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William J. Bernstein

On Efficiency, Rationality, and Arbitrage

Efficiency, Rationality, and Arbitrage

I spent most of the Internet Boom in a disoriented fog. For example, I could never decide which part of speech the corporate moniker Yahoo! was supposed to represent. Was it an interjection, reflecting the technologic and economic ebullience of the time, or was it simply a noun, meant to describe the company’s shareholders?

The definitive history of the Great Internet Bubble has yet to be written, but there are a few observations that can already be made, as we’ve all had bestowed upon us a morbid historical privilege, not unlike witnessing the 1906 San Francisco earthquake. I still remember the sheer wonder of my first reading of Mackay’s Extraordinary Popular Delusions and the Madness of Crowds, which described the Dutch Tulip, South Sea, and Mississippi Company episodes—what must it have been like to live in such a time! Now you and I know. Not since the diving and bubble companies of the 17th and 18th centuries have entities with so little substance commanded such high prices. If we were not personally touched by these Internet shooting stars, we all knew folks who were.

The Morningstar April 2000 stock module occupies an honored place on my hard drive, and from time to time I sift through the names with awe: Terra Networks, selling at 1200 times sales; Akamai Technologies, 3700 times sales; Telocity, 5200 times sales. Not a one with earnings. What were we thinking?

But my all-time favorite is Internet Capital Group. On August 5, 1999, it went public at $6 per share, rose to $212, then fell back to under a buck. Nothing unusual, really. What made it such an enchanted soul was that it was the direct descendant of the 1920s leveraged investment trust—its holdings were small private companies operating in the wildest, woolliest part of the Internet scene, business-to-business (B2B) enterprises. This company actually issued bonds (of about the same quality as those my butcher at Safeway might issue, if only the SEC would allow him to do so). The frosting on the cake was that Internet Capital Group common stock sold at an estimated 10 times the value of the companies it held. So not only did it own pure fluff, but was valued at 10 times this fluff.

Surely, you say, such a market is not efficient. From time to time, markets do go stark raving mad or, on the other more subtle extreme, become toxically depressed. Shouldn’t the intelligent investor find it easy to garner excess long-term returns by keeping his head when all about him have lost theirs? Such doubts about market efficiency get to the heart of how we define it.

Two papers shine like lighthouses on a foggy night for the thoughtful investor trying to navigate these treacherous shoals. The first is an editorial by Mark Rubinstein in Financial Analysts Journal (May/June 2001) entitled, "Rational Markets: Yes or No? The Affirmative Case." (If the author’s name rings a bell, it should: Rubinstein and his Berkeley sidekick Hayne Leyland, in response to their deteriorating lifestyles, gave us portfolio insurance 15 years ago, just in time for the 1987 crash. So much for Adam Smith’s "invisible hand.") The second, which I’ll get to further below, is a piece by Andrei Shleifer and Robert Vishny, "The Limits of Arbitrage," in Journal of Finance (1997).

Rubinstein’s editorial defines three types of rational markets (which correlate only loosely with the strong, semi-strong, and weak forms of the Efficient Market Hypothesis):

  • Maximally Rational: All market participants are maximally rational. This means that there is no trading. Rubinstein points out that no one takes this seriously—just look at market volumes.

  • Plain-Vanilla Rational: The markets behave as if all participants are rational. One group of investors may be inappropriately optimistic about a security; another, inappropriately pessimistic. But the net effect is rational pricing. Most investors may be grossly under-diversified, but the overall market portfolio is efficient.

  • Minimally Efficient: The markets themselves are not rational, but still do not provide opportunities for excess returns. Yes, Rubinstein says, closed-end funds trade with irrational discounts, prices are too volatile relative to information (Quickly now: do you recall the news that triggered the 1987 crash?) or certain stocks are grossly overpriced. But there is no way to reliably profit from this information.

  • Rubinstein surveys an impressive litany of market irrationality. He presents the case of the behavioral finance proponents (Richard Thaler and his many disciples) who are fond of pointing out common investor errors as evidence against market efficiency, listing no less than 35 examples of investor irrationality. He then goes on to detail six major market anomalies (excess volatility, the risk-premium puzzle, the value and size effects, closed-end discounts, calendar effects, and the 1987 crash).

    Finally, Rubinstein discusses exactly one real argument in favor of market rationality: the sorry story of mutual fund non-performance and non-persistence, citing the literature from Jensen to Carhart. True, only one area of hard data versus a whole panoply of anomalies and behavioral deficits; but, he argues,

    It [mutual-fund nonperformance] should not simply be put on one side of the ledger and given equal weight with any market anomaly on the other side. In fact, just to pile on the metaphors, the behavioralists have nothing in their arsenal to match it; it is a nuclear bomb against their puny sticks.

    The gauntlet is thrown down: Where are the behavioralists’ yachts?

    Rubinstein concludes that the markets are at least minimally rational; he rejects maximal rationality and is mute on the possibility of plain-vanilla rationality.

    For my money, the classic in the behavioral finance field on the topic of market efficiency is Andrei Shleifer and Robert Vishny’s paper, "The Limits of Arbitrage," published in Journal of Finance in 1997. (Hey, what is it about these academics? Shleifer recently found himself the unhappy target of a federal probe surrounding Russian investments made by his wife while he was directing the Harvard Institute for International Development.)

    "Arbitrage" refers to operations which produce riskless profit. The example used by generations of economics professors is that of a newspaper simultaneously selling on one street corner for a nickel and on another for a dime. This is a riskless venture: one simply buys the papers for five cents and sells them on the next corner for double the price.

    The only problem, of course, is that since no operation is truly riskless, arbitrage doesn’t really exist (until someone coined the oxymoron "risk arbitrage," which most often refers to trading in the securities of takeover participants). Our mythical newspaper trader has a number of problems. First, it’s possible that in the interval between buying for a nickel and selling for a dime, the price differential may collapse. Second, and of greater relevance to the capital markets, a nickel profit is just not very much money. To make the venture worthwhile, he must turn the trick with hundreds of thousands of newspapers; he’ll likely have to borrow money to buy all those nickel papers. Creditors may not be as patient as he is and may decide to pull the plug if things go slowly, leaving our "arbitrageur" bankrupt. Last, but not least, he will run straight into market impact costs; he’ll rapidly run out of pigeons willing to pay ten cents for a paper and will have to lower prices to unload the rest.

    Shleifer and Vishny point out that in the real world of finance,

    . . . arbitrage is conducted by relatively few professionals, highly specialized investors who combine their knowledge with resources of outside investors to take large positions. The fundamental feature of such arbitrage is that brains and resources are separated by an agency relationship.

    The problem then is, although the arbitrage professionals (which I broadly define to include active mutual-fund and pension managers) allocate resources rationally according to future expected returns, their investors allocate among professionals according to past results.

    This is the key point. Imagine that a fund manager believes value stocks have a higher return than growth stocks in the long run and, further, that over very long time horizons (say, greater than 20 years), the manager is always right. But value does not beat growth all the time; it is quite common for the opposite to occur for a few years. As growth stocks temporarily appreciate in price relative to value stocks, two things happen: First, the expected return of the value-versus-growth bet increases. And second, uninformed investors start pulling money out of this manager’s fund. So, the typical money manager finds that the greater the opportunity, the less assets he has to manage. The reverse happens when things are going his way; he will be awash with assets just when expected excess returns disappear or, worse, when they become negative.

    Now just imagine that this money manager runs into a bad stretch, say, 15 years, which is just what we’re hopefully emerging from, with value-versus-growth stocks. Shleifer and Vishny refer to this situation with a sneer as "performance-based arbitrage." And it can get even worse: What if you are leveraged? Your creditors are almost certainly "uninformed" and will want their money back, forcing you to sell your positions, adversely impacting prices in the bargain.

    But worst of all, a bad stretch can make even the most disciplined players lose heart. The authors assign the lowest circle of hell to "Bayesians": managers whose return expectations move with the market, not counter to it, as any rational manager’s would. (In unlovely econ-jargon, "a sequence of poor returns may cause an arbitrageur to update his posterior and abandon his original strategy." Well, not quite; when you abandon your strategy, you are not so much updating your posterior as kissing it goodbye.) At the end of a bubble, almost all investors are Bayesians; this was certainly true of tech-fund managers.

    The authors make a few other salient points:

  • Quoting them, "the long-run ratio of expected alpha to volatility may be high, but the ratio over the horizon of one year may be low." We covered this ground in the last issue—it is not a peculiarity of some asset classes, as the authors imply, but a general quality of all financial assets. In plain English, in the long run, return compounds faster than risk. Unfortunately, for arbitrageurs there is no long run, only a ferocious series of short runs in which volatility eventually overwhelms return and, with it, their employment.

  • The overwhelming majority of arbitrageurs hold highly undiversified portfolios; therefore they are very concerned about the unsystematic risk of assets and "price" this risk, i.e., lower valuations so that returns will increase to compensate for the additional risk. Thus, a pricing model (read as, the Capital Asset Pricing Model) that prices only unsystematic risk is inappropriate. As an amusing aside, the folks at Dimensional Fund Advisors, who constitute the Efficient Market Hypothesis’s best and brightest, freely admit that one of the risks of value investing, where one is rewarded with higher expected return, is that it is not as diversified as the market portfolio and will often temporarily underperform. They cannot quite bring themselves to utter the words "tracking error."

  • Finally, Shleifer and Vishny attack the value-premium controversy: is it risk or behavior? To wit, "arbitrageurs trying to eliminate the glamour/value mispricing might lose enough money that they have to liquidate their positions. In this case, arbitrageurs may become the least effective in reducing the mispricing precisely when it is the greatest. Something along these lines occurred with the stocks of commercial banks in 1990-1991."

  • Their paper, published in 1997, gets my Nostradamus Award for the decade, foreshadowing the slaughter of those who, correctly perceiving the massive overpricing of tech stocks in the late 1990s, shorted them and ran out of margin long before the cavalry arrived in March 2000. In other words, just when the returns from shorting tech stocks were the greatest, the ammunition necessary to maintain their position was thinnest on the ground.

    The occasional prolonged, massive failure of even the most coldly calculated strategies gets to the heart of the rationality/efficiency conundrum: The markets are at best "minimally rational," as defined by Rubinstein. The market frequently misprices securities and, every once in a while, entire asset classes. But the market is highly efficient—because of the limits of arbitrage, it is very difficult to make much money from the irrationality. First and foremost, to make it worth your while, you have to deviate from the market portfolio—that is, place bets—with a significant chunk of assets, perhaps not all your own. And therein you sow the seeds of your own destruction. In the case of the money manager, his vocational time horizon is usually much shorter than that of the pricing anomaly he identifies. And in the case of the small investor, this happens because he is prone to "reevaluating his posterior." When the cheap asset class or stock that you originally allocated 5% of your portfolio to, becomes 2% over the course of a decade, do you really have the fortitude and conviction to repeatedly rebalance back to 5%, let alone increase the bet? There are few things more discouraging than a bad asset class gnawing at your posterior for years at a time.

    I do believe that it’s possible to earn excess returns from market irrationality. But because the above considerations mandate very small bets, the rewards are tiny, highly uncertain, and quite probably not worth the trouble. The rational investor treats concentrated positions and substantial deviations from market sector weighting in the same way that Burton Malkiel treats the "mad money" portion of his portfolio—a very small corner of the show, mostly for entertainment. One occasionally does find $10 bills lying on the ground, but the intelligent investor does not attempt to make a living doing so.

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