Asset pricing: liquidity, trading, and asset prices.

• Author: Cochrane, John H.
• Position: Program Report

Members of the NBER's Asset Pricing Program produce over 100 working papers in a typical year. These papers are spread over an astonishing range of topic areas. Naming the papers written in the four and a half years since the last program report, let alone providing any sort of intelligible summary of their contents, would quickly fill the available space and exhaust the most dedicated reader's patience. Therefore, I'll describe in depth one area that strikes me as particularly interesting and that may be novel to likely readers of this report. I proceed with an apology to all the authors whose papers are thus omitted. In addition, I confine myself to papers in the NBER Working Paper series or presented at Asset Pricing Program Meetings in the last four and a half years. I apologize in advance to non-NBER authors and to authors of older papers whose work should be discussed in a comprehensive literature review.

My focus here goes by a variety of names, including liquidity, trading, volume, market frictions, short-sales constraints, and limits to arbitrage. For a long time, there has been an implicit separation of effort in asset pricing: Researchers operating in the frictionless macroeconomics--based tradition study the broad level of prices, while researchers in the market microstructure tradition--filled with non-Walrasian trading, asymmetric information; and so on--pretty much study small (but interesting) refinements, where prices fall in the bid-ask spread rather than where the spread is in the first place.

Recently, this separation has begun to erode. At one level, this erosion is the beginning of a long-expected understanding of trading and volume. The classic theory of finance has no volume at all: prices adjust until investors are happy to continue doing what they were doing all along, holding the market portfolio. Simple modifications, such as lifecycle and rebalancing motives, don't come near to explaining observed volume. Put bluntly, the classic theory of finance predicts that the NYSE and NASDAQ do not exist. Lifecycle stock trading could be handled at a retail level, like (say) life insurance. The markets exist to support high frequency trading. They are at bottom markets of information (or, some might say, opinion), not really markets for stocks and bonds.

Now, perhaps prices are set as if volume is zero, and then volume and the attendant microstructure issues can be studied separately. But perhaps not; perhaps volume, trading, liquidity, and market structure effects spill over to affect the level of prices. This is the issue I focus on. I start with empirical work, and follow with economic modeling that tries to understand the emerging set of facts.

Empirical Work

3Com, Palm and Convenience Yield

Work by Owen A. Lamont and Richard H. Thaler most vividly brought this constellation of ideas to my attention. They start with the case of 3Com and Palm. On March 2, 2000, 3Com sold 5 percent of Palm in an initial public offering. 3Com retained about 95 percent of the shares, and announced that it would distribute those shares to 3Com shareholders by the end of the year at about 1.5 shares per one 3Com share. Thus, one could obtain 150 Palm shares in two ways: buy 150 Palm shares directly or buy 100 3Com shares and end up in six months with 150 Palm as well as 100 3Com.

Surely the latter strategy should cost more. But in fact, the latter strategy was cheaper. Palm prices exploded, 3Com prices fell, and at the end of the first day of trading the "stub value" of 3Com shares (the value of 3Com less the embedded Palm shares) was negative $63! This violation of the law of one price lasted for quite a while, as shown in Lamont and Thaler's Figure 3. The event was not unique. Lamont and Thaler study six additional cases of persistent negative stub values in a carve-out followed by a spin-off.

Lamont and Thaler carefully document that these events did not present exploitable arbitrage opportunities. Most simply, a trader might want to short Palm and buy 3Com. But the costs of shorting were so high as to make this trade unprofitable or impossible. Rationed out of the short market, a trader might try to buy put options. But this strategy did not work either. The option market became delinked from the stock market; there were wide violations of put-call parity, precisely because arbitraging between stocks and options required shorting stocks.

The absence of an exploitable arbitrage is a little bit comforting, but it does not address the basic question: why were the prices so out of line in the first place? Lamont and Thaler's view is simply that there were a large number of "irrational" traders, who just did not see the chance to buy Palm embedded in 3Com, and for whom buying Palm rather than 3Com (and similar cases) was therefore "simply a mistake."

Intrigued by this paper, I investigated (2) the issue a bit further. 3Com and Palm remind me of money and bonds. Just as 3Com and Palm are both claims to Palm shares in six months, so money and a six-month Treasury bill are both claims to a dollar in six months. Yet the bill is cheaper and the dollar is "overpriced."

You might object that nobody holds money for six months. The whole point of money is that you hold it only for a short time, in order to make transactions. But few people held Palm for six months either. Lamont and Thaler document that 19 percent of available Palm shares changed hands every day in the first 20 days after the IPO, and several of their other cases have even larger volume. Furthermore, Palm had a 7 percent standard deviation of daily returns, or a 15 percent standard deviation of 5-day returns--as much as the S&P500 moves in a year. If you can predict any of this movement, then the 2/10 percent per day expected loss due to "overpricing" is trivial; it's less than the commissions and bid-ask spread facing these active traders.

You might object that money is "special" because you need to hold it to make transactions. Palm stock was special too. To bet on information about Palm, you had to hold Palm stock. Even to short Palm, you must first find a lender, borrow Palm shares, and then sell them. Options trading or trading in 3Com stock (3Com still held 95 percent of Palm shares) were poor substitutes, as both markets became delinked from high frequency movements in Palm stock market in this period.

Palm and money behave similarly in many other ways. Money is more overpriced--the interest rate is higher--when velocity is higher. The same is true for 3Com and Palm: the "overpricing" was highly correlated with Palm volume. The monetary overpricing (interest rate) is lower when the money supply is larger. The same is true for 3Com and Palm. Palm started with only 5 percent of total shares available, and less than that available for trading, because those receiving IPO allocations are strongly discouraged from flipping (selling) or lending their shares. Short selling provides an extra "supply" of shares, just as checking accounts provide extra money for transactions. Short selling in Palm built up quickly after the IPO. Palm peaked at 146 percent short interest--the average share had been lent out to short more than once--more than doubling the supply. As this supply increased, the overpricing fell. 3Com fell during the Palm IPO, even as the latter was exploding in value and even though 3Com still held 95 percent of Palm shares. With no horrible news about the rest of 3Com, this fall only makes sense if the Palm-information traders all coordinate on trading Palm shares, so that "convenience yield" for trading in Palm prospects suddenly moves to Palm and away from 3Com.

In sum, these observations suggest to me that trading generated a "convenience yield" for Palm shares, just as physical trading generates a convenience yield for money. People wanted to trade on information or opinions about the fortunes of Palm's invention, the PDA. To do this, they had to hold Palm shares, but Palm shares were in short supply. This "convenience yield" nicely links a large number of phenomena: 1) "overpricing" of seemingly identical securities; 2) "overpricing" is higher when volume is higher; 3) "overpricing" is higher when share supply is lower; 4) "overpricing" is higher when there are fewer substitutes for trading (options, correlated stocks); 5) "overpricing" is higher when there is more price volatility (a sign of more information flow); and 6) 3Com stock fell at the Palm IPO.

Most stories for 3Com-Palm are at best silent on points 2-6. In particular, "irrational investors" or "rational bubbles" do not link "overpricing" with volatility and volume, whereas all of the famous "bubbles" have featured tremendous turnover and volatility. If something about the psychology of evaluating risks makes traders irrationally attracted to Palm, why do 20 percent change their minds and resell their Palm shares on any given day?

You might object, "How could convenience yields or liquidity premia be that large?" First, recall that monetary "overpricing" can be quite large as well. In a 100 percent per year hyperinflation, currency trades at twice the value of six-month bills, and probably still with less than 20 percent daily turnover. Second, recall the Gordon growth formula: that the price-dividend ratio is the inverse of expected return less dividend growth, P/D = 1 (r-g). If a stock has a price-dividend ratio of 50, r-g = 0.02, so a single percentage point change in expected return can double the price if it's persistent. Liquidity premia of one percent or so are observed in the bond market, so one might not be surprised by substantial liquidity premia in stock prices.

Is this an isolated incident, or is a substantial "convenience yield" for trading one important part of stock valuation in general? Some simple facts in my paper suggest the latter possibility. In particular, "high price" stocks trade frequently, both in the cross section and in the time...