VenChar

Collaborative divorce

Via Catallarchy, this interesting article in the NYT on a new practice known as collaborative divorce:

In some ways, the method resembles mediation in its problem-solving approach. But rather than a neutral mediator, each party brings a lawyer to the sessions, as advocate and adviser. But the very format changes how lawyers behave. The cornerstone of the process — and its most controversial element — is that the two lawyers sign a pledge to withdraw from the case if either of their clients decides to go to court. This gives the lawyers an economic incentive to leave adversarial habits behind. It also encourages clients to stay at the bargaining table, since bolting means starting over with new counsel.

Furthermore, this approach attempts to avoid the winner-take-all litigation scenario which inherently poses greater risk to both parties. As Jonathan Wilde points out in his post:

There is a clear difference between dispute resolution in public and private domains. Public dispute resolution is nearly always a winner-takes-all game, because coercion is used to back up verdicts. Judges are not working for a profit, and thus, do not have to please both parties in order to attract future business.

In contrast, lawyers specializing in collaborative legal resolution have to build reputations not just for being strong advocates for their clients, but also for expeditious resolutions without the usual emotional nastiness and financial trauma that accompanies state-based divorce proceedings.

The ideal resolution to a divorce dispute should leave both parties with at least some degree of satisfaction. The state legal system is loaded with incentives against this type of bilateral benefit.

eBay auction data and the economy

Via Infectious Greed comes this very interesting USA Today piece. I had written earlier about eBay's stated move towards licensing its auction data and what that might mean. Well, this article takes a look at the year 2003 through the lens of eBay auction data. Some excerpts:

There are many ways to analyze 2003. You can sift through major news events. You can chart best-selling books and top-rated TV shows. You can dissect the stock market. But if you want the gestalt of America — the unified essence of this nation at this time — there might be no better place to turn than the massive databases that run eBay.

There sits a repository of culture and commerce unlike any before it. No executive decides what eBay sells. Instead, millions of individuals post items on the Web site in response to shifting nuances in the marketplace. Because it is so fluid, the site captures the collective mood and unique extremes of the 86 million people who use it.

Though government numbers show the economy is rebounding after more than two years of doldrums, the eBay economy suggests something different. In fact, it seems to show a lag effect. People and companies downshifted as 2003 wore on.

For instance, eBay tracks searched words, which in turn are indicative of what buyers are looking for. Word searches for all of 2002 reflect a society still spending freely. Among the top 10 searches for the year were BMW, Louis Vuitton, Prada and Coach. Similar terms dominated the top 10 into early 2003, until August, when there was a sudden shift. The Iraq war was dragging on. Companies were still cutting jobs and keeping raises flat. The blackout hit. California was in political chaos with its recall vote. And just then the luxury names dropped off eBay's top 10, replaced by more mundane words such as Ford, Chevy and diesel.

In September, "salvage" made it to the top 10.

"I don't see any huge economic recovery," says Neal Sherman, whose company, The Advantage Group, uses eBay to liquidate goods for companies and public entities. It recently listed the entire contents of a supermarket, minus the food, and sold a yacht for the state of Maryland for $275,100.

"Take coffee equipment and mixers — a good operator in flusher economic times would buy those new," Sherman says. "When times are tough, they save money and buy it in the aftermarket." From everything Sherman sees, the aftermarket for used business stuff is turbocharged.

Some other tidbits about 2003 from the eBay files:

* The Aug. 14 blackout in the Northeast shook confidence in the power grid. In the week after the blackout, sales of portable generators jumped 67% vs. the previous week. But it wasn't just a knee-jerk spike. Generator sales on eBay are running at an annualized rate of $12 million, up 191% over 2002. It seems we're sure another outage is coming, and we want to be ready.

* The war proved a boon to eBay's category for pieces of gold. Sales are up more than 70% over a year ago. People generally buy gold when they believe bad times will drive down the value of the dollar.

* In October, when the Cubs seemed on the way to their first World Series championship in more than 80 years, everyone wanted a piece of that, too. EBay's sales of Cubs paraphernalia shot up more than six times over the year before.

* During Arnold Schwarzenegger's campaign for California governor, everyone wanted a piece of him. EBay's sales of Schwarzenegger-related items — from a 1969 Iron Man magazine with him on the cover to Terminator 2 talking dolls — climbed 1,500%.

* eBay's industrial products market took off in 2003. As an example, doctors and dentists, squeezed by insurance companies, turned to eBay in 2003 to buy medical equipment. In general, medical professionals are wary of buying used equipment. But the category is up more than 100% over last year.

This is a treasure trove of information: about the medical equipment market, about the market for used cars, the likelihood of success of gubernatorial candidates and sports teams, estimates of the likelihood of power failures, and consumer confidence and spending. There should be a rich aftermarket for eBay auction data analytics.

Mispricing in information aggregation markets

I recently read a survey paper on behavioral finance (written by Nicholas Barberis and Richard Thaler at the U of Chicago and available here). One of my key takeaways from reading the paper was the idea of limited arbitrage (subject of my previous post). The basic idea is that mispricing may persist because arbitrage is costly and/or risky.

I've also been watching information exchanges and information aggregation markets (such as the Hollywood Stock Exchange, the Iowa Electronic Markets, the aborted terrorism futures market, etc.) with interest and the problem of mispricing is an especially important one in this context. This raises the following question: Is it possible to create controlled market environments (either through the intelligent design of tradable securities or through qualifying traders who are allowed to participate, etc.) such that the probability of enduring mispricings is reduced significantly? This would seem to be an important question. From reading the survey paper it would seem that reducing implementation costs, making substitute securities available, reducing the number off noise traders, etc. are obvious ways to reduce the effects of mispricing. Anyone out there know of any pertinent research?

Limits to arbitrage

I recently read a survey of behavioral finance by Nicholas Barberis and Richard Thaler at the University of Chicago – the paper is available here. What follows are some of my notes:

Traditional finance seeks to explain and understand financial markets using models in which agents are “rational”. Rationality means two things:

1. When they receive new information, agents update their beliefs correctly, in the manner described by Bayes’ law.
2. Given their beliefs, agents make choices that are normatively acceptable, in the sense that they are consistent with Savage’s notion of Subjective Expected Utility (SEU).

Behavioral finance argues that some financial phenomena can plausibly be understood using models in which some agents are not fully rational and analyzes what happens when one or both of the assumptions about agent rationality are relaxed. There are two building blocks to the theory: limits to arbitrage (the price of an asset may not equal its fundamental value – this represents a mispricing. However, this mispricing may persist for long periods of time because arbitraging it away may entail significant risks and costs) and psychology (if agents are not rational, in what way are they irrational? What is the theoretical framework for describing the deviations from rationality? How can experimental psychology inform the construction of economic models for agent behavior?).

In this post I will discuss (what I understand of) the notion of limits to arbitrage, mostly drawing from the review. But first some background on market efficiency, etc.

(click below to continue reading)

In the traditional framework (rational agents, no friction), a security’s price equals its fundamental value (i.e., the discounted sum of all future returns). The underlying hypothesis – that prices reflect fundamental value - is known as the Efficient Markets Hypothesis (EMH). If the EMH is true, it follows that there is “no free lunch”: “no investment strategy can earn excess risk-adjusted average returns, or average returns greater than are warranted for its risk.”

Behavioral finance argues that some features of asset prices are most plausibly interpreted as deviations from fundamental value brought about by the presence of at least some traders who are not fully rational. A well-known objection to this argument (attributed to Friedman) is that even if irrational traders were to create such deviations, this effect would quickly be undone by rational traders arbitraging away the deviations. The authors of the survey use the following example to illustrate Friedman’s argument:

Suppose that the fundamental value of a share of Ford is $20. Imagine that a group of irrational traders becomes excessively pessimistic about Ford’s future prospects and through its selling, pushes the price to $15. Defenders of the EMH argue that rational traders, sensing an attractive opportunity, will buy the security at its bargain price and at the same time, hedge their bet by shorting a “substitute” security, such as General Motors, that has similar cash flows to Ford in future states of the world. The buying pressure on Ford shares will then bring their price back to fundamental value.

This argument, while superficially compelling, has some weaknesses. In particular, it is built upon two assertions: (1) that such mispricings create attractive investment opportunities, and (2) that rational traders will quickly snap up the opportunity and thereby correct the mispricing. Behavioral finance takes issue with the first of these assertions: it is argued that “even when an asset is wildly mispriced, strategies designed to correct the mispricing can be both risky and costly, rendering them unattractive. As a result, the mispricing can remain unchallenged.” This is the key explanation for the survival of mispricing – that it can be risky or costly to correct.

The authors point out a corollary of this line of thinking: while there can be no free lunch in an efficient market, the same may be true in an inefficient market – “just because prices are away from fundamental value does not necessarily mean that there are any excess risk-adjusted average returns for the taking.” The relevance of this observation is the following: “many researchers still point to the inability of professional money managers to beat the market as strong evidence of market efficiency. Underlying this argument, though, is the assumption that “no free lunch” implies “prices are right.” If this link is broken, the performance of money managers tells us little about whether prices reflect fundamental value.”

What are the possible risks and costs associated with correcting a mispricing? Here are a few (exemplified in the context of the example of Ford, whose fundamental value is $20, but which has been pushed down to $15 by pessimistic noise traders):
• Fundamental risk: the most obvious risk facing the would-be arbitrageur is new information that causes the fundamental value of Ford’s stock to fall – negative news on earnings, for instance. The arbitrageur can insure against this risk by shorting a substitute security (such as GM stock). While this insures against risk that equally affects all industry players, it doesn’t insure against idiosyncratic risk specific to Ford. In other words, there may not be perfect substitutes that can be used as insurance.
• Noise trader risk: This is risk associated with the fact that the effects of the mispricing might worsen, in the short run, but not due to a change in the fundamental value. “Once one has granted the possibility that a security’s price can be different from its fundamental value, then one must also grant the possibility that future price movements will increase the divergence.” Noise trader risk matters because this worsening of the mispricing may force the arbitrageur to liquidate early and sustain steep losses. Here it is relevant to note that there may be agency effects (the arbitrageur may be managing someone else’s money and may face pressure to liquidate underperforming holdings or face withdrawal of funds) and time-horizon effects (if it takes several months for the mispricing to correct itself and the arbitrageur needs liquidity in a month, this risk may dissuade him from the investment). This source of risk was first pointed out by De Long and others (Bradford De Long maintains a blog, BTW).
• Implementation costs: These include transaction costs (bid-ask spreads, etc.), short-sale constraints (financial as well as legal (“for a large fraction of money managers – many pension fund and mutual fund managers in particular – short-selling is simply not allowed”))

When such risks and costs are present, the mispricing may persist because arbitrage is too risky or too costly. This is known in the theory as “limited arbitrage”.

Given these sources of cost and risk associated with attempts to correct mispricings, what are the conditions under which we can expect such mispricings to persist? Here are a few scenarios:
• No close substitute: in this case, the arbitrageur is exposed to a good degree of fundamental risk.
• Short horizons: Even if there exist perfect substitutes and there are no implementation costs, a degree of risk aversion combined with short investment horizons on the part of the arbitrageurs can imply that the mispricing will persist due to noise trader risk.

The survey paper also has several examples (twin shares, index inclusions, carve-outs) of systematic and large mispricings that persisted for long periods of time.

Winner's curse

Winner's curse is one of the reasons why prices determined by auctions deviate from "true values" (I mentioned it recently in the context of eBay's apparent plans to capitalize on their transaction data) - auctions, by their nature, tend to favor those bidders who have most overestimated the value of the item for sale. Even if some of the bidders have accurate (unbiased) estimates, the auction favors (or selects) those bidders who have a (postively-) distorted estimate of the value. The winner, therefore, finds himself having overpaid, relative to the true value of the item - this is the winner's curse.

The magnitude of this effect depends on the number of bidders: the more the bidders, the more likely it is that the winning bid seriously overestimates the value. This is intuitively obvious. It turns out that the effect of the number of bidders can be quantified (under the assumption that the bidders' estimates are derived from an underlying normal (Gaussian) distribution): for example, with 2 bidders, the winning bid overstimates the value by 0.56*SD (SD = standard deviation); with 500 bidders, the overestimation is 3*SD; with 1000 bidders, the overestimation is 3.25*SD, etc. [The dependence on N, the number of bidders, seems to be logarithmic, with the multiplier approximated by Log(N) + 0.25. I'll try to derive the general result this weekend and see if this logarithmic rule is correct.]

This suggests a way to correct for winner's curse effects in the eBay example from yesterday - eBay should release the number of bidders, as well as relevant stats on the individual bids, along with the sale price of the item.

What the foregoing also implies is that bidders should reduce their estimates of value by the corresponding factors, to correct for winner's curse. Of course in sealed-bid auctions, in particular, it may be hard to estimate (and correct for) the number of bidders. The standard deviation can also be hard to estimate, in general.

Shifting gears slightly and looking at the problem of auction design, it turns out that, it is desirable to minimize winner's curse effects. This is somewhat counter-intuitive, but the reason is this: visibly reducing winner's curse risk encourages experienced bidders to be more aggressive in bidding, since the risk of overpaying is reduced. The result is that the policy of reducing winner's risk actually increases the amount paid.

Ways to reduce winner's curse effects:
* Release relevant information about other bidders' bids as well as information vailable to the seller. Availability of better information reduces risk of overestimating value.
* Royalties (tie the buyer's payment to the realized value of the item). "For example, the right to broadcast the summer Olympics held in Seoul ... was auctioned with a royalt payment - the amount paid would depend on the size of the television audience." Again, this reduces winner's curse risk by tying at least a fraction of the payment to the actual value realized by the bidder.

I learnt about the winner's curse effect from Preston McAfee's 'Competitive Solutions', which I read recently.