The system [of finance] is too complex to be run on error-strewn hunches and gut feelings, but current mathematical models don’t represent reality adequately. The entire system is poorly understood and dangerously unstable. The world economy desperately needs a radical overhaul and that requires more mathematics, not less.

This article in the Guardian is a little late to the party and has an intentionally misleading headline, but brings up some points that are usually too esoteric to survive in print:

Any mathematical model of reality relies on simplifications and assumptions. The Black-Scholes equation was based on arbitrage pricing theory, in which both drift and volatility are constant. This assumption is common in financial theory, but it is often false for real markets. The equation also assumes that there are no transaction costs, no limits on short-selling and that money can always be lent and borrowed at a known, fixed, risk-free interest rate. Again, reality is often very different.

There are more false assumptions like Gaussianity of log-returns, complete markets, martingale price paths, etc., but these are merely technical complaints, which can be patched (as many are doing). The real issue is, as the author notes, “… instability is common in economic models … mainly because of the poor design of the financial system.” Namely, there is a lack of accounting for behavioral effects that result in feedback, which give rise to rather more fundamental issues that would require the “radical overhaul” alluded to in the opening quotation to resolve. There are some problems that could be tackled in this area.

• Damping: As posed here and here, could damping of price and flow mechanisms in markets create more stability? And at what expense to liquidity or other notions of efficiency? Are there fundamental trade-offs between liquidity and stability — e.g., something like the Gibbs phenomenon in filter design?
• Redundant beliefs: As explained here, risk sharing (e.g. via CDS) stops working when the network of institutions becomes densely connected (and therefore causes short risk feedback cycles.) Is there a way to calculate the correct network risk in a distributed way, by something like iterative message passing, and share that information in a way that does not reveal proprietary information?
• Impact: More generally, price of risk products is set based on some static model of markets, e.g., statistics and predictions assuming things remain the same. However, when risk is mined and sold, it changes the decisions of participants (viz. allowing hedging makes it possible to take larger risks) in a way that could invalidate the data on which pricing was based. Is there a relatively simple, separable model for decision propagation (e.g. a correction term, or an amplification term or filter that modifies a parameter on which the price is based)?

Beyond feedback issues, there are many other questions, such as:

• Heterogeneity: What is the real effect of heterogeneous participants, especially those with different time horizons or risk appetites for asset purchases, on price discovery? What, if any, notion of fairness can we guarantee in these cases? Or, what notion of fairness is actually being computed by standard markets?
• Large systems: How do we pass from small-scale game-theoretic models to large-scale system models? For example, in thermodynamics, we can identify macroscopic variables like temperature with microscopic variables like kinetic energy. Can we identify market variables like volatility with any underlying behavioral variables? What are the “right” (e.g. fundamental, minimal) variables to completely describe a market?
• Instrument design: Are expiring instruments like bonds fundamentally better than infinite-horizons ones like stocks? Can we design market instruments to have certain guarantees on things like volatility? Can we design atomic risk instruments that have payoffs in easy-to-understand terms?

Maybe this list will inspire the field to advance past its current medieval state.

Eduardo … I’m talking about taking the entire social experience of college and putting it online.

When the movie “The Social Network” came out, this line caught my attention. I’m not sure this thesis — let’s call it the “replication thesis” — was what Monsieur Zuckerberg had in mind rather than something the screenwriter came up with, but it makes sense as to what actually undergirds online social platforms of today.

In all likelihood, Zuckerberg did not at first intend Facebook to be more than its namesake — a dorm facebook. Just as, in all likelihood, Twitter was meant as no more than a status message broadcast system, at first. The fact that Facebook became something of a gathering place and Twitter became a “microblogging” service — in essence, taking over functions that used to be conducted in other ways — I think owed something to their use of a “correct” user graph for certain contexts. It was the user graph that allowed, then limited, the range of social functions that people were willing to port over to the online platform. With the undirected graph, Facebook (and clones) modeled something like a big gathering, maybe a party. With the directed graph, Twitter (and clones) modeled something a bit more nuanced, like a groupie-celebrity relationship. (Is it any surprise, then, that celebrities drove the latter’s popularity?)

But I get the sense that neither Facebook nor Twitter truly believes in the replication thesis. They’ve construed their challenge narrowly as one of periodically pushing out new “things you could do,” most of which are nowadays ignored by users, or adding more places at which you could interact, but in the same way. They don’t see that users voluntarily do on a platform only those things that are compatible with their perception of the modeled social space. You can’t push anything on them any more than you can force people to play some game at a party. Yet I see no movement to revisit the user graph and better model real social relationships with all of their complexities. If left unchanged, the inevitable result will be that the range of social functions these platforms support stagnates, and therein should lie their eventual downfall. In fact, that probably solves the supposed “mystery” of Myspace’s decline, too. It is in this context that Google+ arrives.

Why has Google+ “succeeded” in a way that Orkut and Buzz had not? For one, Google+ posits an even more complex user graph in the form of circles. It’s a colored directed graph, not only directed like Twitter, but each user’s edges to other users are colored by the circles these neighbors belong to. Instantly, the range of social functions is expanded. We don’t have to wait for new applications to take advantage of this to make the realization: imagined possibilities are sufficient. It is like going to a new space. You leave the party, and the groupie session, and come to this space that is novel in a way that is defined not by its location or the people in it, but by its different arrangement.

By accident, Google is also a provider of several useful web services. This is an enviable position from which to make suggestive proposals on new interactions that people can have on this particular user graph. And unlike on Facebook or Twitter, some of Google’s more productive collaborative applications may actually require the Google+ user graph. The former two platforms are already shackled by their user graphs to “unserious” applications that are not coincidentally popular there. However, while Google+ will have a while to go before it exhausts these unrealized possibilities, it isn’t immune to the same questions of what is a “correct” user graph model or, what “correctly” replicates the “entire social experience”. Colored directed graph models social relationships in greater detail but is this model complete, or fundamentally right?

I recall reading Zuckerberg’s recent comment in which he quipped (about Google+) that it would be too much trouble to keep track of many circles, and that Facebook Groups is more transparent in that everybody knows who else is in the group (again, like at a party). I think he’s on to something even if his own model isn’t really moving forward. The fact that you can put people into circles gives you a false sense of privacy, because there will always be common connections and information leak. For example, you can go to a particular circle’s stream page and read only the stuff shared by people in that circle. But when you comment on something there, unlike being in a cloistered room which this metaphor would have you believe, you’re actually talking to all the people whom the original author has decided to include into the conversation. You see them but you don’t really see them. It jars the mind a little bit. Will you really spend mental energy to keep track of where your comments will be seen? Not likely. So you either decide to ignore this “leak” with even more embarrassment potential than on Facebook, or you decide there is no privacy despite circles and revert, in behavioral terms, back to the Facebook model. Something is amiss.

That thing is the fact that there is no concept of “spacetime” online like in real life. Everything happens at one time and in one place despite efforts to counter it (RIAA discovered this). What you write can be read ten years later, and it can be transmitted everywhere, too. It has your identity attached to it as if you did it right then and there to all the people you have no control over.

Let’s reconsider social relationships. Circles is an attempt to model the different groups in which a person moves. These groups may be “socially independent” as Google researchers have found, but they are not disjoint. If they were or if they were nearly so, Google+ would have fully modeled the situation, so a “Colleague” circle and a “Family” circle may indeed be easy to keep track of (unless your coworker is also your brother). But once there are more than about 2-3 circles, things surely muddle up. So why do people feel the need to separate their communication to different groups in real life? Maybe it is less so about who are in a group, and more about the identity that the person wants to project in a group. The need for circles isn’t really one for categorizing other people, as much as one for categorizing your own identities. It is this need for compartmentalizing identities (code for “hiding” certain parts of a composite identity) that drives the need for privacy across group boundaries.

In my mind, a more powerful and frank model of social relationships recognizes this. It is a classic one that a generation of online users have already grown accustomed to. You shouldn’t have multiple circles for one identity, in the false hopes that they be disjoint. It defeats the whole purpose. You should have multiple disjoint identities, but easily accessible under one account. Maybe you have a “model child” identity to your family, an “industrious worker” identity to your colleagues, and I don’t know a “troll” (er, I mean “free-speech protected”) identity for your political rants. This probably requires complex per-item ACL, or simply pseudonymous identities. Some people cringe at this, but I don’t see why. Pseudonymous identities can be every bit as authentic as real ones. (Google+ has already run into a dilemma on this issue.) Moreover, each identity actually has to be accepted into your chosen cliques, so behavioral norms are already enforced intra-clique; identity labels are largely inconsequential. I think the replication thesis demands this since there is no spacetime disjointness online as exists in real life, so we can only go for identity disjointness. There are of course those (including Zuckerberg) who believe in radical unprivacy, and that is a utopian ideal, but for those opposed to it, Google+ unfortunately didn’t solve the problem.

This is an interesting question because at first thought, one would think that in a large enough network, a sufficient number of independent reads on the truth will occur in the aggregate to allow at least the later-deciding nodes to get a really good estimate of the truth. This is the basis of the folk belief in “wisdom of the crowd.” However, this is not what happens all the time.

The problem really lies in the fact that a social network is (inadvertently) running a rather constrained version of belief-propagation, not the full-fledged belief-propagation that we would like, in which the nodes are more sharing. For example, in belief-propagation, full distributional beliefs are passed instead of these binary decisions, where estimation information is abridged and suppressed locally. If the observed decisions embody estimates so compressed as to be heavily distorted and not very indicative of the truth, then given certain network topologies, error propagation may not decay away. Then there is also something about single-pass decision-making that makes it impossible for nodes with the wrong answers to correct themselves and for the network overall to always converge on the right answer. Of course, some cooperative protocol could solve the problem, but we can’t really assume all nodes in a social network are cooperative, or even not adversarial.

So the crowd is not always right. In fact, it can be manipulated by “excessively influential” nodes in bad network topologies, as some other results in the talk indicated. Learning occurs a little more robustly in network topologies where some small (but non-negligible) fraction of nodes are “independently observing” ones that don’t listen to other nodes, but are listened to.

This undirected graphical model stating conditional independence relationships of senate voting behavior was shown.

If two nodes A and B are connected only through a set of nodes C, then A and B are independent, conditioned on C. Basically it says if you want to predict anything about B from A and C, then C is enough, because A won’t tell you anything more. As pretty as the graph looks, this is a rather odd visualization. Without seeing the (Ising) model parameters, especially where the edge weights are positive or negative, this graph is hard to interpret, and the conclusions in the paper are especially questionable to me. In particular, being in the middle of this graph does not necessarily imply “moderation” or “independence”, (unlike in let’s say this graph). We would expect moderates to exhibit weak dependency to either party’s large cliques. But if, for example, the edge weight between Allen and B. Nelson is a strongly negative one (which it very well may be, since the two parties are not otherwise connected via negatively weighted edges), then the graph seems to imply that how the two parties vote can largely be predicted from the votes of the likes of Allen or B. Nelson; in that sense, they are the indicators for their parties, disagreeing on exactly those party-disambiguating issues.

There is some additional funny stuff going on. According to the paper, a missing vote counts as a “no” because they only solved the problem for binary and Gaussian distributions. I also count only about 80 nodes in there, while there are 100 senators. The graph structure also seems a bit too sparse, but this may be intentional, in order to drop weak dependencies from the graph. One does wonder though, whether the results weren’t really that good without manual fudging.

Unrelatedly, this reminds me of another famous academic paper graph, the high school dating graph:

If you look carefully, there is some oddball stuff going on here, too.

Now let’s turn to the other model of behavior, where things are swapped around. Here, consumption is the default. To consume is what happens if you do nothing; that is the raison d’etre. All other actions service that need. In other words, why bother to “save” or “invest” or “work” if you do not consume? See how this is inverted? Again, this is tightly coupled with the notion that borrowing is a tool of persistent leverage for greater return. This is typically risk taking behavior, in technical parlance of course.

To make the cases even more distinct, here are two graphs of model behaviors:

“savers”

“consumers”

So people try to analyze why East Asia saves so much and why China especially cannot get internal demand going due to excess savings, whether it’s because of the lack of a social safety net, or because of an inequitable distribution of wealth. Yes, these have some effects, but no. I don’t think those are why. It has to do with how personal financial behavior is internalized from the past, as much as influenced by conditions in the present. I think risk averse behavior is ingrained into people in times of scarcity (credit scarcity or capital scarcity) and how long this behavior lasts depends on the severity of a downturn and the subsequent period of prosperity. (As an aside, it can be argued that risk taking behavior isn’t entirely risk taking behavior but partly a bad estimation of the actual risk.)

One is to use all services that Google provides, which are entirely built on web applications. I don’t believe this is the right model.

That guy in the link was able to “survive” for a month, sure, but only because he had very boring things to do. The amount of stuff I have installed on the desktop are not going to be services anybody is going to provide any time soon. Besides, it is almost impossible to get people to change set habits to use a whole new set of cloud software. Are you kidding me? Change all the software you use? This is a no go.

The more promising model is virtual machine hosting, in other words, the Citrix on crack model. To a large extent, I already roll my own using Remote Desktop and an always-on machine. But much more useful is having a huge server farm hosting lots of virtual machines that belong to users … possibly sharing installed software and other redundant stuff. This is a “compatible” path, in that users will not see any difference from their desktop experience and so will adopt it. Once they adopt it, you can tweak the backend however you want to wean users off of the desktop. This is something that many companies are trying in different forms, and of course so is one particular large desktop OS manufacturer … that happens to have server software also, and which happens to support virtualization. So I wouldn’t write off said company just because there is a cloud.

Incidently, Google is now supporting offline mail because they find it necessary to support the blended cloud/offline experience.

In the simplest of examples, you pay some entry fee to play the game, $1 is put in a pot by a counterparty, then a coin is repeatedly flipped and the pot is doubled on every coin flip by the counterparty, until “tail” comes up. You receive the money in the pot. The expected gain of this game is infinite, regardless of the initial entry fee. So it would seem that one should always play the game, regardless of the amount demanded as entry fee. But, as the article points out, “few of us would pay even $25 to enter such a game.”

(This seems to be one of many variations of the paradox.) The explanations given in the link to resolve the paradox aren’t satisfactory. “One can’t buy what isn’t sold” can only be considered a joke, while “expected utility” is somewhat plausible, but doesn’t strike at the central issue, because it can be circumvented with an equally counter-intuitive paradox fitted to the chosen utility function. In contrast to the Gambler’s ruin paradox, I don’t think that an artificial finite bound on the money supply (in this case, of the counterparty) makes sense as an explanation, but what it reveals as the logarithmic growth of the expected gain against the money supply and the general consequence that imposing some kind of finiteness may explain the paradox, is instructive.

Of course, the only way to get any gain is to actually play the game. If you repeatedly play the game, your gain does eventually go to infinity. So why would you be reluctant to pay even $25 to enter? It must be because those large pay-offs are so infrequent that to make the initial money back would take too long. Suppose the entry fee is \(W\). Suppose you call it a day when you have a positive pay-off. For that to happen in round \(n\), it must be true that

where \(f_i\) is the number of flips before tail comes up in round \(i\).

Let’s call n-tuples \((f_1, f_2, \dots, f_n)\) that satisfy the above by the set \(S_n\). The probability of winning in round \(n\) is then

from which we can surely get the average number of rounds it will take to win the game \(\sum_{i=1}^\infty n p_n\). If this is incredibly large even for modest \(W\), which is likely the case, then that would explain the paradox, since a game that on average takes longer than a lifetime to win would be played by no one.

Stock Prices Are Still Far Too Low

By Kevin A. Hassett, James K. Glassman
Posted: Saturday, January 1, 2000

ON THE ISSUES
AEI Online (Washington)
Publication Date: March 17, 1999

The U.S. stock market, despite astonishing price appreciation over the past seventeen years, could triple or quadruple in value without exceeding its true worth.

A year ago, with the Dow Jones Industrial Average at 8,782, we published an article in the Wall Street Journal headlined “Are Stocks Overvalued? Not a Chance.” The piece drew criticism from a financial establishment that had been preaching imminent disaster, pointing to high price-earnings ratios and low dividend yields and predicting that stock prices would fall when this zany euphoria wore off. They were dead wrong. As this goes to press (on April 5), the Dow has closed at a record 10,007, and the S&P 500 and the Nasdaq Composite are also at all-time highs. Including dividends, the 30 stocks of the industrial average have returned 15 percent since our piece appeared, while the stocks of the Standard & Poor’s 500 have returned 21 percent.

Dire warnings from professionals have accompanied nearly every step of the Dow’s rise from 777 on August 12, 1982. Could it be that the model that Wall Street has been using to assess whether stocks are overvalued—a model based largely on historic price-earnings ratios—is deeply flawed? We think so. Investors are ignoring the old shibboleths and pricing companies like Gillette at a P/E of 64 or Microsoft at a P/E of 66. This reflects not their nuttiness but their sanity.

Rationally Exuberant

Contrary to Alan Greenspan’s famous warning—made on December 5, 1996, with the Dow at 6,437—investors today are rationally exuberant. They are bidding up the prices of stocks because stocks are a great deal. Dow 10,000 is just for starters. How high will the market go? We’ll give you a hint: The title of our book, to be published this fall by Times Books, is Dow 36,000. Using sensible assumptions, we are comfortable with prices rising to three or four times their current levels. Our calculations show that with earnings growing in the long term at the same rate as the gross domestic product and Treasury bonds below 6 percent, a perfectly reasonable level for the Dow would be 36,000—tomorrow, not 10 or 20 years from now.

What do we mean by a “perfectly reasonable price”? If traditional P/E ratios or dividend yields no longer apply, then what does? Our model looks at how much money a stock will put in your pockets through the profits generated by the company that issued it. Then, using those returns, we put a price on a stock that is in line with the price of another asset that carries roughly the same risk.

That other asset, believe it or not, is a government bond. Extensive research by Jeremy Siegel of the University of Pennsylvania’s Wharton School has found that over 20 years and more, stocks are no more risky than Treasury bonds or even bills. “The safest long-term investment for the preservation of purchasing power has clearly been stocks, not bonds,” he has written.

Stocks and bonds should offer similar returns at the very least. But according to Ibbotson Associates, large-company stocks have since 1926 been producing average annual returns of 11 percent, while long-term Treasury bonds have returned just 5.2 percent.

Why do stocks return so much more? That question has vexed economists for decades. Their best answer is that investors are irrationally fearful of the volatility of stocks, and therefore demand an extra return to compensate for their fears. What has happened since 1982, and especially during the past four years, is that investors have become calmer and smarter. They are requiring a much smaller extra return, or “risk premium,” from stocks to compensate for their fear. That premium, which has averaged about 7 percent in modern history, is now around 3 percent. We believe it is headed for its proper level: zero. That means stock prices should rise accordingly.

It is this declining risk premium—not higher earnings or lower interest rates—that is the true explanation for the ascension of stocks. The increase in the number of buyers has naturally pushed up the price. To argue today that stocks are overvalued, you must believe that the risk premium, once so irrationally large and becoming rationally small, will move back to that irrationally large state again.

The bears’ view of the world is a contradiction. When the equity risk premium was high, it was a “puzzle,” and economists like Richard Thaler of the University of Chicago came up with complicated explanations for why investors were behaving in such a screwy fashion. Now that investors have smartened up and begun to buy stocks, economists are accusing them of being screwy again. Our colleague Lawrence Lindsey said recently: “We have all the signs of a bubble. . . . People get greedy, and they think nothing can go wrong.”

Will stock prices rise forever? No, they’ll rise until they reach a level where stock returns (the money stocks put in your pockets over a long period) equal bond returns. We are not there yet, but we’re on the way—as four straight years of 20-plus percent returns attest.

Assume Treasuries yield 6 percent. To equalize that cash flow, stocks can yield much less than 6 percent, because, unlike bonds, stocks increase their earnings and dividends each year. In inflation-adjusted terms, earnings per share have been rising by an average of 3.3 percent annually since World War II.

Our conservative calculations show that an earnings return of about 1 percent—or a P/E of 100—is adequate to match cash returns from bonds over long periods. Since the P/E of the Dow is currently about 26, stocks could nearly quadruple before becoming overpriced.

But 36,000 or 40,000 is not so much a precise target as the outer limits of a comfort zone for long-term investors. Certainly, stocks could fall sharply in the short term—as they did last summer after the Russian default—but, ultimately, prices reflect three things: interest rates, earnings, and the risk premium. As long as rates stay reasonable, earnings rise with GDP, and the risk premium keeps falling, stocks will remain the investment of choice.

Why is the risk premium dropping? First, investors have become better educated about stocks, thanks in large part to mutual funds and the media. They have learned to hold for the long term and to see price declines as transitory—and as buying opportunities. Look at 1998, a year in which, by some indicators, the stock market registered its highest volatility in history. Investors did not cut and run; they added $151 billion to equity mutual funds. A study by the Investment Company Institute found that during the market’s 19.3 percent decline over six weeks last summer, investors redeemed only 0.3 percent of their stock-fund holdings. And a study by the Boston firm Dalbar, Inc., concluded: “In a dramatic reversal of the behavior first identified in Dalbar’s 1993 report on investor behavior . . . the 1998 investors see the down market as a buying opportunity.”

Long-Term Holding

Second, partly because of new laws, 31 million Americans (an increase of 48 percent in less than a decade) keep stocks in tax-deferred retirement accounts, which force long-term holding. Third, businesses themselves have restructured and become more efficient, thanks to shareholder pressure, global competition, and computer technology. They are less likely to suffer devastating reversals in a recession. Fourth, government monetary and fiscal management have greatly improved. Fifth, the regulatory and tax environment—while far from perfect—is more benign. Sixth, foreign threats have diminished.

In short, investors’ enthusiasm is well founded. The risks of stock investing—never so great as imagined—really have declined. In 1952, a New York Stock Exchange survey found that only 4 percent of Americans owned equities; today, the figure is nearing 50 percent. It is this broad ownership of stocks that is the most profound evidence that investors have become more rational and that Dow 10,000 is only the beginning.

James K. Glassman is the DeWitt Wallace-Reader’s Digest Fellow at AEI. Kevin Hassett is a resident scholar at AEI. Their book Dow 36,000 will be published this fall by Times Books.

Source Notes: A version of this article appeared in the Wall Street Journal on March 17, 1999.

AEI Print Index No. 10347

Yes. Actually this isn’t that nutty, but unfortunately still wrong. The authors were wrong on the call that the risk premium declined in such dramatic fashion in explaining the market rise. Clearly, the risk premium cannot approach zero, as long as there is undesirable uncertainty in stock performance over any time period (including short-term) and over the collection of stocks. There is also a funny sentence in there about historically rising earnings per share justifying a lower (current) earnings return… but in the past, rising earnings per share led rising share price — earn more and then higher share price follows to reflect it; before every company can guarantee a rising income stream, they would have to borrow money to reflect current earnings or, if it were to reflect future earnings, then at a significant risk premium. And since no company (and not even an entire economy) can guarantee clockwork-like earnings rise, this article’s premise is unfounded.