Assumption Management

Regardless of the discipline you practice, be it market neutral quant or deep value or event driven or what have you, it might be of value to think more carefully about assumptions.

To put it simply, if we didn't make assumptions we would probably cease functioning. Investment philosophies necessarily carry with them implicit assumptions; the question then becomes what assumptions are your model making and what impact do those assumptions have on your model's perception of reality relative to reality itself... and most importantly, in what sorts of situations will your model systematically deviate from reality and why? Not fully knowing the assumptions underlying a model that you trade seems to me to be similar to going into battle with a gun that you know nothing about. What happens when the gun jams? This is also very similar to accepting tips from a well regarded friend. He might be extremely smart. Hell, he might be right. But should the investment being tipped start tanking like a stone, it feels like shit. I'm sure you've probably had this happen at least once or twice. I sure have.

If you know how and why your model may not be working as well as expected, you can move to the sidelines and tune your model. If you don't, well, sorry.

Take, for example, a 'simplistic value-biased' investor who each year longs stocks in the S&P whose P/E's are in the bottom decile of S&P stocks and shorts stocks whose P/E's are in the top decile of the S&P. What assumptions is he making in constructing such a portfolio? He essentially is assuming that returns of stocks in the S&P are mean reverting over time conditional on the P/E decile one is in. But is it always that way? Maybe we can shine some light on that assumption by pulling up return data over the past 50 years or so to see how empirically mean reverting returns have been. In some years it may work better than in other years-- can we explain this? Intuitively one would expect a strategy like that to underperform during bubble times (ie. internet bubble). Is there some way we can forecast the occurrence of bubbles? Probably not. What is the worst that could possibly happen? Can we stomach the maximum drawdown? What's the expected return? What's the expected volatility of that return? Is there any way we can improve the risk-reward profile of the strategy? Throwing the model into the real world, do we have to worry about liquidity issues on the short end? Might we get squeezed out, causing the model to deviate from the real world? And these questions probably make me only half comfortable with my fundamental assumption.

Why does a deep value investor buy a stock? Because the stock will go up over time... but why? What assumptions are we making and why do we not have to worry about them?

Assumptions and risk are similar in some senses. When I make an investment, I am exposing myself to a plethora of different risks. Liquidity risk. Mark to market risk. Perhaps counterparty risk. Market risk. As an employee at an investment vehicle, I am also exposed to operational risk. What if my boss dies, leaves, loses his desire to work, or fires me? What if the electricity goes out in my building? What if my internet goes out?

The reason it has been said that derivatives are a good thing is because they allow for more efficient transfer of risk. In doing so, the people who want to expose themselves to more particular forms of risk are able to do so, perhaps making the market more efficient as a result. It's like the deep value investor who gobbles up huge tons of the market's individual idiosyncratic stock risk. They do so because they have thoroughly researched the risks they will be taking on and are in the best position to accept that risk. From a market stability standpoint, this is a good thing.

Managing risk is very important. By managing your assumptions you are managing your risk.

Unspoken Languages

The past few entries have been quite focused on the thought process and foundational elements of trading/investing. For good or for bad, expect more of the same this time around.

I read a blog today comparing a bottoms-up approach to investing with a top-down approach. I think it's great that people are throwing out their opinions and notions like this because that's the sort of thing which spurs on knowledge and intellectual discovery. That being said, the blog troubled me. It wasn't even the content which troubled me; it was the paradigm underlying the ideas (I have written about this in prior posts). I am very much open to the notion that the bottoms-up approach is fundamentally flawed, and that filter rules or other such quantitative measures aren't "optimal" for a first pass-through analysis of the market. But it seems a little silly to me to extrapolate the performance of one mutual fund onto the whole field of bottoms-up value investors (extrapolation bias). It seems just as silly to discredit filter rules by discrediting a rolling P/E ratio on the market. Following insider trading doesn't work on average; numerous papers have pointed this out (although Professor Metrick among others falls into the other camp). Maybe it doesn't work on average, but then again, maybe it does *ahem ahem*

Taking a step back, imagine for a moment that you knew nothing of insider trading and were told to construct a trading strategy around it. What was your split second reaction? Read all news articles with the words "insider trading" in them? Go to Google Scholar or SSRN to pull up all academic studies? Find all books published on the topic?

My initial reaction was basically what I would now call exploratory data analysis followed by quantitative analysis with an overlay of academic papers. It wasn't necessarily the best approach, but it seemed to work decently well.

That sort of exercise really makes me think about what it is that makes a trading strategy successful. One element of my hypothesis is that it has to do with our ability to think, speak, and write in useful foundational languages. I would consider accounting, for example, to be as much of a language as French or SQL. If I can familiarize myself deeply with accounting mechanics and principles, it allows me to open up books that I simply wasn't able to open up before (literally). I don't really see how that is functionally different from my ability to speak a foreign language allowing me to converse with others who speak the same language. My ability to understand quantitative concepts allows me to understand quantitative trading strategies-- if I didn't speak the language, I would probably have attempted at another strategy which I had access to given the languages I did speak.

The implications of the above schema are interesting. For example, languages are not mutually exclusive, and languages can be mutually reinforcing. Perhaps this whole notion is silly and trite, but I've found it puts things in the right perspective when I attack problems. The languages we know, no matter what those languages may be, are nothing more than tools; no more and no less. How you choose to leverage those tools is up to you, but the tools are there nonetheless. There is nothing forcing you to use just one tool, and with time, there is arguably no tool you can't pick up by learning the appropriate language(s).

I would say that bottoms-up and top-down investing are as good as your ability to lever the tools you've picked up over time.

Categories: theoretical_intersections

Simulations Or Mathematics

I can't make this terribly long because I will need to get home soon, but I believe the relative merits of simulation-based and mathematics-based valuation are an important thing to think about.

To put it briefly, I think it's safe to say that mathematics, and closed form solutions/analytic tractability were the primary tool we used to value securities all of, say, 25 (30? 35? More?) years ago. Black Scholes is obviously an analytic equation derived from the heat equation with a few changes of variables having time run backwards. One can just as easily derive analytic equations for binary options. One can also value numerous other types of derivatives in a similar fashion. One simply needs to assume risk neutrality (that is, that the underlying has a risk neutral drift equal to the risk free rate and a volatility assumption) and you're good to go. But derivatives got a lot more complicated. How do you value a path dependent security like an asian option? How about a rainbow option? A range option? Or how about an option on a basis swap which pays a fraction of floating LIBOR and receives floating BMA, the municipal rate? Suddenly one is interleaving multiple stochastic processes in contorted ways, making it more and more difficult to value things with traditional mathematics.

Enter simulations. As derivatives were getting increasingly complicated, computers were getting increasingly powerful. Raw computing power isn't elegant, but it can surely get the job done. Rather than spend days or weeks searching for the proper way to value a CDS with a variable floating notional dependent on the level of interest rates, one can simply make an assumption on the laws governing its motion (as was done mathematically with the assumption of risk neutrality!), and simulate that stochastic process over and over and over again with a good random number generator. The simulated average terminal payoff is ones best guess for the value of that security. As the number of simulations, this should indeed converge to the theoretical value, assuming that ones assumptions on motion were correct. Furthermore with variance reduction methods, one can decrease the number of simulations necessary to converge to a solution that one is satisfied with; a solution with a standard error below some threshold amount (ie. .5% of the terminal value). Simulations do more than allow you to remain ignorant of mathematics while still getting approximately correct solutions, however. They also give you more flexibility regarding the laws of motion the underlying must follow. Stocks tend to jump up and down randomly at different points? Well, just add in jumps of random magnitude at random times (ie. jumps following a Poisson process with magnitudes that are Gaussian centered around some mean jump amount). Suddenly your model seems oh so much more accurate.

However the flexibility of simulations regarding laws of motion like those stated above are only half of the pie.
1) We cannot live for 1,000,000 years. We cannot possibly enter into 1,000,000 variable notional CDS contracts right now, so even if we assume the correct law of motion, hopefully we can see that the theoretically correct expected terminal value will in all likelihood diverge dramatically from realized terminal value. Over shorter time horizons, other factors become increasingly important. In fact it could be argued that they are so important that the simulated value is useless, to some degree. One must remember liquidity. As I've said before (see "A Refocusing On Liquidity Risk"), a security is worth the cost of hedging that security's risk. As a financial institution issuing a financial derivative, my job is not to take on positional risk. I want to avoid making directional bets on individual companies or asset classes. I am a business, and I want to make money regardless of what happens to the underlying stock. Therefore to me, the value of a derivative security is most definitely proportional to the basis risk I expect to incur while hedging that security. It is not (or should not) be a function of my expectation of what will happen to the underlying stock. Said differently, banks are financial intermediaries facilitating the transfer of risk from those who want to avoid risk to those who want to expose themselves to risk. To do so, I create financial derivatives which have very tailored risk profiles so that individuals or financial vehicles can expose themselves to specific forms of risk while remaining unexposed to others. Equities are an aggregated, somewhat clumsy way of exposing oneself to risk, because equities themselves represent huge multi-dimensional clusters of risk. So I create financial derivatives; I attempt to sell them to one party and then hedge off my risk by synthetically buying the same security somehow (or vice versa). Other people may drive the value of that security up or down, but when it comes down to it, the value of that security is then, once again, a function of the basis risk between my hedge and my short financial derivative.
(As a side note, deep value investors then may be able to successfully make money, year in and year out, by identifying fundamentally undervalued companies whose financial situation subsequently changes for the better. These investors are (hopefully) able to ride out the mark to market gains and losses which they may incur over shorter time intervals, and are thus willing to expose themselves more to mark to market risk. The reason is because they are able to carry that risk (hopefully) without blowing up, under a reasonable set of assumptions. Deep value investors typically play with equity because derivatives are in some sense more of a zero sum game, and their values are simply derivatives of that of the underlying, making an adjustment for liquidity. Not only do you get killed on the bid ask, but seriously, if you want to make a directional bet, wouldn't it make sense to take a position in the underlying?)

So I suppose this is something of a paradigm shift. One must make a fundamental choice between establishing a position and taking on position risk, and exposing yourself to basis risk. They are quite different, and it seems that in some ways simulations may be left a bit lacking. Mathematics may be lacking as well, of course :)
-Danny

Categories: theoretical_quant portfolio_management theoretical_intersections

A Refocusing On Liquidity Risk

I met an interesting guy today.
One point that he made was a fundamental paradigm shift from 'risk' to 'capital', and how it might be of more value to think of things not necessarily in terms of risk but in terms of capital-- how the accumulation, flow, supply and demand of capital is in many ways a more 'pure' driver of profit and loss. He mentioned having a discussion with another of the top brass at Citigroup regarding the lack of performance Citi was getting from a certain variant of a spread option. They reached the conclusion that it was not model adequacy necessarily which was creating issues; rather, it was the simple fact that it wasn't a liquid enough instrument. He spent the greatest amount of time on GM and Ford as a case in point; how it was an ideal example of how the supply and demand of capital (or lack thereof) wreaked havoc on hedge funds and banks alike. The correlation died, and while people can attempt to backfit in exactly how those securities (the mezz, the equity, and the super high grade debt piece) co-moved in the way they did, it essentially came down to supply and demand-- a large number of people putting on one position, another large number of people putting on another, a trigger event causing a spark, and there simply being no bid.
Discussion of capital flow is a perfect segue into another extremely important concept to keep in mind-- markets are non-Gaussian. Yes, we have all heard this numerous times and yes, Black Scholes is fundamentally flawed as a result, but I'm not sure it's possible to reinforce this enough.
We value derivatives by figuring out how much it will cost to hedge them. Other people may value things differently, but other people are probably wrong, to be honest. A distinction must be made between basis risk and position risk. When you put on a correlation trade on GM as was done before, and you know that in the event of structural shocks to GM, the bid will dry up on the security which secures the hedge will dry up, it is simply stupid to call your risk anything but positional. You are putting on a position-- yes, it might be fucked up, but it is nevertheless a position because you can't hedge away the systematic risk.
The important thing when putting on a derivatives position then becomes-- who are the other people in this market, where are the bids and the asks coming from, and how can I exit my trade, either synthetically or physically, should an event occur which may trigger a need to sell? If there are one or two constituencies dominating the supply of bids and/or offers, you are probably looking at a market which will be vulnerable to a dislocation. Think GM and hedge funds. Think convertibles. These are where the potential profit opportunities may come from.
Last thought. Two equivalent securities are trading at different prices in different markets. Does this mean the market is stupid? Not necessarily in the slightest. It probably means there is a capital flow imbalance creating the difference in price. How can one re-align the prices of those two securities? By finding a way to transfer risk from the less liquid security to the more liquid security. Find some way to get capital flowing. If you can create a financial instrument which will get capital flowing into the less liquid security, more power to you- you will make your profit, and you will also have distilled/disaggregated/de-concentrated the risk of that security. The main risk I am referring to is liquidity risk, which goes hand in hand with hedging costs, the ability to hedge, tying back into the discussion of basis vs position risk. That is what derivatives can do for us more easily.
Final idea. CDS is an example of a market where, in essence, we the banking community are net short. Quite a bit. While we may be actively trading these instruments to some degree, it is arguably safe to say that as the primary issuers, we are net short the securities (please correct me if I'm wrong). We are short way more than there is notional for the underlying corporate bonds. Not only that, the underlying corporate bonds are illiquid. This touches on the final point, which is that derivatives trading is changing in some ways. There is credit risk to these derivatives. Financial instruments like CDS have become extremely liquid- why? Well, for one, we haven't really worried all that much about counterparty risk. Too complicated! But where has that counterparty risk gone? It is still out there, and it is a systematic risk. We cannot fully hedge these securities, no matter how hard we may try, so what will happen when (not if) the CDS market sustains a serious shock which makes clear to the world the supply demand imbalance?

On Trading Strategies, THeir Dynamics and How That May Change

Sorry I haven't been able to write too much. Finally on break so I think I'll jot some thoughts down which I thought were interesting. First I'll start with a couple claims regarding autocorrelation. "Autocorrelation" is nothing more than a fancy term to describe a particular dynamic that some processes follow, be they stock or bond prices, the ebb and flow of a government regime, or the performance of a class of trading strategies-- autocorrelation answers the question "when a stock goes up today, does it tend to follow that trend and go up tomorrow (positive autocorrelation), and does it revert to the mean and go back down tomorrow (negative autocorrelation)?" I posit the following: (1) autocorrelation exists when people aren't entirely able to detect and/or trade on it effectively or economically, for whatever reason, and (2) autocorrelation, once detected, tends to decline in absolute terms over time to a steady-state (and negative) level. There are some interesting consequences for where we are right now.First of all it's pretty much a moot point that detected autocorrelation tends to dissappear rather quickly. Our own Professor Mackinlay with Andy Lo detected positive autocorrelation within the S&P with a coefficient of around .3, which is huge, back around 20 or 25 years ago I believe. .3 means each move one day in percentage terms implied a move 30% as strong on average in the same direction the next day. However since then it's all but evaporated. A similar form of autocorrelation was later detected in certain industries... then it was detected in certain industries on intraday data. Arguably there is still some autocorrelation to be found intraday in semiconductor stocks (at least as of say 9 months ago). All getting arbed away.I bet that at this moment, the highest degree of autocorrelation exists broadly in 'trading strategies.' The performance of trading strategies themselves are at times very positively autocorrelated. It's something that we've all seen or at least felt to some degree, and it's been statistically detected for generic pairs trading portfolios. It makes intuitive sense, and up until recently, I'm not terribly convinced that the investment community has been able to take advantage of anything of this sort-- due to personnel risk, complications due to having multiple managers, inflexibility transitioning from one strategy to another, and personal bias towards certain skillsets relative to others by the person in charge. After building up a competitive advantage with a particular trading strategy, autocorrelation of trading strategies is the one killer which becomes almost impossible to avoid. All of these frictions in conjunction with one another make it very difficult to effectively "trade" trading strategies.My bet is that some of that may be changing now, or at least that it should, especially with the rise of fund of fund managers. Trading strategies themselves in a fund of funds context are becoming more tangible-- more like real assets-- because they have become so well defined. While diversification across strategies is great, I bet more aggressive effective flexible tactical allocation among strategies by a person very well versed with multiple unrelated strategies would have some pretty good juice to it. Multiple layers of performance fees can be a big problem, but I'm not sure anyone has as of yet been able to actually execute on this idea terribly effectively.Examples of positively autocorrelated strategies are numerous. Take for example convertible arbitrage. It isn't like their current problems just came out of nowhere... they've been around for a while, and they just got worse. More than that, their weakness then feeds on itself, as fund redemptions force funds to unwind their positions-- but of course their positions are probably more or less highly correlated to all the other funds out there in the convert arb space, so the unwinding of one portfolio naturally inflicts mark to market pain on most others. Another example is statistical arbitrage. I have a hunch that a class of traders may be next on the list... more on that later perhaps.I'll try to go one layer deeper. Note that there is a distinct difference between stating that trading strategies are cyclical and stating that trading strategies are trend following or positively autocorrelated. A cyclical industry is an industry which is in some sense both trend following and mean reverting at the same time. Cyclicality implies mean reversion over longer time horizons because no industry stays hot or dead forever. At the same time it implies trend following over shorter time horizons because success and failure tend to feed on themselves. In that framework then, I'm implying only one leg of the cyclical dynamic. I guess the reason is I'm not terribly optimistic that trading strategies in general will survive in the long haul. On a fundamental, some will live and others will die. Now I guess I'll bring up my example of a class of trading which I believe may diminish in importance to a large extent.I'm hesitant to believe that some forms of cash trading will remain around for much longer as well from what i've seen at my own desk and some of the others that i've seen/the people i've talked to. Hedge funds have the ability to lock up capital for 2 to 3 or more years and maintain that longer time horizon without having to worry about marking to market all the time. At banks though a ton of their trading simply doesn't have that flexibility. Very few traders are allowed to have that longer term outlook from what i've seen when things start to turn south. It raises an interesting question: when the primary activity of a desk, be it prop trading or market making, is to create really short term profits on a wide range of credits, is that a job that a large flock of cash traders should be doing in steady state? Or should it be a small handful of traders supported by computers and computer scientists? Some short term traders call it a battle of man vs machine on their desks, and some are saying the machines are making things a hell of a lot more difficult. Machines have that level of efficiency over short time horizons that is difficult to match both in speed and in scale by humans. Which brings back that old topic of quantitative methodologies vs qualitative-- quant shines with really high frequency data and with a large universe of liquidstocks on which to operate for obvious reasons. humans can't possibly absorb really high frequency data, let alone for 1000 stocks at the same time. high frequency data tends to work best over shorter time horizons, which implies that if we are to employ primarily qualitative methodologies, we may not want to be cash trading. haha. So yeah, trend following a agree with a lot when it comes to trading strategies. mean reversion i'll agree with sometimes (high yield being one of them... as well as deep value), but there seem to be a lot more exceptions. lemme kno what you think! -danny

Thoughts on Quantitative Trading, Again

Food for thought. First part is a lead in to a discussion of the surprisingly complicated question of what "good" analysis really is. In my opinion at least, to attempt to bridge the divide between true quantitative finance with qualitative, it helps to have a robust definition for what good analysis is, regardless of its origin. I attempt one at the end of this long winded piece.
Parametric complexity refers to the number of factors that are analyzed in the investment process. Various price processes are examples of factors, but so are more qualitative things like the weather, the number of buildings a company has, the quality of a CEO’s education or the tenor of his voice.
Depth of understanding refers to how deeply one comprehends a given factor in question. So rather than evaluating a thesis, model or strategy based on how many parameters were analyzed, this evaluates just how well one understands the parameters in question.
I’ll use option valuation as an example to better explain what I mean by these definitions. The Black Scholes equation is what many use to value an option, evaluating the option’s price with 5 parameters—the current price of the underlying, the current volatility of the underlying, the current risk free rate, the time to maturity and the strike price. So even though a stock’s price is governed by an infinite number of factors (fear, greed, sentiment, etc.), no arbitrage restrictions have reduced this plethora of factors down to just 5. This model is pretty sparse in terms of parametric complexity—I believe the reason it does so well has to do with the depth of understanding of the parameters used. Only by fully understanding just how the option’s value is derived from the cost of its replicating portfolio can you model its price in such a succinct way.
Depth of understanding is also responsible for the more advanced incarnations of the model. People realized volatility wasn’t constant so they found ways to model volatility.
GARCH can usually give a much better estimate of one-period-ahead volatility with only one additional parameter, the volatility of the prior day.
Volatility functions try to give better estimates with a couple more factors, like money-ness and time to maturity. People realized interest rates weren’t constant so they were also able to adjust for stochastic interest rates. These are all adjustments which add few new parameters and yet in some cases can greatly improve the estimate of the parameter in question. This is possible through a depth of understanding of the variables in question. No one can say what makes a successful quant (I definitely can’t), but at least from what has happened in the past, it seems like some of the biggest breakthroughs have come not through constructing an incredibly parametrically complex model, or vastly increasing the complexity of an existing model, but through reaching new depths of understanding of whatever process or processes you are looking at with a manageable parametric complexity. What would a deep value investor look at when deciding on whether to buy an option on a stock? I can guarantee you they will allocate their time in a completely different fashion, probably focusing more on what is driving the stock process itself. They will probably take in way more factors than would ever be healthy for a quant model—the difference in the number of factors is probably orders of magnitude in size. Even the IVF, which is supposed to factor in the seemingly obvious skew factor, empirically does little better on out of sample data than constant volatility! The depth of a manager’s understanding of each of the factors that go into that manager’s model is probably one of the big differentiators of quality among investment managers. Parametric complexity can only go so far before one runs into some serious problems. I’m not entirely sure that deep value investing has such a limit on complexity. The commoditization of many quant strategies may correlate with how parametrically complex the process is.
Ways to Evaluate Analysis:
Temporal Relevance: if one were to decompose the information given in an analysis into its component factors, what is the time horizon for the various factors? Is that time horizon so short that it isn't grasping all relevant information pertaining to that factor, making the analysis not robust? Is the time horizon so long that you are incorporating irrelevant information in your analysis? Keep in mind that the time horizon can be a group of disjoint sets, and is in no way limited to only one continuous time period.
Idiosyncrasy : If one were to decompose an analysis into its component factors, how idiosyncratic are the various factors? Can we get outright datasets for the less idiosyncratic factors to improve the robustness of the analysis? Might it be possible to create 'fuzzy datasets' of our own, using pre-specified classification rules and a large news database, for the more idiosyncratic variables? Could we make our analysis more "rich" by incorporating more idiosyncratic elements instead of strictly hugging the data? Finally, could we be placing an irrational amount of weight on idiosyncratic elements to make up for a genuine lack of numerical data?
Dimensionality: If one were to decompose an analysis into its component factors, just how many factors are there, and are we weighing our factors rationally? How sensitive is our valuation to each of our assumptions? Did we make sure to construct a full dataset for each factor? If not we again run into robustness issues. In general, the more factors you introduce at the same time, the greater the risk that you are witnessing a random permutation which just so happened to fit a relevant back-test.
Orthogonality: In our analysis, are we using the same one general line of reasoning the whole way through, or are we calling on a large number of distinct and unrelated factors (or sources of information for those factors)? The more unrelated our factors and their sources are, the better, because that means our conclusion is less sensitive to any one factor or source and our inferential ability could be higher.
Popularity: If you've found a factor which is important that other people either don't know about, or are weighing improperly, you have much to gain. However if everyone knows that your factor is important, then that factor ceases to be useful as an input for inferential purposes—the update happens too quickly. Once that happens you would then need to find factors which have inferential power over the original factor which other people either don't know about or are weighing improperly. So an important question to ask yourself becomes—if one were to decompose an analysis into its component factors, how popular are those factors? For the more well known factors, are their values themselves predicted using other factors which are perhaps less well known? For the less well known factors, are we sure they aren't less well known for a reason?
A Factors-Based Approach:
In the same way that two orthogonal unit vectors can form the basis for 2-Space, perhaps a substantial number of factors of various forms can form a basis for our prediction space. A factors-based approach makes some theoretical sense to me because the factors you create can be used over and over again for different predictions. Factors can also be used to predict other factors, should your original factors become very popular. I suppose the key driver of this approach is the belief that everything is interconnected. You will also probably end up as a market historian as well as a mathematician—I think the skill-sets of both complement one another. Btw, I would be interested to see that proof on high dimensionality without overfitting. Unless the explanatory variables are completely unrelated to one another on at least a couple levels, it doesn't make intuitive sense to me why I should be able to avoid overfitting.

Indexation

Indexation:
Arnott is a smart man. Finally got a chance to read through his unabridged articles and they contain some real gems. For instance, this is something to really sink your teeth into: "An efficient market in the pricing of individual assets, with pricing errors relatiz}e to true fair value, requires an inefficient market in the capiveighted indexes—and vice versa."
If one makes the assumption that there is some-- any-- deviation of stock prices from their true value, then it can be shown mathematically that market cap weighted indices will underperform other methods.
Interestingly enough, I'm going to see if I can take an opposing viewpoint to Arnott. I am not quite so sure that we necessarily must give up a valuation-based weighting schema for indices, unless the empirical mean reversion in the valuation component of company valuation is super duper strong. I think there might be ways to construct a more efficient index under this alternative schema.
I'm sorry if this entry doesn't make sense. Ask and I'll send the reference papers. One word of warning though, they are slightly complicated. Below is the commentary I've written up thus far.
----------------------------
Rob Arnott wrote an interesting paper in the March/April edition of the Financial Analysts Journal and I think he brings up some good ideas. I had some thoughts regarding his paper and a possible extension.

Arnott adds another layer of insight into the question of just what 'the market return' really is in finance literature. He cites CAPM as a somewhat valid economic theory which relies very heavily on what the assumed market return is. Some people posit that it's the S&P 500 return or some weighted average of past S&P 500 returns. His paper and subsequent articles dig into why some current assumptions (and Bill Sharpe!) are a bit silly. This is an important question because if the assumed market portfolio differs from the real market portfolio, our risk/return benchmark statistics will all be wrong, which is a bad thing.

Here are a couple key points I got from the paper, which may or may not be 100% accurate (please let me know if anything doesn't sound right).
To be completely theoretically accurate, the CAPM market index should be a measure of (1) the fair value of (2) pretty much all things which are able to be invested in, so that it's representative of the market as a whole. Finally, the CAPM market index is by definition mean-variance efficient.
Under the above definition, the S&P 500 return is a fundamentally flawed measure of the market return on two levels. First off, the S&P doesn't satisfy (2) above: "the simple fact is, the capital asset pricing model works if your market portfolio spans everything: every stock, every bond, every house, every office building, everything you could invest in on the planet including human capital, including the NPV of all your respective labors going into the future. There's no such thing as an index like that, it doesn't exist. So right off the bat you can say that the S&P 500 is not the market, and anyone who says that it's efficient because it is the market is missing the point: it's not the market." Second and perhaps more importantly, the S&P also doesn't necessarily satisfy (1) above either, because the S&P 500's weighting of stocks by capitalization maximizes the chance of having a 'fair value flawed' portfolio. Unless one believes that stocks do not fluctuate (even randomly and unknown to investors) from their fair value sometimes, then it can be more or less proven that cap-weighted indices will underperform over time. Below are a couple important points.
Price inefficiency, or deviation of stock prices from fair value, need not immediately suggest arbitrage! Suppose we merely know that some companies are overvalued and others are undervalued. We have no simple way to trade away this idiosyncratic noise in prices because we do not know which stock is currently overvalued and which stock is undervalued. Therefore this assumption is not all that crazy.
The cap weighting return drag thesis in my mind comes down to the following really cool statement: " An efficient market in the pricing of individual assets, with pricing errors relative to true fair value, requires an inefficient market in the cap weighted indexes—and vice versa."
The cap weighting return drag thesis may also at least partially explain the relative outperformance of value over growth, and of small caps over large caps.
It is valid to create a market portfolio indexed by more "fundamental" metrics instead of market cap if the alternative metrics can in some way remove the biases inherent in cap weighting schemes without introducing new risks or problems of their own. For example, one may weight stocks by some measure of historical free cash flow instead of market cap.
The kicker: a very robust sampling of 'more valid' valuation metrics consistently outperforms the S&P 500 in both returns and in risk control!

A number of points merit mentioning before I bring up one possible extension.
A market index is more 'valid' as a suitable CAPM market index if it can correct the S&P by underweighting the components which are most statistically likely to be overvalued and overweighting the stocks which are most statistically likely to be undervalued.
Rydex's equal-weight S&P touches in some way on this notion, but not entirely. Equally weighing all S&P components corrects for some of the bias inherent in the S&P's cap weighting, but it isn't perfect because it is in some ways blind to the "real" value of the S&P stocks.
Arnott brings up some interesting statistics regarding the performance of highest market cap companies as well as the performance of the top 10% of all companies on the basis of market cap in the S&P 500, and finds that there is a large and seemingly statistically significant probability that they will underperform the overall market over most time horizons. More than that, the expected underperformance is really big. He calls this a 'return drag,' and implies that this is what is causing the problems for cap weighted indices. He then offers valuation-agnostic metrics as a cure to the problem.

My possible extension:
Going Deeper Into Some of the Implications
Below are some of the implications which I think might be important but weren't satisfactorily covered in his articles (in my opinion at least).
First off the return drag he mentions is very striking but isn't 'clean' in my opinion. Market cap can be broken down into a more fundamental component like earnings or EBITDA and a multiple component like PE or EV/EBITDA. To say that high market cap implies mean reversion over some time horizon is equivalent to saying that high (PE and/or earnings) or high (EV/EBITDA and/or EBITDA) implies mean reversion—so which piece is it? To be cleaner, wouldn't it be better to analyze each component individually? Is it the earnings which mean reverts, or the PE? I bring up this specific way of decomposing market cap because Arnott's proposed solution implies the multiple component of market cap is the dominant mean reverter, because it is clear that all he is doing is weighting entirely off of the more fundamental component—earnings, EBITDA, cash flow, head count… these are all fundamental components. So why not do out the actual statistics on how much mean reversion there was in the components??? Doing them on market cap is nice looking but it isn't focused and 100% relevant to his proposed solution.
It seems that Arnott doesn't really attempt to correct for the implied mean reversion in the multiple. Instead, he throws out multiples completely and uses valuation-agnostic metrics, stating that his indices outperform the S&P. Does all this imply that it is not possible (or not economically worthwhile) to correct the market index for mean reversion in the multiple component? Where are the numbers?

So overall, I think that Arnott's papers are amazing and house some really crucial ideas. I also think that his proposed solutions are great, and correct for a lot of the inherent bias in the S&P 500. Furthermore the strategies used are extremely simple, which adds to the credibility of the underlying theory.

But that being said, it seems like he might be jumping the gun slightly by throwing out all information contained by multiples. By going straight off fundamentals, he seems to imply that multiples are irrelevant. But this is an inherent contradiction with his findings on market cap mean reversion. For example: suppose you have two companies, A and B, spitting out the same free cash flow this quarter. However A is valued at 50 and B at 150, implying that the multiple of FCF is higher for B than for A. Arnott's schema considers these two companies equal to one another. But Arnott himself admits that there is mean reversion in the multiple, so we could adjust for that by allocating more to A and less to B.

Thoughts on Quantitative Trading

Being able to identify homogeneity in the financial markets seems to be a driving concept when doing quant trading. Classification and homogeneity are two sides of the same coin-- if all securities in the financial markets were unique, all being driven by uncorrelated processes, it seems that you're shit out of luck. A useful classification is able to identify things which tend to trade the same way-- and of course when two things trade the same way, a proper long-short of the two leaves you with a nice stationary, mean reverting process (this, by the way, is the essence behind cointegration-optimal hedging and indexing). So let's assume for a moment that the goal is identifying homogeneity in some way, shape or form in the financial markets. Where the hell do you begin. I believe you begin by making the decision of whether or not to adopt an inclusive or exclusive paradigm. The inclusive paradigm, which seems to be the most popular (perhaps because it relies on the least granular information?), is to identify very broad trends in the market. For example, there may be tens of thousands of stocks trading right now, but if I were to bucket them into capitalization-based deciles, trends begin to form when looking at one-year-forward expected returns. In other words, broad-based homogeneity begins to surface. At that point, we may attempt to identify what we consider to be "the next best classifier," which would then split the deciles into subdeciles, each of which is then even more homogeneous. I bet a lot of people have made good money adopting this paradigm, and to be honest, it's the paradigm I personally have had the most experience with up until this point. But inclusive classification has many downsides which aren't entirely obvious. First of all, the sometimes extreme level of broadness makes it all the more difficult to identify what classifier is indeed the 'best'. Second of all, inclusive classifications tend to carry with them longer time horizons, which aren't necessarily able to be traded on by desks or funds which need strong enough mean reversion to ensure them a decent probability of success over shorter time intervals. That being said, there are some serious benefits to a proper long-short-based inclusive classification trading strategy. Most notably, the broader the set of stocks involved in the long-short, the less exposed you are (obviously) to the idiosyncratic risk which is so prevalent in equities. Maybe in equities, the nature of equities' idiosyncracy makes this the best paradigm to choose. But the same isn't really true of more quantifiable securities; especially fixed income securities. Take municipal bonds, for example. While it may be conceivable to construct a broad trading strategy around municipals, a ton of polluting factors make things more difficult. First of all there is the issue of liquidity (this actually exists with equities as well). Two securities may look the same and be structured in the same fashion, but if one happens to be less liquid than the other, the more liquid security in an efficient market should demand some sort of a premium. This would then require quantifying the bid ask spread. But that is a classification nightmare in and of itself, if one makes the assumption in the first place that there is some way to quantify it (and yes, there is). Next take the fact that bonds can be issued in any number of states, have all sorts of varying call provisions, bond types (ie. revenue, GO, double barrel, water and sewer, credit rating, insurance, ..., ). It's a fixed income instrument, but it has quite a few idiosyncratic elements. Broad categorizations inevitably fall into the trap of being too general. So rather than pursue the inclusive paradigm, the paradigm then becomes that of exclusion. That is, find on some truly granular level those securities which tend to be homogeneous in some fashion. Then (as long as your dataset is granular enough), peel off the layers of idiosyncracy from your generic set to other sets, quantifying the various credit spreads which should be applied relative to your reference rate (in the case of municipals, the municipal curve). It's interesting that these paradigms are so vastly different from one another. It's also interesting to contrast these lines of thought with that of value investing. Value investing seems to thrive on the idiosyncracy of individual stocks. And yet that is what in some ways kills quant strategies.

Information Flow (April 24th 2004)

Information Flow is an extremely powerful and important concept. There are many forms. We absorb and give off information constantly. Being in the "inside circle" is simply being in near a valued information source.
To become powerful is to find and hang around good information sources. Most industries are almost completely information run. If you are "in the know," it is infinitely easier to be at the top. Take advantage of asymmetric information. Leverage it. Harness it.
Information dissemination can bring people up and tear them down. The world runs on information. With a proper information distribution system, some things are inevitable. Bush may experience this firsthand in the coming months.

CAI analysis (Snapshot trade on May 29th 2004)

Well guys I'm putting on my value investor hat, so watch out... today I'm looking at CACI (ticker: CAI). First I go through who they are and the general industry they are in. Then I look at trends and bring them into perspective in light of recent events.
To put it simply, CAI is a contractor for the government. The company is among the largest government information technology contractors, providing a wide range of services including systems integration, network management, software development, and engineering and simulation services. CACI also develops marketing software and databases for sales tracking, demographics reporting, and other market analysis applications, and it provides debt management and litigation support services. Contracts with the US Defense Department account for about 64% of its annual revenues.
While on the topic of revenues, lets take a look at the numbers. Sales is growing.
The story is pretty clear: topline growth because of the war in Iraq-- new contracts.
Growth is expected to continue going forward. CACI has plans to reach $1 billion in revenue in 2004 so it can better serve large clients such as the Department of Defense, which is increasingly trying to do business with a smaller number of large contractors. The company plans on joining that select group by growing through acquisitions and by making technology services a high priority.
Two of CACI's main clients are already part of the Department of Defense: the Defense Information Systems Agency (DISA) and the US Army's Communications-Electronics Command (CECOM). CACI also holds a significant GENESIS II contract with the United States Army Intelligence and Security Command (INSCOM). In addition, civilian agencies such as the Department of Justice (CACI staffs its litigation support services and maintains an automated debt management system), the Department of Veterans Affairs, the Securities and Exchange Commission, the Space and Naval Warfare Systems Command's Naval Tactical Command Support System, and the US Customs Services drive a large portion of CACI's revenues.
CACI acquired intelligence contractor Premier Technology Group, Inc., or PTG, for an undisclosed amount in mid-2003. PTG had revenues of $43.4 million in 2002. Most of its 360 employees hold high-level security clearances and are experts in intelligence analysis, information technology and security services, and logistics. CACI picked up some of the juicier government contracts through this acquisition.
Growth catalyst: Military aptitude (or lack thereof). I like CACI's industry, because frankly I don't see war going away anytime soon. However this fact by itself wouldn't mean much for government contractors. What makes contractors promising is the fact that government needs their help. Since the gulf war the government has been steadily increasing the amount of non-military related outsourcing it performs to: (1) cut costs, and (2) make up for the general diminution in military strength. (1) is highly debatable, especially in light of wasters like Halliburton and KPR . However trend (2) is real. So in come companies like CACI, responding to the increased demand for their services.
Present situation:
So now we zoom to the present. The company came under fire in early 2004, when CACI employee Steven Stefanowicz, who worked as an interrogator at the Abu Ghraib prison in Iraq, was accused of participating in the abuse of prisoners held there. CACI manages various facilities for the US Army under a blanket purchase agreement inherited when it acquired Premier Technology Group in 2003. When the scandal broke out in May 2004, various government agencies, which together oversee the contract, launched an investigation to determine whether CACI should continue to assist the US Army in placing new interrogators in Iraq. The results of the investigation will determine if CACI will be able to fulfill and collect the approved $66 million funding for the blanket purchase agreement. The company had collected $16.3 million when investigations started.
Now from what I've read, the stir over Stefanowicz isn't the issue, CACI isn't vulnerable over this. It is vulnerable because it had an IT contract with the Interior Department, and yet ended up in Iraq doing interrogations for the Army. Does IT have anything at all to do with interrogations? Frankly, no. Technically, what CACI did was illegal.
So what is going to happen?
-- First, hypothetically lets say that CACI loses its government business-- is there anyone who could replace them?
Were CACI to be fired, from what I’ve read it would be unlikely for other companies to enter into the interrogation line of business too easily. Titan, another of the big interrogators-for-hire, was also implicated in the Abu Ghraib snafu, so I doubt that they would be eligible as a substitute. Other companies could substitute CACI’s other legal contracts though, if the government decided to take away all of CACI’s contracts.

This is the other thing that was passing through my head as a read some of these articles—people were surprised as hell at the sensitivity of the tasks that private contractors like CACI were doing. Contractors for the gov’t routinely provide little information on the nature of the contracts it has with the gov’t, and sometimes can’t even acknowledge that certain contracts exist. This means two things: (1) There is good potential hidden upside for the private contractor industry, in the form of classified contracts, and (2) the companies which are now working with the gov’t on sensitive activities (ie. Interrogation) will naturally obtain classified information. The obtained classified information should create some good lock-in with the gov’t for future deals, and general leniency should the companies go on trial. You don’t want a large number of private companies to be walking around freely with classified information.
--Could the military take over what CACI employees were doing?
While the gov’t could possibly try to replace private contractors with army guys, it’s unlikely. The army is coming to the private companies and not the other way around b/c of (1) big need to keep costs down and be more efficient and (2) lack of manpower, general weakness of the military. (1) is debatable and might not leave CACI in a defensible position. The company is making a shitload from those guys. However trend (2) is here to stay. The government needs help badly, that’s why it’s outsourcing so much. I also think this may push the trial towards the lenient side, especially in light of the above point concerning CACI’s current stockpile of classified information.

-- An extra little tidbit:
One of the articles I read mentioned something interesting—“due to a loophole in prosecuting law, it may be difficult to pursue the contractors in court. The 2000 Military Extraterritorial Jurisdiction Act applies only to Pentagon contractors.” CACI is an Interior contractor, so some of the more snappy laws don’t apply to it… could come in handy.


I see Martha Stewart-like politics being the biggest potential downside risk for the company.

Short term: In general I see a 5% up movement as pretty darn reasonable, even assuming some shit does happen. There’s a general consensus among analysts that the recent situation shouldn’t affect the company’s long-term prospects, which gently implies to me that this downtrend might not carry its own weight for an extended period of time (the stock has dropped around 14% in teh past two days alone).

Long term: I see growth here as long as they don't lose business in Iraq.

Oh, and the chief executive bought $380k of the stock the day the stock initially went tumbling down, at 38.306. He increased his holding by 33%. It's now at 37.14.

My two cents.

Decomposition, Applied. A Few Thoughts

I was poring over a set of 10K’s and 10Q’s to prepare a financial model when I started thinking about how inadequate it was. Many if not most of my thoughts are… imprecise and inaccurate. Thoughts have a tendency to carry a lot of underlying thought baggage.

Obviously the point of a financial model is to forecast a company’s performance going forward, usually for the next year or two. So here I am examining the company’s trends associated with its revenue, cost of sales, SG&A… that’s all of fairly limited value.

Thoughts should be decomposed. Revenue goes up and down, but revenue is an umbrella term which is simply the stitching together of multiple underlying revenue streams. The underlying revenue streams are of course the company’s various lines of business. In my case the company had three main segments: ambulance sales, bus sales and construction truck sales. However even these individual revenue streams can be decomposed. The ambulance segment for example is simply a stitching together of a bunch of ambulance product lines. Doing this drill one more time, each of the various product lines can be decomposed into all the factors which affect the product lines.

So now instead of looking at one number, “revenue,” we’re looking at, say, 250 numbers, each of which represents the various factors which affect the sales of the various products the company sells. Imagine repeating the same drill for cost of sales, SG&A, depreciation and amortization, … you can see how assessing the performance of this company is actually very, very painstaking.

But now we can finally start thinking for real. How will interest rates affect this company’s business? Well since the company manufactures its own chassis for its ambulance, bus and truck lines, one can get started by assessing how much interest rates will affect each group individually. How will a change in the value of the dollar affect the company’s position? Well a good portion of the company’s construction truck business comes from exports, as does ambulances, but to a lesser extent. Buses aren’t affected very much at all by such matters. You can see how each of the stimuli is being systematically thought through on this underlying level. Each of the stimuli affect the factors, which come together to affect the products in the product line, which come together to affect the product segment, which come together to affect the company’s revenue.

So you want to forecast the company’s earnings for the next four quarters? I’d start by seeing how each of these decomposed units will be affected by stimuli. Then I’d look for trends in the data which may point to the occurrence of some stimuli over others. Such as the coming rising interest rate environment. I’d work out how changes in the value of the dollar will affect the company. I’d examine how much competition there is in each of the segments, and if it will perhaps crunch that unit’s margin going forward. Is the company’s position pretty defensible? So lets say it is, and lets say you assume that unit is on a certain growth trajectory. Great, now what.
What will happen to cost of sales in this case, and SG&A? Which costs are fixed and which are variable? In other words, how much sensitivity will the costs have to the top line growth?

In other words, we’ve gone from examining a company at one instant in time, to examining a company in motion. With motion comes the notion of stationarity. But that’s a whole other story.

For now, I’d conclude by saying this. It’s good to think about very high level concepts. It’s just that a lot of thought is necessary to break down the high level concepts, so that one can think and assess the concepts accurately. The first step to understanding complicated issues it to acknowledge the issues as complicated in the first place, and to begin decomposing.

For myself, I can’t forecast where I’ll be in a year because I not only haven’t thought about it properly, but also there’s a lot of it which I can’t control. One low level concept I do know, though, is that adequate sleep will leave me feeling better rested and alert than inadequate sleep. And I need to be alert tomorrow so that I can finish that model.

Intellectual food for thought, major notions proposed in Fooled By Randomness, a good book.

--We are subject to hindsight bias--the "I knew it all along" bias--so that past events will always look less random than they were. While discussing our past, for example, we tend to backfit explanations concocted ex post. We create reasons for why certain events occurred ('this happened for so and so reason, b/c I was this and that, which led to...), choosing (subconsciously?) not to accept the fact that chance may had at least some part in spurring on the event. Were we successful because of skill, or b/c we were lucky?
My solution: before making a decision, write down what decision you are making, and most importantly write down why. Write down what you would do under the various possible future states of nature, and if the future surprises you in some unexpected way, sell, get out, write down what surprised you and why. See what effect that surprise has on the stock, and attempt to incorporate that new possibility into your next decision. It is hoped that the reasons why you made that decision, if correct, will cause you to reach your expected conservative estimate of what will happen in the future. If they don't, then perhaps you will need to readjust your expectations on a more fundamental level.
--It is difficult to apply probability to real life-- unlike a gambler at a roulette table, mother nature doesn't tell you how many holes there are on the roulette table, nor does she deliver problems in a textbook way. In the real world one has to guess the problem more than the solution.
My solution is to make an active effort to conjure up the various possible states of nature, and then to assign probabilities to each. Erring on the side of caution is probably the best course of action. This notion is analogous to Graham's margin of safety.
--Risks are not good in and of themselves-- An example of naive empiricism-- the author of "the Millionaire Next Door" looked for traits that many millionaires had in common and figured out that they shared a taste for risk taking. Clearly risk taking is necessary for large success-- but it also necessary for failure. Had the author done the same study on bankrupt citizens, he would certainly have found a predilection for risk taking.
At the lower level, it is clear that risk in and of itself is not good. The effectiveness of risk is a function of the downside risk, the upside potential, and the underlying probability distribution for the various states of nature. So for every decision we make, there will obviously be only one final outcome (ie. I have made a profit of $1,000 off of that trade). However that final outcome means very little-- it is the product of only one state of nature. The "real" outcome of that decision is the sum of the outcomes under all possible states of nature, weighted by their respective probabilities discounted for volatility. An interesting point, though, is that it is easier to think of possible states of nature ex ante-- after the event has taken place, it is very very difficult for us to look at the past and examine all the other things that could have happened.
At the higher level, 1) we need to look not only at the characteristics of winners-- we also need to look at the characteristics of losers. 2) 'Necessary' qualities of winners does not imply causality, that certain qualities will necessarily cause winners to come about. 3) Finally, it's probably a good idea to get "the whole picture" before coming to a conclusion regarding the effects of certain qualities. Before I make the assumption that risk-taking is a good thing, I would like to examine its correlation to everything which has an impact on me. I would examine its correlation to financial success and failure, as well as emotional side effects. Finally, I would seriously consider whether risk-taking is right for a person like me--given that I am who I am, given that I have certain personality traits, how do the odds of financial and emotional success and failure change?
--Our assessment of risk is flawed even on a fundamental biological basis-- it is a fact that our brains tend to go for superficial clues when it comes to risk and probability, and these clues are largely determined by what emotions they elicit. Both risk detection and risk avoidance are not mediated in teh "thinking" part of the brain but largely in the emotional one (the "risk as feelings" theory).
This is a bit harder to control for, but to know of this fact's existence alone is a good thing. All we can do is strive for objectivity in our decision making and risk assessment processes.

Thoughts on Fooled By Randomness

"I believe that the principal asset I need to protect and cultivate is my deep-seated intellectual insecurity. My motto is "my principal activity is to tease those who take themselves and the quality of their knowledge too seriously."" --Nassim Taleb
I begin with a look at black swan dynamics.
A black swan is an outlier, an event that lies beyond the realm of normal expectations. Most people expect all swans to be white because that's what their experience tells them; a black swan is by definition a surprise. Nevertheless, people tend to concoct explanations for them after the fact, which makes them appear more predictable, and less random, than they are. Our minds are designed to retain, for efficient storage, past information that fits into a compressed narrative. This distortion, called the hindsight bias, prevents us from adequately learning from the past.
a)
So for starters, because we have a tendency to consider many elements of our past with more causal links, more narrative attributes, and less randomness than had actually existed at the time, we effectively are doing two things. One, we are tricking ourselves, because there are many circumstances in which the causal links we 'create' are simply false-- they aren't actually there. Therefore two, because there is a disconnect between perception and reality, we are misjudging what we know. In other words, we are misjudging the quality of our knowledge. This is one aspect of Taleb's statement.
b)
"Lucky fools do not bear the slightest suspicion that they may be lucky fools-- by definition, they do not know that they belong to such a category. They will act as if they deserved the money. Their strings of successes will inject them with so much serotonin (or some similar substance) that they will even fool themselves about their ability to outperform markets (our hormonal system does not know whether our successes depend on randomness)... Scientists found out that serotonin, a neurotransmitter, seems to command a large share of our human behavior. It sets a positive feedback, the virtuous circle, but, owing to an external kick from randomness, can start a reverse motion and cause a vicious circle. It has been shown that monkeys injected with serotonin will rise in the pecking order, which in turn causes an increase of the serotonin level in their blood... Randomness will be ruled out as a possible factor in their performance, until it rears its head once again and delivers the kick that will induce the downward spiral."
The point is that random events, good or bad, have a suboptimal effect on our behavior which we cannot control. Because our bodies have great difficulty differentiating between a good stimulus having been caused by our own ability or by randomness, we unconsciously pump ourselves up when there is no logical reason for it. Undeserved confidence in one's abilities is dangerous. Our perception of our ability to perform certain acts changes to incorporate the newfound confidence. Thus when we perform those acts the next time, we subconsciously increase the odds with which we will be believe we will be successful at what we are doing, when in fact the odds should remain the same. In essence, we have subconsciously increased our perceived self-aptitude at performing that task-- we have subconsciously (wrongly) increased what we believe our knowledge level is. This point is another angle at which Taleb discusses the 'quality of knowledge' in his motto, because again there is a disconnect between personal perception and reality. It also highlights the correlation between the seriousness with which we treat ourselves, and the quality of the knowledge we possess.
When making decisions which require us to make intelligent guesses at what will happen in the future, it might be helpful to keep a few things in find. The first have to do with the points mentioned above-- any source of information or any assumption we lever to make a decision should be vigorously tested for its quality and validity. We should only very reluctantly believe anything as being a certainty, simply because there are so many cards stacked against our making an optimal decision. We shouldn't overly rely on past information, because each event which happened in the past was one of countless other possibilities.
Counterintuitively, the most important test of whether or not our decision was indeed a valid one is not what ended up happening as a result, because that result could have been one of any number of other equal or more possible other results. The most important test is how intelligent that decision was in the face of all information that one had at that point in time-- the optimality of that decision is a function of its expected value, factoring in all other possible future states of nature, and its variance when compared to all other decisions one could have made at that point in time.
To shine some light on this, consider the game of russian roulette. Lets say that a man hands you a revolver with one bullet in it. The rules of the game are as follows-- if you fire the gun at yourself and do not die, he will give you a million dollars in cash. If you do die, well, sorry. Lets say the man accepts, fires the gun and gets lucky. He is left with a million dollars, but his decision was obviously not the optimal one. We know that because we know all the rules of the game; the risks, the payoffs, and the underlying probability distribution. [The thought process going into the decision is called the 'generator.'] The whole point is that in real life, we don't know all the rules of the game. We don't know all the risks, the payoffs, and the underlying probability distribution because there are so many factors involved that it would be impossible to incorporate all relevant variables into a rational, optimal decision. So when we look back on historical events, we see the end result (the man getting the million), but we almost never are able to see the generator. Without knowing all the other alternative histories, we must be very very careful when making a decision now because it worked some times in the past. We can, and often will, end up with the metaphorical bullet in our heads because of an over-reliance on past data and an underappreciation for the only thing which really matters-- the generator, the search for the rules of the game.
One final thought while on the subject of using past data to draw inferences on the future: survivorship bias. Survivorship bias is another reason why we must be very careful when drawing on past data. I'll go back to the example of the authors in the book "The Millionaire Next Door" citing that risk-taking is a common quality shared by many rich people. The authors then imply that risk taking is a good thing; it is something we may need if we want to become rich ourselves. The natural reaction when testing this claim is to get an estimate of how many people are risk takers, and how many of those risk takers are rich. We can then reach some conclusion about the probability that a risk taker will end up rich.
There is one flaw to this measure of probability though. What it doesn't take into account are all the people who were risk takers, but through their excessive use of risky policies, went bust and cowered away into obscurity. All the real losers won't be taken into account in our statistic, because only the winners have survived up until this point.
One can see that the proper way to run this test would be to find all the people, rich and poor, who are risk takers today, and see where those very same people are in 10 years time.
But we can't really do that with history or historical information. Do most risk takers end up rich? Or did all the risk takers who didn't make it go bust, so that there weren't many "losing" risk takers left by the time the test was done?
The whole point is to be very careful about what you consider to be true. Chance plays a larger part than we tend to think, and there are numerous biases we have and we are subject to which will cause us to be swayed from what is indeed true.

More to come on black swan dynamics, which are profoundly interesting.

HTV-- the next MWY? (Aug 30th 2004)

The essential characteristics of MWY’s story—

The company was in a losing position. It had been losing money for 5 years, and wasn’t well followed.
Sumner Redstone had been buying for 9 months, raising his stake in the company from 30% to 75%. He decided to buy all of his shares in the open market instead of tendering, which was odd. His actions only recently really became very noticed—looking into a database of news articles, it seems the first was written in April. So five months of buying went without much mention. Finally, looking to the transcripts of the conference calls, the CEO of MWY was very reluctant to shed any details. In the Q4 earnings call (which was held in February) made no mention of Redstone. Even in the Q1 conference call, when people asked questions about it, the CEO provided no answers at all. The price had gone from 2 in November to a high of 13 in July as a result. This move has inflated the company’s valuation metrics above the industry average (MWY’s EV/EBITDA is 22 while that of its peers is in the mid teens). It has also brought in the short sellers, because the fundamental underlying value of the company is undoubtedly lower than the current value. Short sellers now account for approximately 30% of the outstanding shares.
To take the company private or do a related transaction, Sumner needs 80% or more of the company’s stock. He seemingly reached this point, but in a surprise twist, the company disclosed that it had another 12mm more shares than it had previously disclosed. So he continued to buy.
HTV

Financials
Not much top-line growth at all. Revenue has been about the same for 5 years in a row after a ramp up period (1999 to 2003, in $mm): 661.386, 747.281, 641.876, 721.311, 686.775. Seems sinusoidal, doesn’t it?

However margins have improved dramatically over the past 2 years. After a multi-year period of low profit margins [(1999 to 2001, $mm): 4.89%, 6.01%, and 4.84%], margins jumped to 14.98% in 2002 and 13.72% in 2003. In general, margins are very nice right now. The EBITDA margin is at around 50% because HTV has very low operating costs.

Debt has gone down by about 25% over the past two years or so. Finally, the cash position has been rising steadily. Two years ago, the company only had 4.359mm in cash. Starting a year ago, it started to add to its cash position very heavily—5 quarters ago, cash stood at 7mm. It then tripled to 21.85mm, then tripled again to 71.53mm. Since then the cash position growth has leveled off, jumping to 116.7mm two quarters ago and 138.1mm last quarter.

Company Analysis

General
Hearst-Argyle Television is one of the country’s largest independent, or non-network-owned, television station groups. It manages 27 television stations reaching approximately 17.8% of television households in the US.

This is how the company makes money. The company gets the rights to broadcast certain TV shows and news reports on the channels that it owns. A large number of those channels which HTV owns are local. So it puts on its shows and tries to get people like us to watch them, which is of course contingent on a number of factors, but the main ones which the company can control is the quality of the TV shows it puts on and the quality of the news broadcasts. It receives advertising revenue from major companies (25% of its revenue is currently from auto manufacturers, however it also receives a large percentage from retail, some from pharmaceutical companies, as well as political advertising both local and national, among others). Obviously HTV wants as many people watching its shows as possible, because the amount of money and the general demand for HTV’s advertising spots will depend on two things mainly—the demographic watching the shows, and the total number of eyeballs. This accounts for over 90% of the company’s revenues.

Programming
It gets those programs in a number of ways. (1) It sets up agreements with networks like NBC and ABC to broadcast those network’s shows in exchange for the right to sell some of those ad spots. This is called a network “affiliation agreement.” It’s a symbiotic relationship. These transactions are called “barter and trade transactions.”

(2) It must compete for non-network programming, which involves haggling with national program distributors or syndicators that sell the types of shows which HTV buys, called “first-run (like the Oprah Winfrey Show)” and “off-network” packages, and “off-network reruns (like Seinfeld).”

HTV’s competitive advantage is its strong news offerings. Lots of people watch them apparently, as they are highly ranked and command a premium for the ad spots. HTV is weak during prime time. So its ad spots are much cheaper there because of the lack of demand.

Competition
Cable-originated programming is becoming a bit more prevalent. Made-for-cable programming has been gaining market share over the past year or so. This is an alternative to HTV’s broadcasting.

Also, of course because HTV touts itself as one of the largest non-network-owned TV station groups, networks are competition. HTV currently has network “affiliation agreements” with most of these companies and has had the agreements for a while now, but there is no saying that the networks won’t turn on HTV if the payoffs were right. The terms of the affiliation agreements was stated above—HTV gets network shows, network gets the right to sell some of HTV’s ad space. It seems like the networks have been playing off this point already. They used to compensate HTV for the broadcasting of network programming—but this is coming to a halt. Also, there is no saying that the networks won’t cut off agreements once the contracts run out.

Direct broadcast satellite (‘DBS’) programming is the final threat, which I think has the potential to be the worst. EchoStar (DISH Network), and DIRECTV, which transmit programming directly to homes equipped with special receiving antennas, bypass HTV entirely. Those customers don’t watch HTV’s broadcasts, they watch the dish network’s.

Cyclicality, Seasonality
Highly cyclical business. A quarter of the company’s revenue is coming from auto manufacturer ads. Things may be swinging in HTV’s favor right now, but that is not to say they won’t in the future. I get the impression that a recession would hurt this company very badly.
HTV is also seasonal. It has seasonally stronger first and third quarters. It also experiences higher sales in the even years because of political elections and the Olympics.

The Current Situation
The company is doing well, aided by double seasonal effects and a semi-cyclic upturn. It is an even year, it was the first quarter, and auto manufacturers have started to increase their ad spending to market new model cars. The company says organic growth will be driven by macro-economic factors, which leaves a bad taste in my mouth.

The last quarter basically had a revenue increase of 18mm on the prior year. 9mm of that was from political revenue (seasonality). The other 9mm can be further broken down into 5mm which was lost last year due to the Iraq war. So this means only 4mm came from the company’s core business—and remember, most of that must have come from the auto segment. There’s some doubt that the company will be able to keep its costs in check, sonsidering how much it may have to spend to provide adequate coverage of the political events coming up. In general, I am not impressed with the underlying fundamentals of the company and think there isn’t an adequate downside risk for me to make a trade.

I have gone into the “going private scenario” fairly in depth in the document below on HTV’s situation.
Hearst-Argyle’s Situation—

Hearst-Argyle Television (HTV ), spun off in 1997 by media giant Hearst, has been on the ropes since January, when it traded at 29. Now at 23, guess who is buying stock? Hearst itself. Since April, Hearst has bought -- through its Hearst Broadcasting unit -- 1 million shares of Hearst-Argyle in the open market, bringing its total stake of Class A shares to 35%. Hearst-Argyle owns 25 TV stations and manages three others, reaching 18% of U.S. households. The company also manages two radio stations. "It's one of the largest non-network-owned groups," notes Amy Glynn of Standard & Poor's (MHP ). Hearst Broadcasting already owns 100% of Hearst-Argyle's Class B shares, whose holders pick most of the board. These buys have led some hedge funds to buy, too, in the belief Hearst will take Hearst-Argyle private. They note that Cox Broadcasting recently said it would go private at a 16% premium to its stock price. Meanwhile, Hearst-Argyle has also repurchased 180,000 shares this year. Sean Butson of Legg Mason (LM ), who rates the stock a buy with a 12-month target of 35, sees earnings of $1.30 in 2004, up from 2003's $1. Both companies declined comment.

Analysis—
So this company is also on the ropes, as was MWY. The buyer, media giant Hearst, has an obvious direct relation to HTV, which probably increases its chances of being taken private because the integration would probably be more smooth. It would definitely be an odd move for Hearst, because it would be essentially reversing its decision in 1997. It does call the shots on votes though, because of its large ownership of the class B shares. HTV’s share repurchases also shine favorably on the probability of HTV’s being taken private. MWY didn’t have share repurchases, to the best of my knowledge. MWY might have been trading at relatively “cheap” valuation before, but not really. It was cash flow negative with negative earnings and negative EBITDA. HTV seems to be in a better position financially, which I think would be a plus. It has an EV/EBITDA of 8.45 and a P/E of 21.13. It has huge margins. Profit margin is 15%, and EBITDA margin is around 50%. It trades at from 5.5 to 8 times free cash flow, which (at the lower end) is good considering that this company has a market cap of 2.3B.

The underlying situation is better than it was, and the company is currently doing well, but seasonality and cyclicality make this a risky investment from a value standpoint. I’d like a better idea of the environmental situation.

I think this situation looks more similar to what is currently happening at TROY. TROY, a family run company, has owners controlling 67% of the outstanding shares. The stock had been languishing (what a strong common trend!). It is alleged that management is purposefully keeping the price down so that it can take the company private at a low valuation. TROY is a good value, attracting the likes of value investor Whitney Tilson. However it seems like HTV has a stronger financial position than both TROY and MWY. HTV has very wide margins; EBITDA, and profit. It trades between 5.5 and 8 times free cash flow. TROY has a trailing P/E above 40 and an EV/EBITDA of 19. TROY and

HTV diverge on the cash trend also. TROY used up a great deal of its cash four quarters ago, dropping their cash position from 8mm to 1.7mm. HTV’s cash position went from 4.5mm to 138mm. It was a debt laden, low cash, lower margin company with lower revenue. Over the past seven years, it has knocked off some debt (I believe), increased its cash position, expanded margins and brought the top line to a level it has maintained for five years. It indicated in its conference call that this is most likely because it intends to acquire another company, or do a major deal, in the near future. Regulatory issues are holding up HTV’s ability to do anything at the moment, so if those problems get squared away, then HTV will go and act. I don’t like the sound of that. That will knock away their cash position once again, and they will probably be at a higher leverage ratio like before. Also, I’m not sure how this factors into the probability of HTV’s being taken private.

TROY tells a different story though. It wants to take itself private (management is taking the company private, not an external company). Secondly, it is being pursued by Westar Capital, which wants to acquire the company and pay a premium on the price. Cash is well-known to make a company an attractive target of an acquisition, so a logical reason for the diminishing cash position could be as an acquisition deterrent. MWY is interesting. A year ago it had around 60mm. It then burned around 20mm, and had its cash hand at around 40mm until last quarter when it added 100mm to its cash position. It was truly against the ropes. It wasn’t talking about acquisitions, it was simply floundering.

Finally, Hearst filed with the SEC its intention to buy up to 20mm shares of HTV in the open market. As of the end of 2003, it had purchased 19.3mm of the 20mm. After the recent spate of buying, it has 20.58mm. In other words, it has gone above the limit. I am not sure what this could mean, but I would tend to think it means something. This and the industry consolidation trend interest me. The rest of the situation doesn’t. It seems to me like making a trade on this would expose me to too much risk so I’m staying on the sidelines.

A Few Thoughts on the Art of Forecasting, Reference to 'Fooled By Randomness

To sum up the relevant facts from Nassim Taleb's 'Fooled By Randomness'--
-Traditional statistical inference is severely marred by the presence, the prevalence, and the staggerring effect of rare events, aka black swans. The example I used was an individual picking balls out of a container one by one to determine the underlying distribution of the balls. Knowledge acquisition creeps up so slowly as to be almost useless.
-Try to avoid biases. Trick yourself if necessary. If we get too caught up in "noise" we diminish our ability to see what really matters-- the bigger picture. Try not to take action until you feel you have done your utmost to gather all the relevant information you deem necessary. Once you are finished, take note of what you know, and most importantly, what you don't know. Try not to get 'married to a position'-- if information presents itself later which goes contrary to your thesis, be prepared to toss away your position entirely. Avoid the temptation when in a bad trade to wait until you break even-- admit your mistake and move on. Try to avoid getting sucked into herd-like behavior. Try to acknowledge the randomness in trades which ultimately work out.
-Watch out for deceiving statistics. The example I gave was that risk taking is not in and of itself a good thing.
-When analyzing historical information, look to the generator, not the result. The two are completely distinct. Try to get a feel for what the possible outcomes were and the probabilities and payoffs associated with those outcomes. If there is a terminal probability, a probability that you will lose or die or something equally bad, stop. It will inevitably happen.
So in this context I believe we are in a reasonable positition to make a rational forecast of the future. I believe forecasting is a two part game.
The first part of the game is gathering as much historical information as is possible from as diverse a library of knowledge as you can find, then distilling that information into a usable form and forming an opinion based on that. It is a large scale inference, basically, which can be decomposed into qualitative and quantitative elements. Essentially what one has done is look backwards to project forwards. This is powerful of its own right, and can probably do well over most short time horizons, but it is still very vulnerable to possibly lethal rare events.
The second part to my general methodology attempts to correct for the vulnerability of the first. I would try, to the best of my ability, to flush all historical information out of my head. I would look very hard at the company's business model, industry, and upper management and simply throw out all scenarios I can think of related to anything affecting all three. I would not constrain myself to the realm of possibility or rationality. The whole point is that black swans cannot be thought of rationally beforehand. Once all ideas have been thrown on the table, I would analyze the repercussions of the underlying scenarios. Basically, what are the payoffs associated with those scenarios? I then sort the list of scenarios by increasing payoff and go through the list one by one. I would then look for weaknesses-- how can the bad scenarios actually happen? Then I would find ways to counter the plug the dam-- to counter the weaknesses.
As an example, consider 9-11. It was a most tragic black swan. However because it has never happened to us in the past, it was pretty much out of the scope of normal possibility at the time-- I doubt almost anyone thought such a thing was possible. The whole point is that the ideas are almost by definition deemed crazy ex ante. The second step might be vague, but something along those lines seems to be the only way we can expect the unexpected.
If anyone has any thoughts I'd love to hear them.

Thoughts on a Variant of Information Cascades; Examples; Relationships to Hedge Funds

When disaster strikes, all correlations go to one. Why look at information cascades only? Situations may cascade as well. For example, private equity firms and many hedge funds frequently use large amounts of leverage. The pain inflicted on them by losses and by rising interest rates is not really a linear one. Once a hedge fund, for example, loses a certain amount of money it will probably need to de-lever to hold steady its target leverage ratio. Where will it get that money from? From its existing portfolio. Should the company need money enough, it doesn’t matter whether the stocks in its portfolio are good or not. The fund will need to liquidate in either case, because it needs the money. Stock sales by one fund will have little impact on the overall market, but if the market turns on a wide enough base of funds (it has a tendency to do that), and a decent number of funds induce selling pressure in an effort to de-lever, the market will decline further. As the market declines further, all those people out there with long positions will again take a beating, and once again the funds are faced with rising leverage ratios—a potential vicious cycle has been created.

Putting on the forensic hat, one can notice similarities between cascading situations. Most notably, cascades form when the support which has fueled your gain will not be there to support you in loss-- cascades typically have weak support. Leverage is a weak support. And there is widespread leverage in the marketplace today, especially due to the prevalence of hedge fund on funds, which have multiple layers of leverage.

It would probably be very profitable to identify situations in which cascades have formed, because these are the situations which have the potential to spiral out of control in a logical, pseudo-predictable manner. They are usually situations which over shorter increments follow a linear pattern, but past a certain threshold, become non-linear.

Adding distinctions to the ACF

The ACF we use assumes a form of linearity. For example, we can look at the lag one autocorrelation of a stock, assuming that the stock follows an AR(1). The return today in this model equals rho times yesterday’s return plus some epsilon. To calculate that rho we use the method of moments, multiplying the above equation through by yesterday’s return. When we take the expected value, the epsilon term goes to zero. We are then left with the expected value of yesterday’s return times today’s return is equal to rho times the expected value of yesterday’s return squared. For example, for the expected value of the return at time (t-1) times the return at time t, simply take the time t demeaned returns times the time t-1 demeaned returns, sum up over all T data points and divide by T. The ACF doesn’t make any distinction between large price fluctuations and small ones—all data in the return series is weighted by T; no more no less.

Perhaps there is some significant autocorrelation conditional on there being a large price movement, but when the price movement is no longer significant, the autocorrelation subsides, hiding the true value of the autocorrelation under the typical weighing scheme.

It would be interesting to be able to construct some sort of ANOVA test, where one divides up return data into 5 deciles, and compares the autocorrelation function in each case. If the data were truly as it should be, there shouldn’t be much if any statistically significant difference between the various deciles. It would be interesting to see if the 5th is the same as the first. What one can look for—if there is any sort of trend in the autocorrelations as one moves from one decile to the next for a single stock, that would be interesting. Then one could potentially reduce the forecasting error inherent in the prediction. One could also create an EMA, weighted by returns, in the same way that the ‘typical’ EMA weighs by time.

One could look at a large number of stocks and determine if there is any return-size-dependency on the ACF inherent in all stocks in general. If that data provides any sort of information, perhaps it too can be used to augment single stock predictions in a univariate sense. Or it could be used in an ordered univariate sense by looking at all stocks in the market, ordering them by absolute returns in descending order, and making bets on the top few.

I would further distinguish between industries, and determine if there are any sector-specific relationships which differ from those of the industry.

The catch? Cutting up your price series into smaller bits means you’re dealing with a smaller sample size, which means your results aren’t nearly as robust.

Generalized Methodology

In general, to properly gain more insight into the ACF, one should focus on all the various data points which we typically (dumbly) categorize into lags and then average together to form an autocovariance. Instead of averaging them all together blindly, I would take a step back and decide why I am using the damn thing. In the end, what I am looking for is a methodology which generates situations for me in which the autocorrelation between tomorrow’s return and that of one of its prior lags is high. That way, I can make a directional bet for which the probability of my guessing the future return on the stock is higher.

In essence, the ACF should be one of many functions which forecasts future returns using lag dependency as its starting point (certain lags are important while others aren’t) in past return data. The ACF is a one dimensional test in that it makes no other distinctions beyond that of lag dependency.

I would modify the ACF. I would also begin my endeavors by calculating a massive pool of data points-- returns multiplied by lagged returns, as the ACF does. Some data points will be high will others will be low. However rather than simply adding together all the data points which have the same lag relationship, I would add a vector of characteristics to each data point. For example, one cell I would add is volume data. To do so, for each data point, I would calculate the volume which occurred on the lag’s date. I would also add the absolute return on the lag. Perhaps industry makes a difference, so add an entry for industry classification. I would also add what the lag is, which is basically at the heart of what the ACF does. And so on.

I would then take an econometric standpoint. Finding a “good” autocorrelation value from an ACF involves nothing more than taking all of the above data points, indexing them by what the lag is, throwing all data points with the same lag into distinct piles, and averaging the predictive power of the lagged return on the non-lag return for each pile. Good piles have high average values for predictive power. Along the same lines, perhaps returns data has different properties when the volume is high rather than low. Or perhaps tech stocks which experience sharp return shocks on high volume tend to have higher predictive power than non-tech stocks moving on low volume. So I would run tests to find out if such relationships exist. I would first look at each variable in isolation and determine whether or not, all else being equal, variations in that variable have an impact on autocorrelation. I would also look at combinations, for example determining whether or not sharp returns in conjunction with variations in volume have an impact on average predictive power. I ultimately end up with many more piles. Instead of dividing all of the returns into piles categorized simply by their lag, I would aim to divide up all of the returns into piles, categorized by all variables which have a statistically significant effect on the predictive power of a lagged return on its non-lag counterpart. Thus, I would aim to make more distinctions on the data than the typical ACF function, without throwing out the ACF methodology entirely.

Market Dynamics

Question: What does the issuance of put options to the open market do to the dynamic of the overall marketplace?
Hypothesis: The issuance of puts (1) exerts a stabilizing, mean reverting dynamic on the stock process, and (2) decreases the market implied volatility.
Basis Behind (1): all else equal, the market has bought and absorbed the put options. This decreases the market delta, and increases market gamma, and vega, all else equal. Why? Because the general public is buying from the company and not from other investors. If the company were buying from other investors, the net effect would theoretically be zero. However the general market is buying from the company, bringing those options into existence for the first time. Furthermore it is easy enough to track whether or not the put issuance has been hedged-- without loss of generality we can assume that it is not (or else we would simply retract all hypotheses). Finally assuming that the market absorbed the options with no problems, while it is theoretically possible that they fully hedged their position by longing the underlying, this is highly unlikely. The residual market delta is most likely to be negative.
So now let's think about what happens when the stock goes up. If the stock goes up, the puts get more out of the money, and the delta, which was negative, becomes less so. Assuming that at least some of these investors track their market exposure, some of the bigger investors will see this happen and attempt to re-establish their market exposure. They would do so by shorting off the delta increase. If the market goes down, they would conversely long off their delta decrease. Thus, the market stabilizes.
Basis Behind (2): Let us assume the issuer of the options is MSFT. MSFT has sold put options, so it's vega is negative. The market has bough the put options, so their vega is positive. We know MSFT won't hedge its vega. It should also be a reasonable assumption that the market will not hedge its vega either. We need to look at this from a supply/demand point of view. The supply of options has increased, while the demand can be assumed to be fairly constant- MSFT was the issuer after all. Supply and demand would imply that IV would have to go down as a result.
Also, we can think of MSFT as the initiator of the transaction in this case. The market in this case is nothing more than a counterparty. If that's the case, then even if you make the argument that on a net-net basis the change in vol should be zero (because you have a buyer and a seller at the same time), the fact that it was MSFT who initiated the trade indicates something.
Structured Products, I believe, are part of the reason why implied volatility is down so markedly.