The essence of the argument can be shown in the demand-and-supply dia- gram shown as Exhibit 5.1. Here there are only two opinions about a stock. One group of investors has a higher estimate and will be referred to as the optimists. The other group has a lower estimate and will be referred to as the pessimists. Later the types of errors that might be made will be
discussed. For simplicity, each investor who desires a security in his port- folio will be assumed to buy a certain quantity of that security. (This ignores the intensive margin in which the more that is bought the more optimistic an investor is about a security.) As can be seen in Exhibit 5.1, the demand curve for a security then consists of two horizontal lines.
With the assumption of no short selling, the supply curve is a vertical line at the number of shares issued by the company. By the standard argument, the equilibrium price is where the supply and demand curves intersect.
The interesting question is whether the intersection will occur at the higher or the lower price. Is the price set by the optimistic or the pessi- mistic investors? The length of the higher line is the product of the num- ber of optimistic investors multiplied by the number of shares each purchases. If this exceeds the number of shares outstanding, the price is equal to the willingness to pay of the optimistic investors. Otherwise, it equals the willingness to pay of the pessimistic investors.1
Should we think of prices as typically being set by the optimists or the pessimists? Notice that the market value of any stock in current markets is just a small fraction of the market value of all stocks, and
1In the very unlikely case that the supply curve intersects the demand curve in its ver- tical section, the price is indeterminate.
EXHIBIT 5.1 Demand and Supply Curves Argument
that the typical investor has a position in only a small fraction of the large number of stocks that are available. The result is that typically the intersection occurs on the upper horizontal line, so that the prices typi- cally reflect the opinions of the more optimistic investors.
As an illustration of the relevant type of arithmetic, imagine a com- pany has a total market value of $1 billion dollars and 10 million shares outstanding, implying a market price of $100. If each investor holds as little as one round lot (100 shares), it will take 100,000 investors to absorb the full supply of the stock issued by the firm. If there are more than 100,000 investors who are optimistic about the stock, the upper horizontal line will extend beyond the vertical line indicating the supply, and the price will be at the upper value.
Typically, with two types of investors (optimists and pessimists) the price will be set by the optimists if the percentage of optimists exceeds the percentage of all investors who own the shares. Given that typically only a small percentage of investors will own any particular share, this condition appears to be commonly met. Thus, the optimists set the price. Obviously, this example requires that the average size of holdings be the same for the pessimists and the optimists, but this seems a reasonable first assumption.
Likewise, dividing investors into only two groups is usually a gross simplifi- cation (which can be relaxed without altering the essence of the argument).
That prices are set by optimists is not the same as the textbook state- ment that the price reflects the opinion of the average or typical investor.
We can expect that some optimistic investors are unaware of publicly available information or misinterpret it. These can be referred to as over- optimistic investors, and they can be expected to set some prices. With some prices set by the overoptimistic investors, it follows that there will be some overpriced stocks. The demonstration that, with restricted short selling and divergence of opinion, there could be overvalued stocks identi- fiable from publicly available information is, of course, inconsistent with efficient markets. This implies that it is possible to use security analysis to beat the markets (i.e., outperform indices on a risk-adjusted basis).
That there are obstacles to short selling is critical to the argument because if the pessimists were willing and able to sell short, their short selling would eventually saturate the demand of the optimists.
Since in a short sale the buyer of the shares gets ownership of the shares issued by the company (and the certificates if any exist), these shares still exist. However, the lender of the shares retains the right to call back his shares and sell them. He will still receive the dividends he expects (the borrower will pay these). The stocks he lent will show up on his list of holdings. Indeed, if he is a retail investor he will never know the shares were lent. Thus, the lender of the shares will act as if he still owned them.
In effect, the short seller has created new shares that are identical to the old
shares (except for voting rights). In a portfolio these new, synthetic shares are a perfect substitute for the shares lent. The market acts as if the total quantity of shares in existence is the sum of the shares issued by the com- pany, and the shares created by short sellers. Thus, in the Exhibit 5.1, the extra shares created by short selling can be recognized by altering the sup- ply curve. In this simple case, the number of shares is shown as increased.2
Because the quantity of stock sold short is typically very small, usu- ally less than 1%, allowing for realistic quantities of short selling does not change the conclusion that prices are set by the optimists.
Ofek and Richardson3 find that in February 2000, studying 3,946 non-Internet firms with prices over $10, that the mean short interest was only 1.8%. For the Internet firms the mean was only 2.8%. Even for the top 5% of the 273 Internet firms, the short interest was only 10.6% of the shares outstanding (versus 7.85% for the non-Internet firms).
Asquith and Meulbroek4 analyzed the data for firms listed on the U.S.
major exchanges (the New York Stock Exchange and the American Stock Exchange) for 1976–1993 as a percentage of the number of shares out- standing. The short interests showed a strong tendency to increase over time. Most firms have very low short interests. For 1993, the median short interest was only 0.82%. The mean was only 1.78%. However, a few firms were found to have appreciable short interest. Ten percent had over 4.46%
short interest. Five percent had over 6.93% short interests. The top 1% has short interests of 12.92%. For the time period studied, the peak of the top 1% short interests was in 1990, when it was at 14.04%.
These are all relatively small numbers. Even for the most heavily shorted firms (the top 1%) the quantity of stock available for holding is increased to only 115% of the quantity issued by the company. Thus, as a first approximate model where the quantity of stock available for purchase equal that issued by the company are quite realistic. Thus, only a small per- centage of investors can absorb the full supply of stock on the market.
Models of the academic type where unlimited shorting is permitted can result in total quantities of stock available for investors that are many fold the number issued by the company. These are further from the truth than
2While not relevant to this discussion, since the number of shares sold is expected to increase as the price increases, the effect is to replace the vertical supply curve by one with a slope. This makes slightly more likely the possibility that the supply curve in- tersects the demand curve in between the prices set by the optimists and the pessi- mists. Then the price is above the valuation of the pessimists, but below that of the optimists. This complexity does not change the basic point being made.
3For an academic view, see Eli Ofek and Matthew Richardson, “Dotcom Mania: The Rise and Fall of Internet Stock Prices,” Journal of Finance (June 2003), pp. 1113–1138.
4Paul Asquith and Lisa Meulbroek, “An Empirical Investigation of Short Interest,”
working paper, Harvard Business School, Harvard University, 1995.
the approximation that the stock available for purchase is only that issued by the company. Models where the only stock available for purchase is that issued by the company are the models with no short selling.
Recognizably Overpriced Stocks Can Exist
This simple observation that prices are set by the optimistic investors and that these are sometimes wrong is useful. It can explain why there do appear to be overvalued stocks that are widely agreed to be overvalued.
Lamont and Thaler present evidence of gross mispricing in some technology carve-outs in which the IPO exceed the value of the original firm.5 These appear to be clear errors that were not arbitraged away because of the costs of shorting.
The classic example is the recent Internet boom. Most observers were saying the stocks were overvalued, but yet they stayed at these high levels.
For instance, in 1999, Perkins and Perkins wrote a book showing why the Internet stocks were overpriced.6 An appendix to their book provided esti- mates of how fast the companies would have to grow over the next five years to justify the current (June 11, 1999) prices. At that time, this portfo- lio had a market value of $410 billion dollars based on combined sales of
$15.2 billion (most of that from only AOL and Qwest), and with whopping losses of over $3 billion. Only 22 of these companies actually showed prof- its. The Perkins closed their book with an open letter to investors entitled,
“Sell now.” Here they say Internet stocks are overvalued and urge, “If you hold any of these stocks, it is time to sell.” Their advice proved correct.
Similar arguments revealing the overpricing could have been found in many magazines and newspaper articles. Textbook and mainstream academic finance theory argues such overpricing is impossible since trad- ing by informed investors would eliminate it. The problem for financial theory has been to explain how such obvious overpricing could have sur- vived. A review article of mine summarizes it and explains how the Inter- net bubble was possible.7 In essence, enough short selling did not emerge to prevent the optimists from bidding the prices up to these levels.
Ofek and Richardson interpret the Internet boom in terms of the theory of this chapter.8 They document substantial short sale restric-
5Owen Lamont and Richard Thaler, “Can the Market Add and Subtract: Mispricing in Tech Stock Carve-Outs,” working paper, University of Chicago, 2001. Also see Chapter 7 in this book by Lamont.
6Anthony N. Perkins and Michael C. Perkins, The Internet Bubble (New York:
Harper Business, 1999).
7Edward M. Miller and M. Imtiaz A. Mazumder, “The Internet Bubble,” Journal of Social, Political, and Economic Studies (Winter 2001), pp. 683–689.
8Ofek and Richardson, “Dotcom Mania: The Rise and Fall of Internet Stock Prices.”
tions, for Internet stocks using evidence on short sales, short sale rebate rates, and option pairs (situations where put-call parity was violated).
They also show a link between heterogeneity of opinions and price effects on Internet stocks.
Most interesting they show that the expiration of lockups on Internet stocks is associated with substantial declines in prices. They show that by the summer of 2000 almost $300 billion of shares had been unlocked in a short time. They argue this had much to do with the ending of the Inter- net bubble. They describe the large number of investors (insiders, venture capitalists, institutions, and sophisticated investors) who were freed by the expiration of lockup agreements to sell their Internet shares.9
The idea of the investors who value something most setting the price is widely accepted in the art market. We may agree that the average per-
9The only weak point in the argument is “that to the extent these investors did not have the same optimism about payoffs that existing investors had, their beliefs would now get incorporated into stock prices.” The problem is that the selling by most of these investors need not be caused by less optimism about returns (although this was probably true of some), or even about risk in some absolute sense, but merely by a desire for diversification. The incremental effect of a share of the risk of a portfolio is greater when there is already much of the stock in the portfolio than when there is little. The result (using Markowitz optimization or something similar) is that the pre- mium (often called a risk premium) over the return on other stocks needed to retain the share in the portfolio is much greater for these undiversified investors than for diversified investors. One can easily imagine a company founder, other insider, or an angel investor being undiversified, and hence being willing to sell to a diversified in- vestor who is actually more pessimistic. The company founder might expect 13% on a stock that he thinks has a beta of 1.2 but rationally sell to a diversified investor who expects 10% and believes the beta to be 1.4. However, even if the sellers are actually more optimistic than average, the only way the increased supply resulting from their sales can be absorbed is for the price to fall. The sloping demand curve here arises from there being divergence of opinion and restrictions on short selling.
Of course, some of the sellers following a lockup expiration may indeed be more pessimistic. This is especially likely for the institutions and others who have had shares from venture capitalists distributed to them. These are probably well diversified, so their selling would be due to pessimistic views rather than merely seeking diversifica- tion. Since the venture capitalist rather than the institutions had decided to buy the stocks originally, these receiving institutions are likely to have opinions much closer to the mean. Because the mean valuation is usually lower than that of the optimists (es- pecially for stocks with a wide divergence of opinion), it is very likely that these new holders were indeed more pessimistic than the current marginal investors. Finding the stocks overvalued, they would have sold. It is also plausible that many insiders (having access to the information on costs, sales projections, and an understanding of the size of the market and the strength of the competition) had more pessimistic views than the previously price setting optimists. In these cases, the expiration of the lockups would indeed cause the incorporation of more pessimistic views into the marketprice.
son will pay very little for a picture of a soup can to hang on his wall.
However, we understand that if there is an auction, and one person is willing to pay several million dollars for that painting, that will be the market price. Likewise, many do not like Picasso prints, but if there are a hundred originals of a print, the price is the amount needed to induce the person with the 101st highest valuation to sell. No one tries to argue that average opinion sets prices in the art world.
If there are some overpriced stocks that can be identified by publicly available information, it will pay to hire analysts and do analysis of publicly available information. Such investing has the potential to out- perform the market and index funds.
When the Pessimistic Investors Are Uninformed
Of course, in some cases the uninformed investors will not be the optimis- tic investors. The pessimistic investors will be the ones instead who do not realize the potential of a security. This situation is depicted in Exhibit 5.2.
EXHIBIT 5.2 Exhibit with Pessimistic Investors
Notice for the uninformed investors to set the price, in this case there must be a very large number of uninformed investors. If the purchasing power of the informed investors is greater than the market value of the stock, the informed investors will set the price. In the above example of a company with 100 million shares, if each informed investor purchases a round lot (100 shares), the uninformed investors can only set the price if there are less than a million informed investors. With the average being 1,000 shares (allowing for institutions), 100,000 investors are needed.10
Notice that the more shares the average informed investors are will- ing to purchase on average, the smaller the number of informed investors that are needed to eliminate the underpricing. If the informed investors will purchase an average of 1,000 shares, it takes only 100,000 to elimi- nate the underpricing. Of course, the more extreme the underpricing, the greater the potential returns. The greater the potential returns, the greater the proportion of his wealth an investor will commit to an invest- ment opportunity. Increasing the proportion of wealth committed to an opportunity reduces the number of investors who can recognize an undervaluation before it is eliminated. In the extreme, one investor with sufficient resources could act on an idea (by taking over the company), and eliminate the underinvestment. Thus, it is very unlikely there will be grossly undervalued stocks that can be easily recognized.
As discussed below, this suggests a strategy of trying to win, not by searching for grossly undervalued stocks, but by trying to identify and avoid the overpriced ones. The case for this strategy is made stronger when it is realized that while good information is readily disseminated, there are obstacles to the dissemination of negative information.
Informational Considerations
In considering the likelihood of a hundred thousand people being unaware of a factor that should raise the price of a stock (which includes an analysis which puts together information already available), remember that there are strong incentives to publicize good news.
Because of stock options, the threat of takeovers, and the like, cor- porate managements prefer higher stock prices. They can be expected to draw attention to any information that they think has been neglected by the markets (new products in development, an expected upturn in busi- ness with the business cycle, the pending solution of an operational
10This 100,000 is a long-term number based on their being a buyer for every lot of stock owned by the more pessimistic investors. In practice, most investors do not constantly monitor the market, and a much smaller number is needed to purchase any stock coming on the market on a particular day and to bid the price up to the fair value by competition among themselves.
problem, bad luck that has temporarily depressed earnings, and so on).
Virtually never will a firm publicize facts like the obsolescence of their products, the products’ lack of durability, or the stupidity (or senility) of their management. Just imagine what the sales reps for the competition could do with statements such as “Competitor X has a better product,”
“Our product is obsolete,” or “We have found unexpected durability problems with our product.” A plaintiff’s lawyer would love to have a statement on record saying, “Our product is unsafe.”
If analysts or brokers identify a stock that is underpriced, they can be expected to publicize the information that make them believe it is under- valued. They, and their firm, could get an order to purchase the stock by informing investors of the information. Just as an example, a recent news story states, “Keane’s nod carries some punch as his advice reaches 12,000 retail stock brokers at Wachovia Securities.”11 If each broker keeps only nine investors informed, the word has reached 108,000 inves- tors, more than the 100,000 investors discussed above.
In contrast, even when short selling is allowed, few investors will place short sale orders. Only a few investors will own any given stock, so phone calls saying the stock is over valued will typically be greeted with “That’s interesting, but I don’t own any.” In many cases, if the stock is actually owned, it is because the broker making the call sold it to the investor. There are real problems in calling a client up and explaining why the stock you previously urged him to buy should now be sold. Even those who own a stock are unhappy at brokers and ana- lysts who draw attention to a stock’s problems, since this forces its price down, making current owners poorer. The current owner usually has an ego investment in the stocks he owns, and telling him that these stocks are overvalued is to question his good judgment.
The brokerage firms that employ analysts are also investment bank- ing firms that bring out new issues. Publicizing bad news about a firm does not help attract investment banking business from that firm.
Other investors (once they have accumulated a position) have an incentive to publicize the case for making an investment. If others fol- low them, the price may be bid up, making their own positions more profitable. The quicker any underpricing is eliminated by others learn- ing of the investment’s merits, the quicker profits can be taken (i.e., the higher the annualized rate of return from the investment) and the funds invested elsewhere. Also, it is pleasant at social gatherings to demon- strate your brilliance by talking about why the stock you just bought is
11Mark Davis, “Local Stocks: Analyst’s Optimistic Rating Pushes Up DST Stock,” The Kansas City Star Web site (September 30, 2003), posted at http://www.kansascity.com/
mld/kansascity/business/6891701.htm.