Feb 11] On Monday we'll take up the first Mini-project. I have a page that suggests some problems that would make good projects.
[Feb 8] I have created a resource page for Buy-Write Assets. Please look through this with your creativity in gear. We'll soon start working on our first projects.
On Monday Feb 12, we will go over some of the issues that are created by dividends when one studies returns. You may want to review the basic tutorial on the ex-dividend date at Investor-peida. For clean academic work, life is made much easier by using the CRSP return series which handle all the messy dividend stuff. Nevertheless, for real-world work, you sometimes need to dig into the dividend dates (and such) "by hand."
Another "strategy" that has been around for a very long time but which has caused a flurry of recent activity is the dividend capture strategy. The renewed interest was generated in part by the new 15% tax rate on qualified dividends, but it seems that what got the juices flowing was that when people did the analytical work they found that (retrospectively) there really was some extra cheese to be had.
Will the cheese remain? Well, that remains to be seen. Right now we are in a ramp-up in this activity, and one can expect that some funny things might happen. Alpine Global Dynamic Dividend Fund (AGD) is a CEF that came to life in 2007 with a $4B IPO. It has a tax-advantaged dividend capture strategy as a basic (but not exclusive) part of its "pitch."
I will also create a "projects page" with some resources for dividend capture strategies. These strategies have a checkered past (especially internationally), but like anything that keeps reemerging --- it looks like there is something here. At a minimum, its a clear story, and sometimes that is all you need.
Just for fun, you might read BlackRock's slick blurb on CEFs,though keep in mind that is was written to "support sales."
[Feb 5] Concerning, the use of rMetrics, please see the post for Feb 4. Concerning the recently created CEFs that follow a buy-write strategy ... read on.
The Van Kampen Equity Premium Fund is every bit the bandit that I suggested in class, but the Nuveen CEFs (JPZ, JSN, JLA) are --- for the moment --- more reasonable. They may make interesting assets to study. The lead fund is JPZ which is (more or less) long an SP500 basket, short close-to-the-money calls, and long out-of-the money puts. Thus, they are long the underlying and (approximately) short the option-synthetic.
This leaves one with a kind of "fixed income" instrument, and Nuveen provides it to you NOW for 66bp/yr, which is neither great nor obscene --- but this is likely to be a teaser rate where the fund absorbs some expenses for the short-run.
You may want to look at the JPZ assets (as of Sept 06), especially the option positions at the end of the report. The JPZ price should be driven almost entirely by changes in interest rates and market volatility, but I'll bet its not! This is because changes in the NAV tend to smooth the basics of the underlying. Also, niche sentiment is a driver to NAV. [NB: These assertions should all be checked by looking at the series!]
JPZ has a "pay-out-rate" of 8.85%. This would be a fine return, except that the 8.83% is likely to include (in essence) little slices of your own money. All indications are that this fund has been engineered to appeal to "fixed income investors who want larger yields than they get from bonds, CD, etc." This is a retail product, and my guess is that in the long run the purchasers will end up paying a pretty penny for the construction work.
Well, this may be good marketing, but this is a case where there risks that seem almost certain to be poorly understood by many of the asset holders. Incidentally, less than 2% of JPZ is held by institutions, so if individual sentiment changes, JPZ could easily turn to discount. There is not a long history in this asset (or even this asset class), but if it becomes available at a big discount and if they stick to their strategy, it "could" be feasible. In the meanwhile, it would be silly to hold and difficult (and quite unappetizing) to short. More important for us is the fun of modeling a new asset class. It is almost certain to exhibit anomalous behavior.
In this case there is another new instrument that would surely provide an arbitrage opportunity if the Nuveen funds were shortable. This is the CME/CBOE Buy-Write Index futures and options. In fact, this looks like it might be a generally useful asset class, though right now (with VIX around 10.5) being indirectly short the calls may be less interesting now than it would have been at other times.
If there is ever any excess cheese, then new assets are among the best places too look. Nuveen has three of the "buy-write" CEFs and I think we can turn up at least six more, not including EOS. Heck, we could even start an index of these --- and such an index might make a lucrative web site.
{Feb 4] Code. The jury is still out, but based on some of the computations I see in HW2, it looks like there is a lot of benefit to focusing our efforts on the R time series tools provided by rMetrics. Brent Gdula did HW2 with the rMetrics tools, and they seem to provide more bug-free path than some of the alternatives. Brent has kindly agreed to share his code for HW2.
[Feb 3] CEFs. Malkiel and Xu have an instructive paper on the predictability of the discount between the market price and the net asset value of closed end funds (CEFs). It's a good story, with AR(1) and AR(2) at the heart of it. We might have fun replicating part of this, or beefing up part of it with slightly fancier models. CEFs are fascinating animals for which there are already many documented anomalies.
[Feb 3] Financial Engineering --- Covered Call CEFs. One of the "strategies" that one hears discussed as a way to "get income" out of a portfolio is the selling of options while holding the full amount of the underlying --- this is the business of "writing covered calls." Historically this has been a somewhat (?!) reasonable business, so naturally retail versions have appeared in the form of new closed end funds. Keep in mind, this is a "short vol" strategy, so bad times can be very bad indeed.
There are a bunch of these CEFs, and EOS is typical. This CEF has under performed SPY and MDY for the last two years, but it has a 7.5% pay-out that makes the flat price not as quite bad as it looks. The pay-out also comes with a modest tax benefit. Apparently the fund appeals to customers who view it as an alternative to fixed income funds, though an advisor who actually sell it as such is not a very honest advisor.
These funds have lots of equity risk, and to the extent that the option writer is paid an implied interest the rate of this interest is very close to the risk-free rate and no where near the 7.5% pay-out. The extra cheese here all comes from bearing equity risk.
The reason that I mention this fund in a time series context is that CEFs are often alleged to have sesonalities. Future returns may vary, but look at the nice bounce EOS had in Jan06 after the December sell-off. My take-away here is like the Mark Twain quote: "History may not repeat itself, but it rhymes."
[Feb 3] CEF Premiums. Something Insane? The Spain Fund (SNF) is a closed end mutual fund with an interesting history. At one point it traded at twice the net asset value. This bizarre feature persisted for a few months. The fund still sells for what seems to be a silly premium, and without the usual excuses.
[Feb 3] Quant Fund. Mellon has started up a new quantitative fund that fund managers "expect" to provide a systematic 2% out-performance of the Nikkei basket. It might be amusing to snoop around to see what principles are behind the claim (e.g. statements in the prospectus about use of derivatives, leverage, lending stocks, etc.) They say "The fund is one of the first vehicles to offer the expertise of Mitsubishi UFJ Trust and Banking Value Team, in Japanese equity fund management, to international investors. The strategy was developed in the 1990s with a leading academic quantitative investment research institute and currently has over $4.7 billion assets under strategy and over 3,000 clients, predominantly in Japan."
[Feb 1] RE: Futures. You may want to look at some of the general information that is provided by Cannon, which is one of the larger retail futures brokers. I believe that they may also offer a "play money account" that you can test out if you are curious about futures.
[Jan 25] Late Trading. There was a "late trading" scandal in the mutual fund industry that broke a year or so ago. The scandal also brought to light some of the legal (but shady) market timing practices that made a few folks 40% annual returns through the 80s and 90s. You may want to review a brief historical summary. Similar "opportunities" probably still exist off shore, but if these interest you, you will want to choose wisely --- and with the advice of council.
Ethics has a delicate role in financial markets. It is stone-cold-clear that managers have a fiduciary responsibility to their clients, and consequently the managers that permitted "late trading" were simply crooks that deserve to go jail.
On the other hand, if you find that the rules of the game are set up in such a way that you can find some unintended advantage, many economically rational people see no reason for you not to "fill the gap." They reason that your special niche will probably not last too long, and eventually it will contribute to "market efficiency."
Also, the wisest and biggest firms know that there is a "business model" risk to the brutal exploitation of some quirk in the rules. Typically such leaders chose to pass on the opportunity and to disclose the problem to the regulatory authorities and counter parties as soon as possible.
Still such disclosure is not guaranteed. Don Reagan (who became Treasury Secretary after being CEO of Merrill-Lynch) got to his top ML perch in large part because of his success in the exploitation of quirks in the tax law concerning the timing of gains for options and commodities. Certainly, nothing that Reagan did at that time was illegal, but practices that he pioneered are no longer available --- in part due to Reagan's subsequent advice to the government.
There are also many firms that are not among the wisest and biggest. For some of these, one summer of a quirk is all they need to set themselves up for life. In almost any firm one will hear "war stories" where one learns of trading profits that bubbled up from stuff like the discovery that some trading counter-partner is simply "reading the wrong number off the screen."
These situations present an ethical problem, and the most high-minded folks simply point out the counter party's error. Still, my sense of the situation is that there are plenty of firms that choose between either (a) pounding the counter-party into the mud ASAP or (b) bringing in the in-house quants to help "maximize the long-term gains" from this special opportunity.
[Jan 23] On Wednesday we will queue up the Levinson Algorithm. Our approach will follow Jem Corcoran's hand-out.For the HW you will also want to look at the blurb on Rmetrics. You may also want to look at a cultural piece I put together on Yule-Walker, or a piece that points out some Yule-Walker drawbacks.
For your HW you may want to start playing with Rmetrics, which I expect will be our main R package for work with time series. Kevin Lo has put together some information about RMetrics and installation that you should find useful. I have not tested this yet, so we all all in the same boat. If you have hints or comments, let me know. Or you can post nice stuff on your web page and I will put up a link. For the part about testing for the normal distribution, you may also want to review my blurb "Is it noise?"
Finally, if you are having fun, you might want to take a look at the Key Note Address that Peter Bernstein gave at FAME. It's a loose document, but it puts some ideas in play that will have a role in our course. Don't worry if you bump into unfamiliar words or ideas. Just try to get a feeling for his basic pitch about risk and uncertainty. Also, keep in mind that it was written in 2002, after the dot-com bust and before the broader market recovery.