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I hadn’t quite planned on reading about the rise of mathematical financial theory and efficient market hypothesis,  but that is what I did.

As it my wont,  I will digress and say that, a prime theme of Moneyball is not that statistics are better than visual pattern recognition: it is that when markets exist,  so do arbitrage opportunities.  Lewis’s writing style is to group his subjects into opposing camps,  to the detriment of his story. So the tension between scouts and stats geeks dominate the book.  It’s a more interesting book,  if you like people stories.

The moneyball story isn’t simply that OBP is a good statistic; it was an undervalued metric,  in the sense that players with high OBP weren’t paid highly compared to,  say,  batters with high homerun totals and batting averages.  Whether Billy Beane was the first one to “discover” OBP (he wasn’t) is incidental to the observation that no one was actively making use of that information. While GMs at the time were starting to identify other metrics, no one put their money where their mouths  were: high OBP players were not paid a premium. Because of that pricing difference (OBP contributes strongly to runs scored and thus wins, but GMs did not pay well for it),  one might be able to buy OBP talent on the cheap.  Now,  that arbitrage opportunity has disappeared,  as teams with money (read: Red Sox and Yankees)  have bid up the price.  That means high OBP now commands a premium.  Thus what worked before (a winning strategy on the cheap),  no longer works now.  It is a combination of fiscal constraints and incorrect pricing that gave Beane an edge.  The fact that there was a better stat  is besides the point; the fact that there was an arbitrage opportunity is absolutely the point.

This brings us to financial markets. If prices for stocks in a company were set by supply and demand, then rational buyers and sellers essentially agree on a fair price due to the fact that the seller has control of the product (i.e. stocks) and can name its price, while buyers need not purchase the stock if they  find the deal poor. In other words, opposing rational interests create a balance between something being charged too much or too little.

Is this price the correct price?

From a simple question, much of the mathematical economics was developed to help investors, fund managers, brokers and bankers identify the worth of the various products they buy and sell today. The most successful of these theories is that  markets are efficient: prices in a financial market such as the New York Stock Exchange are not only the optimum price for sellers and buyers, but reflects a conclusion about the value of the product. That is, this price correctly valuates the company whose stock is being sold. There are different forms of this efficient market theory: they differ in the emphasis on whether different “information” is accounted for in the price. A weak version of efficient market theory suggests the stock prices reflect all past public information. A semi-strong form of this theory is that new publicly available information is accounted for in the price of a stock, in a large financial market. The strong form of this theory is that even private (i.e. inside) information is accounted for in the price.

This might seem strange to people, given that a) we just saw a financial market meltdown because finance sector personnel did not evaluate sub-prime mortgage bonds correctly, b) such bubbles existed before and even after we have complicated performance metrics (Dutch tulip  mania and the dot-com bubble), and c) that there are enough shenanigans involving inside trading.

At any rate, one difference that I will focus on is that economic scientists (i.e. economists, and a breed we should separate from the operators in the financial market), like most scientists, seek general explanations. Because their tool of trade is mathematics, economists prefer to derive their conclusions from first principles. Generally, statistical analysis is thought of as ways of either testing theory or helping guide the development of a theory. Statistical models are empirical and ad-hoc. They rely on the type of technique one uses, how one “scores” the observation, and they are, as a rule, not good at describing things that were unseen. A good theory is a framework for distilling some “essence” or a less complex principle that governs the events that happen, which led to “observations.” Usually, the goal is to isolate the few variables that presumably give rise to a phenomenon. These distinctions are not so firm, of course, in practice. Good observations are needed to provide the theorists with curves to fit, mathematically. And even good theories fall apart (again, it is still based on observations – boundary conditions are a key area where theories fail.)

What does all this have to do with financial markets and efficient markets? While we have evidence of inefficient markets, these events may have been rare or the result of a confluence of exacerbating factors. However, one thing that scientists would pay heed to is that pricing differences were proven to exist, mathematically, and derived from the same set of equations used to describe market efficiency. Joseph Stiglitz proved that there can’t be a so-called strong form of an efficient stock market, since information gathering in fact adds value and has a cost. The summary of his conclusion is that, if markets were perfect and all agents have perfect information, then everyone would have to agree on the price. If that were true, then there would be no trading (or rather, speculating), since no one would price things differently. When people are privy to different information, it may lead to pricing differences. That in turn, must lead to arbitrage opportunities (no matter how small.) Thus the “strong form” of market efficiency cannot exist.

I was talking with a friend who has an MBA. He wasn’t too keen on hearing that the efficient market hypothesis may not be entirely proper, when I was describing to him Justin Fox’s book, The Myth of the Rational Market. I was approaching things from a scientific perspective; I know that models are simplifications. Even the best of them can be found inadequate. And this is what I want to focus on: that although models may not describe everything exactly, it’s fine. It does not detract from it.

From Fox’s book, and also William Poundstone’s Fortune’s Formula, the reader sees some difficulties with the efficient market theory. For one, the theory was originally posited to explain why prices, in the very short term (daily), varied around some mean. Sure, over time, the overall price increases, but at every iota of time, one can see that prices ticked up and down by a very small fraction of the price. This is known as the random walk, first mathematically described in the doctoral thesis of Louis Bachelier. One bit of genius is that, Holbrook Working pointed out that these random price fluctuations may in fact indicate that the market has worked properly and efficiently to set a proper price. Otherwise, we would see huge price movements that reflect the buying and selling of stock due to new information. In other words, the price of a stock constitutes the mean around which we see a “natural” variation.

And from that, much followed. Both Poundstone and Fox talked at length about pricing differences. In some sense, market efficiency, although implying both speed and precision, did not address the rate of information propagation.  Eugene Fama suggested that information spread in a market is near instantaneous (as in, all pricing changes are set and reset constantly at a proper level). In the theory’s original form, I think this instantaneous rate resulted from a mathematical trick. Bachelier was able to “forecast” into the near, near future, showing the stock price can tick up or down. His work was extended into many instants by a brilliant mathematical trick. By assuming that stock transactions can be instantly updated and without cost, one can build up a trajectory of many near instants by constantly updating one’s stock portfolio. The near, near future can now be any arbitrary future moment.

Again, my only point here is not that the efficient market theory is wrong and must be discarded. I was fascinated by the description of counter examples and the possibility that some of the assumptions helping to build up a mathematical framework may  need revision.

My boss and I were talking about the direction of our research. He thought that models of cell signaling pathways were lacking in rigor (by that he means a mathematical grounding). He, having a physics background, scoffed at the idea that biology is a hard science, because biological models are mostly empirical and does not ‘fall-out” from considering first principles (i.e. based on assumptions, postulates, and deductive reasoning). I, being the biologist, tried defending this view. Biology, like any sort of system, is complex. There are some simple ideas that can help explain a lot (for instance, evolution and genetic heritability). The concept of the action potential, in neurons, can in fact be derived from physical principles (it is simply the movement of ions down an electrochemical gradient, which can be derived from thermodynamics). In fact, neurons can be modeled as a set of circuits. For example, one recent bit of work my supervisor and I published on, using UV absorption as a way to measure nucleic acid and protein mass in cells, is based on simple physical properties (the different, intrinsic absorption of the two molecules to light), which can be described by elementary, physical mathematical models.

However, the description of how networks of neurons may work, and how such physical phenomenon can give rise to animal and thoughts, and in turn how individuals may act in concert with others and form a societal organism, are wildly complex. Further, there can be multiple principles at work, none of which are necessarily derivable or deduced from a common set of ur-assumptions. For example, Newton’s laws of motion can be derived from Einstein’s theory of relativity. However, some basic ideas about human behavior (such as that leading to pricing correctness in market efficiency and game theory), or how humans may interact (as described by network theory), and how something as seemingly nebulous as and human-dependent as “information” can actually be described by Boolean algebra and a mathematical treatment of circuits.

I should be clear: I am simply noting that some fields are closer to being modeled by precise, mathematical rules than others. Reductionism works; even the process of trying to identify key features underlying natural phenomena is helpful. However, one should also keep in mind that wildly successful theories may change, as we obtain better tools and make more accurate measurements.

I think an important point that Fox makes, then, is that we do have a number of observations suggesting that markets are not entirely efficient. For example, there is price momentum (a tendency for stock prices to continue moving in a particular direction), there is significant amount of evidence suggesting that humans do not always act rationally (they tend to overvalue their property but discount things they do no own), and there are clearly signals that sometimes, herd mentality results (a la price momentum or bubbles). Fox also points out something rather important: even as economists point out inefficiencies in the market, they seem to disappear once known. Part of it could be statistical quirks: by chance, one might expect to see patterns in the noise of large, complex systems. Another part of it is that, once known, the information is in fact integrated into future stock prices. This places economists in a bind: if the effect is false, one might be justified in ignoring it as noise or a mirage of improper statistical analysis. However, if the effect is real, then it clearly suggests that the appearance of price incorrectness reflects market inefficiency. At the same time, the effect disappeared, also suggesting that once known, the market price showed correction, just as efficient market theorists predicted.

As one can imagine, there are opposing camps of thought.

Further compounding the difficulty is the fact that it has been hard to integrate non-rational agents into traditional market theory. current theory treats pricing as an equilibrium, consistent with the idea that information and rational agents pulling and pushing the prices this way and that, but ultimately, the disturbances are minor and the overall price of the stock is in fact the proper, true price. Huge disturbances are interpreted as movements in the equilibrium point, but they must arise from external forces (that is, from effects not modeled within the efficient market model – which actually leads to an inelegance of the variety that mathematicians and physicists dislike.) As the number of contingencies increase, one might as well resort to a statistically based, empirical model. Which brings us back to the original point of how well we understood the phenomenon.

On the other hand, no one who wishes to modify efficient market theory has successfully integrated the idea of the irrational agent. The advantage is that here, pricing changes – correct or incorrect – are based on the actions of “irrational” agents. Thus we are no longer looking at an assumption of a correct price and deviations from that price. We can, presumably, derive the current price by adding into the model the systematic errors made by agents. Thus even huge deviations in proper prices (i.e. bubbles, undervaluations, and perhaps even the rate of information incorporation) would be predicted in the model. However, a model remains just out of reach. In other words, efficient market opponents do not yet have a completed and consistent system to replace and improve the existing one. Be default, efficient market is what continues to be taught in business schools.

My interest in the Fox and Poundstone books is precisely in how difficult it is to incorporate new ideas if an existing one is place. It is this intellectual inertia that results in the concept of memes as ideas that take on a life of its own  (in that ideas exist for its own reproductive sake) and Kuhnian paradigm shifts that have to occur in science. My specific application has always been in how non-scientists deal with new ideas. If scientists themselves are setting up in opposing camps, what must laymen be doing when faced with something they do not understand?

 

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Michael Lewis seems to specialize in telling stories about misanalysis in terms of cowboys-and-Indians. This is clearly a style that gets him into flaps (well, I know of one writer – Buzz Bissinger – who is antagonized by whatever Lewis is trying to sell). I see The Big Short as similar to Moneyball: Lewis has an affinity for people who see something different from the  wisdom, and who are curious enough to explore why that is.

The Big Short is not unlike Moneyball in that Lewis clearly takes a side, even though there is really none to take. It certainly is easy to jeer the big banks, as Lewis finds a cast of characters who, in essence, foresaw the economic meltdown of 2007-2008, led by the tanking of the subprime mortgage market. But they are not heroes; they simply saw something different. By exploiting their observation, the tools they used was every bit as devastating as the subprime mortgage loans in fomenting the crisis. These tools were more devastating than analytical models of baseball player productivity.

I tried describing this book to a friend by saying that, I can simply define several terms and one cannot help but draw moral conclusions about the participants. The terms are subprime mortgages, subprime mortgage bonds, collateral debt obligations, and credit default swaps.

Subprime mortgages –  Normal loans (i.e. mortgages) earn banks money through the interest charged on the loan. The interest rate usually follows a rate set by the Federal Reserve Bank, called the prime rate. Subprime mortgages are loans that banks underwrite but with smaller than usual interest rates (generally under the prime rate, thus, subprime). These loans are attractive to borrowers because they would pay less interest (at the beginning). The banks earn money by eventually raising the interest rate, usually quite a bit above prime rate. This situation is akin to the credit card teaser rates: 0-5% interest for the first 6 months, followed by a raise to 15-23% on the remaining balance. Because of the low teaser interest, it has the problem of seeming more affordable to people who cannot pay for the loan. Some less than ethical banks in fact targeted people who do not have steady incomes or who possess poor credit ratings for these loans. The flip side is that these loans could in fact have done some good. Banks were given an incentive to lend more money so that more US citizens could own homes. The only way they would give money to people who are at higher risk of not paying back is, ironically enough, to charge them even more for the privilege of getting the loan money. Whether banks should have relaxed their standards by so much is a serious question, since there was political pressure for banks to do so. But the issue was not examined properly, certainly not by banks who simply signed off on a loan and then sold it (i.e. originate and sell) to some other bank, who assumed the risk of the borrower defaulting. Banks can make money by selling these loans, hence the motivation for disreputable banks to lend money to people who cannot afford them.

Mortgage bonds – Some other banks thought mortgage bonds are an attractive financial product because the bonds can dilute the risk of the bondholder losing money. As I understand it, in very simple terms, mortgage loans can be packaged into a bond with many subdivisions (called tranches.) What an investor sees is not a set of mortgages, but a bond with a return. This income stream comes from the interest paid to service the loan. More importantly, the purchaser of the  bond (in theory) isn’t lending all the money to a single borrower. The bond doesn’t cut things so fine; in a sense, it doesn’t matter which borrower is paying the interest to the bond-buyer. It could be one borrower paying thousands of dollars; it could be a few pennies from a million borrowers. In theory, one borrower defaulting won’t affect the bond buyer’s expected income. Theoretically. The important point is that the mortgage bonds are simply a collection of many mortgages. Some mortgage loans are given to fairly responsible people. Some to shady characters. Since we are really talking about subprime mortgage bonds, one might expect more shady characters than not. In general, investment banks have an incentive to create these bonds: they can charge fees when they sell these bonds (i.e. a service charge).

Collateral Debt Obligation – The CDO is a financial instrument; it is basically a bond of bonds. Just as a mortgage bond (presumably) dilutes the risk of borrower’s defaulting, the CDO supposedly dilutes the risk of multiple bonds going bad.  The idea is that not all mortgages are equal (that is, not all risk is equal), and thus not all bonds are expected to go bad at once. In another bit of financial genius, one might realize that, it might make some sense to split bonds up before repackaging into a CDO. Again, this goes back to the assumption that a bond contains a great many different levels of risk (i.e. in mortgage bonds, every borrower is presumably different.) So what if one takes the less risky parts of bonds (a part here is termed “tranche”) and package them together? Then what if one takes the next riskiest tranche across all these mortgage bonds, and then packages those into another CDO? What if one does this, all the way down to the riskiest sections of the bond (and remember, the higher interest charged to the borrowers is what underlies the revenue stream that would make this an attractive investment)? If one properly assesses the risk (which is basically equal to cost) and benefit (which is income), then one might see how, at some point, one might actually buy even the CDO that contains the riskiest slice of bonds. Risk is directly proportional to the returns one might expect. What this also means is that, for a while, the buyers of the mortgage bonds are actually other banks – so they can package them into these meta-bonds (CDOs). Naturally, this is adding value; the investment banks that create the CDO can charge a fee as the middleman.

Credit default swap – An insurance policy, which anyone can purchase – even if one is not “exposed” to the risk. As I read it, it’s as if I bought an insurance policy against your house burning down. Of course, I would hope I choose wisely. I might select some house, sitting next to a forest with a history of fires, and during a drought, in southern California. But if I’m doing that, one hopes that the insurance company isn’t selling this policy for cheap (i.e. from my perspective, I’m looking for the underwriter that has improperly priced the risk – the premium they would charge is low given the probability of the worst happening and that they would then pay out). So it is a balancing game; the expectation is that the worst will not happen, but if it does, then the insurers had charged a high enough premium to get enough money stockpiled to pay.

Some questions arise: If the whole mortgage bond market was driven by high returns based on the high-interest rates charged to the borrower, why did so few people not associate the high-interest rates with the higher risk involved. Again, the high-interest rate is charged as a penalty because lender feels that the borrower might not be able to pay. In this context, why would any bank not ask for income information for some mortgages (“Alt-A” mortgages)? Why would banks lend money with a 0% teaser and then jack up the rate to 10%, and then making these loans to the applicants with no steady jobs?

While default poses an obvious problem (i.e. the borrower can’t pay), paying too soon is also another problem. A smart borrower, who is able, would refinance home so that he can get out from the usurious rates. This poses a problem for the bond buyers; the original mortgage would be paid, which means that the total interest gained by the bond buyer will be low (the total income is thus low). Why would banks assume they can get 15 or 30 years worth of returns at these teaser deals? There are two strikes against the mortgage bond: borrowers can prepay. Or borrowers default. What if the borrower can’t refinance? The original reason he got this type of subprime loan is that he was unlikely to be approved for a normal loan. What makes anyone think that a large fraction of these borrowers will stabilize and become candidates for a normal loan through refinancing, after the teaser rate period? This is another risk posed to the bond investor.

The same comments can be made of a CDO. Did investors properly evaluate the downside of owning these bonds? Lewis’s answer is an emphatic no. In all the above definitions, the products were sold because the seller can charge fees. The middlemen  made all the money here. The buyers were playing a game of hot potato.

Lewis cannot contain his disgust at the shenanigans being played here. He reserves his hardest forehead slap for the synthetic CDO. At some point, a few investors got wise and started betting against whoever bought CDOs. Some of these investors looked as deeply as they could and found that the tranches did not represent independent risks, which is the supposed advantage of packaging these loans and bonds together. These short-sellers assumed that at some point (perhaps at the end of the teaser rate period?), the loans will go bad, and then the bonds, and then the CDOs. So they bought insurance against the CDOs failing; they paid a premium now, hoping that things get so bad that the insurers will have to pay out on the policy. Not only that, the default swap allows the buyer to insure specific things. That is, it is almost like a CDO in this regard. Instead of insuring against a mortgage bond defaulting, one can target specific tranches. So one might simply buy a credit default swap on the riskiest tranche, and work ones way up (to the less risky tranches). It’s a reverse CDO. Actually, it is exactly a CDO. Some wit thought it made perfect sense to simply to turn the CDS around and sell it as a CDO. Since this CDO was constructed from the CDS (as opposed to original “research”?), it is termed synthetic.

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Too Big to Fail picks up where The Big Short ends. Bear Stearns had fallen, and the spectre of ruin is playing out through the entire financial market. A part of the problem has to do with the so called asset held by investment banks and investors: they held billion dollar bonds that were about to go bad. While some banks might be able to write off the loss, people who place their accounts and money with various banks do not know that. One reason for the seemingly unstoppable financial meltdown was the result of many people asking for their money back. And why can’t a bank ever pay back everybody’s money at once? Because banks use the money to invest (buy assets, make loans). That is why we all get interest paid on our deposits. How much of the money they can use for investments is subject to regulation. For investment banks like Goldman Sachs, JP Morgan, Merrill Lynch, Bear Stearns, and Lehmann Brothers, they were leveraged to the hilt (their money is everywhere but in a vault). But it still doesn’t matter. Unless the reserved amount is set at 100%, no bank can ever hope to withstand a run.

And scale matters. A bunch of us normal customers making a run may not matter over the short term. The most damaging thing a bank can suffer from is if a few big clients – other banks, hedge funds, corporations – decide to take their business away. For example, the money used by investment banks come from hedge funds that have trading accounts. These are billion dollar accounts. Even JP Morgan, at one point during the meltdown, who was liquid enough to get actual cash of $180 billion,  could not withstand a run. Inside of a week, they were down to $40 billion, with the possibility that after the weekend, they would go bankrupt. Since everyone was panicking and asking for their money back, it fed into a negative feedback cycle. Banks that weren’t in trouble were soon.

That is the essence of Too Big to Fail. I had joked to my wife that, at various parts, things were “getting exciting”. Like when Lehmann Brothers about to go bankrupt, and the fear and panic spreads anew. It seems that there was very little the Treasury Secretary – Henry Paulson – and the Chairman of the Federal Reserve Bank – Ben Bernanke – could do. Every measure caused a small rally, followed by a new cycle of panic and money/account withdrawal. It truly was like watching dominoes: after Bear Stearns. The tension was in the fact that the situation did look hopeless. The contagion in this case was irrational fear. Every investor who feared for his money decided to pull it out. However, the very act of withdrawal was one more chip at the banking edifice. Banks need to pull back their own investments to generate the money to fund the withdrawal. Once they start doing that, then everyone is essentially stuck calling in their marks – you need to pay back loans. Not being able to do so means that you are bankrupt. Whatever one wishes to call it – negative feedback, self-fulfilling prophecy – it is difficult to see how the cycle could stop (lots of money).

Strangely enough, it wasn’t just money; it was the way it was doled out. The string attached to the $800 billion bailout is that the investment banks were forced to become holding banks, which are subject to more regulation. Merrill Lynch was forced to merge with Bank of America, becoming the investment arm of BoA. JP Morgan and Goldman Sachs had also considered such a merger, but they received an out. They were converted directly into holding banks. But the plus side is that all these banks now have access to the discount window offered by the Fed to holding banks. JP Morgan and Goldman Sachs could borrow money from the Fed. This is important. It meant that the investment banks no longer had to sell assets or call in their marks to gain cash to pay off, withdrawals.

Essentially, the guarantors of the investment bank became the American taxpayers. This did stop the meltdown proceeding.

However, there looms the spectre of actual mortgage defaults, and they will have to pay out credit default swaps. Banks will lose money, and it is unclear how they will deal disposition of the properties.

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Too Big to Fail was simply a story. It wasn’t meant to be an analysis of the methods used by the Treasury Department to stave off financial collapse. Instead, it contained reconstructed scenes of the various players, placing them into a narrative history. I realized that I do not like narrative histories. I much prefer dense arguments and presentation of primary data. Most importantly, I wanted analysis. But that is not what the strength of this book is. Too Big to Fail simply documents the what, not the why and how.

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While it is easy to see how writers dealing with the meltdown can develop strong opinions, I think the problem that Lewis has with the banks transcend simple disgust. One undercurrent in his previous book, Moneyball, which I also found in The Big Short is that he can’t understand why people are so lacking in curiosity.

In Moneyball, he juxtaposed baseball statisticians and scouts. But the fact that it was statisticians as the insurgent is meaningless. It could have been anyone who wanted to challenge an existing way of doing things, which had bordered on the ritualistic.

In The Big Short, the problem is more glaring. We are now talking about people’s life-savings and retirement funds and the ability for local and global commerce to happen. Billions of dollars. Fund managers were buying up assets, trusting on Moody’s ratings. No analysis, or, the type that is available to just about anybody. Aren’t Wall St. traders privy to better information and resources? Another reason for the meltdown can be attributed to laziness and incompetence. No due diligence was done, even if billions were on the line.

Exploiting advantages may also have contributed to the problem. For example, if one understood how various banks and ratings agencies valued various assets, it may give some traders an advantage. If done with public information, then  it is simply being aware.  Keep in mind, however, that it is no secret that Moody’s analysts are underpaid relative to the rest of Wall St., and that traders have been known to defect from Moody’s to the investment banking firms, carrying working knowledge of the algorithms Moody’s used to generate ratings. It is possible that Moody’s formulas for valuation is known for certain assets. What is interesting is that this should be a two-edged sword. Investors may be able to exploit the knowledge against someone who does not know, but at the same time, it should give pause to the same banks in placing their trust solely on ratings agencies.

It is not only incompetence; there is the spectre of malfeasance. I became really interested in investment banking, and have Charles Ellis’s The Partnership and Suzanne Mcgee’s Chasing Goldman on my to-read list. Mcgee’s book came out in 2010, and in her foreward, she writes that Goldman is being investigated for fraud. Remember how default swaps were turned around and repackaged as CDOs? At one point, it should have dawned on someone that it’s strange that someone would want to bet against the riskiest CDOs (or specific, worst-of-the-worst tranches of different CDOs), only to have the same instrument be sold as an asset (AAA rated, no less!) to someone else. At the least, the bank is ill-serving their clients. Since Goldman is considered to be the best and brightest, it is unlikely to be a mistake but rather something intentional. Goldman made money on both ends: creating and selling both CDSs and CDOs. It’s one thing for an investor to come and ask for specific instruments to be created (which is what happened with the creation of CDSs), but it would be another if Goldman knew the assets had a high likelihood of default and hid the data in order to sell CDOs. So yes, what seems at the very least… unsporting… is actually rotten.

Lewis story does comment on how traders like Steve Eisman and Michael Burry had trouble tracking down the information regarding the loans underlying the bonds and CDOs. It is not out of the realm of possibility that someone was suppressing the information – whether it was perpetrated in part by Goldman remains to be seen.

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