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112 THEORY AND EVIDENCE ON SHORT SELLING model. (As discussed above, the major exception may be among stocks of different sizes.) Thus, selection among possible additions to the port- folio (especially of the same size) cannot be based on anticipated returns. However, the contributions to diversification (and risk reduc- tion) are likely to differ between securities. Markowitz optimization may be useful in identifying possible risk reducing additions to the portfolio. This procedure is cheap if historical data are used in deriving the covariance matrix (with sophisticated methods used to reduce the large random element in historically derived portfolios 58 ). Normally, candidates for analysis can be identified this way at low cost. If they prove after analysis not to be overpriced, they may be purchased. Hopefully, by repeating this process, diversification can be maintained at low transactions costs. Only if this procedure fails would sales for the purpose of maintaining diversification be done. It is conceivable that the optimal portfolio strategy is to combine analyzed stocks with unanalyzed ones. This might happen if certain cat- egories were believed to have such efficiently priced securities as not to justify any analysis, and other categories had less efficiently priced secu- rities. The most plausible example of this would be where there were believed to be opportunities for analysis in small stocks, while certain large stocks were so well studied that one did not expect to be able to uncover information not reflected in the prices. Yet, diversification might require some exposure to large capitalization stocks. One optimi- zation exercise might combine studied small stocks expected to earn a competitive 12%, with other stocks selected by simple rules and expected to yield 10%. There are firms now that offer to provide com- pleteness portfolios at low cost to provide diversification and exposure to types of securities one does not maintain expertise in. Optimization can help decide whether extra expenses should be incurred in analyzing additional securities. Suppose it was believed that after analysis the chosen securities had an expected return of 12%, when randomly selected securities would have a return of 10%. One could add in different sets of randomly selected securities and then com- pute the expected return and variances for the newly optimized portfo- lios. In general, the portfolios with these additional securities would show lower expected returns (since the additional securities were expected to have a return of only 10%) and also lower risks (as mea- sured by the variance). The best set of additional securities could be identified, and the sacrifice of return to get a reduction in risk estimated. 58 For methods of obtaining a covariance matrix that are superior to brute force cal- culation from historical data see Edwin J. Elton and Martin Gruber, Modern Port- folio Theory and Investment Analysis (New York: John Wiley & Sons, 1995). 5-Miller-Restrictions Page 112 Thursday, August 5, 2004 11:10 AM Restrictions on Short Selling and Exploitable Opportunities for Investors 113 It is possible that the risk reduction (increased diversification) benefits of additional securities would justify adding unanalyzed securities. Suppose one believes that, after analysis, four-fifths of the stocks appear to have no major overpricing. However, a fifth show major over- pricing, such that an optimization program reduces the weight to zero (for simplicity, I have left out the intermediate alternatives). One may then be able to add the alternative of spending the $100,000 to study an additional stock and using the information to decide on whether or not to include that stock. If the stock is included with an estimated return of 12%, one had achieved a reduction in risk for a cost of $100,000. Since all the included stocks are presumed to have a 12% expected return, there is no increase in expected return before expenses and a $100,000 reduc- tion in expected return after expenses. If the candidate stock proves to be overpriced, one forgoes the added diversification benefit. Of course, after the analysis is done the $100,000 is already spent and the portfolio return reduced by this amount. At least conceptually, with knowledge of the cli- ent’s trade off between expected return and risk, whether analyzing an additional stock was worthwhile can be determined. In doing such an analysis notice the only inputs to Markowitz opti- mization (and similar procedures) are expected returns and a covariance matrix. The size of the firm does not enter into the calculations. If one believes it will be cheaper to analyze a small firm (perhaps because it is in only one line of business), the ratio of added benefit to the portfolio from identifying a suitable security to the cost of analysis will be great- est for the smaller stocks. In practice, one usually cannot purchase the required analysis of an additional stock at short notice. The difficulty is not finding someone to take your money and give an opinion. It is not even finding someone whose opinion you think is worth $100,000. The difficulty is being sure the new analysis is comparable with the analysis done by your own staff. Thus, the information on the benefits of analyzing an additional stock is most useful in deciding on how large an analytic budget to incur. In practice, the cost of an analytic staff is fixed in the short run. Pro- cedures such as discussed above aid in determining the budget for analy- sis and the number of stocks to be followed. In the example above, a budget of $2,500,000 per year would permit following 25 stocks. The expected portfolio size would be 20 stocks (allowing for a fifth to be rejected). These 20 would be in the portfolio (with perhaps weights cho- sen by an optimization program) and the analytic resources devoted to following these 20 stocks, plus five more as candidates for purchase and to replace any that became overpriced. Analyses of this type would be done form time to time to determine if the staff size was optimal. There is a role for consultants, because managers are likely to be always in 5-Miller-Restrictions Page 113 Thursday, August 5, 2004 11:10 AM 114 THEORY AND EVIDENCE ON SHORT SELLING favor of a larger budget. The larger budget implies higher fees for out- side managers, and more staff for inside managers. While formal optimization using historical data is cheap, it is an open question whether it is better to use optimization for risk control, or to use traditional rules such as target exposure to industries. Multiple Opinions Case The discussion here dealt with the case where there were only two opin- ions, one of which was right and one was wrong. We presumed that we knew which was right (a strong assumption). With these assumptions we were able to derive many interesting and useful conclusions. The two opinions case was adequate for developing these conclusions, which do hold for more realistic models. However, normally there are many dif- ferent opinions about the value of a security. This situation will be referred to as a divergence of opinion. It is discussed in Chapter 6. 59 CONCLUSIONS Because of restrictions on short selling, many overvalued stocks will be excluded from portfolios by being sold if owned or, otherwise, not bought; however, they will not be sold short. This is because stocks that promise less than a competitive rate of return should be excluded from portfolios but often are not good short sale candidates, especially for those who do not receive use of the proceeds. It follows that prices are set by the most optimistic investors, not by the typical investor. In many cases the most optimistic investors are also the over optimistic investors. The result is sometimes overpriced stocks that can be identified by good analysis. Because of the ease of a minority of investors purchasing enough stock to cause it to be overpriced, accounting rules should err on the conservative side. Conservatism will seldom lead to underpricing since there will usually be enough well informed investors to keep the stock priced at least competitively. However, if the accounting sometimes exaggerates profits, there are likely to be enough poorly informed inves- tors for the stock to become overpriced. The obstacles to short selling, especially failure to receive full use of the proceeds or to receive a market return on them, are more important when the errors in pricing will occur years in the future than when they will be revealed in the near future. Exploitable opportunities to avoid 59 See Chapter 7. 5-Miller-Restrictions Page 114 Thursday, August 5, 2004 11:10 AM Restrictions on Short Selling and Exploitable Opportunities for Investors 115 overpriced stocks are most likely when the overpricing is due to various factors that will be typically revealed only years in the future. Possible opportunities arise from things like extrapolating growth too far in the future, not allowing for new entry or market saturation, leaving out numerous low probability adverse events that in the aggregate have an appreciable effect, and the like. Looking for such events several years out probably has a higher return than trying to forecast next year’s earnings, which is where so much effort is expended. Since competition makes it very difficult to identify stocks that are grossly undervalued, investment success comes from avoiding losers rather than finding great winners. Investing is a loser’s game. If great winners will be very hard to find in a competitive economy, analytic effort should be focused on a small number of stocks which can be extensively studied, rather than on an extensive search for stocks that will double in a year. Typically, investment managers try to follow far too many stocks, frequently failing as a result to uncover relevant nega- tive information about certain stocks. This yields a theory of bounded efficient markets in which there are upper and lower bounds for stock prices, with most stocks at the lower bound, priced to yield a competitive return. However, the competitive return is higher than the average return. This difference is small enough so that it is probably not worthwhile for individual investors to attempt to pick stocks. However, a small percentage advantage applied to a large sum of money does justify analysis in institutions. It is this analysis that keeps markets close to efficient. 5-Miller-Restrictions Page 115 Thursday, August 5, 2004 11:10 AM 5-Miller-Restrictions Page 116 Thursday, August 5, 2004 11:10 AM CHAPTER 6 117 Implications of Short Selling and Divergence of Opinion for Investment Strategy Edward M. Miller, Ph.D. Research Professor of Economics and Finance University of New Orleans ainstream finance theory is developed in a highly abstract world in which, among other assumptions, investors are assumed to be as willing and able to sell short as to take a long position. This is obviously unrealistic. Most institutional investors are not permitted to go short. Most individual investors are afraid to make short sales. There are vari- ous institutional obstacles to short selling (uptick rules, the need to bor- row the stock, and so on). Even for the investor who himself would never go short, the optimal investment strategies in a market with restricted short selling proves to be quite different than in the textbook markets with free short selling. I had earlier proposed an alternative the- ory which is updated for use here. 1 It will be shown here that in a world with restricted short selling that 1. Divergence of opinion tends to raise prices. 2. Thus profits can be improved by avoiding stocks with high divergence of opinion, including those analysts disagree about. 3. When the divergence of opinion drops, stock prices tend to decline. 1 Edward M. Miller, “Risk, Uncertainty, and Divergence of Opinion,” Journal of Fi- nance (September 1977), pp. 1,151–1,168. M 6-Miller-Implications Page 117 Thursday, August 5, 2004 11:11 AM 118 THEORY AND EVIDENCE ON SHORT SELLING 4. Since the divergence of opinion on initial public offerings declines as they become seasoned, these stocks tend to underperform the market. 5. Since risk correlates with divergence of opinion, the return to risk, both systematic and nonsystematic, is less than the typical investor would require to invest in risky stocks. 6. Thus, the typical investors should overweight the less risky stocks in his portfolio. 7. There is a winner’s curse effect in the stock markets such that you tend to purchase the stocks you erred in evaluating. This holds even if every single investor is, on average, unbiased in his or her valuations. This chapter will develop the implications for practitioners of a world where there is little short selling and where investors disagree about the merits of securities. Both seem at least as plausible as the alternatives, that investors trade in perfect markets and always agree on the values for all relevant variables (and successfully do the complex calculations required to construct an optimal portfolio). Textbooks sometimes deduce that security prices should be efficient by assuming homogeneous beliefs. This is obviously wrong since people disagree about all sorts of things including sports, politics, and securi- ties. A more sophisticated version recognizes that investors do disagree about future returns and risks of a security but argues that their beliefs are unbiased (i.e., are correct on average). This, combined with prices reflecting average opinions, implies that the prices will be unbiased esti- mates of fair values. However, with substantial divergence of opinion some investors are likely to believe the security has a negative expected return. This implies that they expect a price decline. The logical action for an investor expecting a price decline is to short the security. It follows that where short selling is prohibited, that such negative opinions will not be fully reflected in stock prices. This implies (contrary to standard theory) that there will be some overvalued stocks that can be identified with publicly available information. Chapter 5 discussed markets with obstacles to short selling in which one group of investors can be identified as right and one group as wrong using publicly available information. This showed how analysts can add value and how to use their analysis to avoid overvalued stocks. However, normally there are many different opinions about the value of a security and it is not clear which is correct. It will initially be assumed that there is no short selling. Later the case will be discussed where short selling is merely restricted. With divergence of opinion (and restricted short selling), lowering the price of a security not only causes investors who already own the security to buy more, but it also causes investors who previously would not have bought 6-Miller-Implications Page 118 Thursday, August 5, 2004 11:11 AM Implications of Short Selling and Divergence of Opinion for Investment Strategy 119 the security at all to buy. There is then a marginal investor who will only buy if the price is at or below some level. Much of this section will be developing the implications of the marginal investor for portfolio management. From a purely logical viewpoint, divergence of opinion implies that at least one of the opinions (and perhaps all of them) is wrong. To make it pos- sible to compare this theory with the efficient market theory, the assumption will be made that investors all have unbiased expectations. Of course, this is just an exposition device. The behavioral finance literature shows that all sorts of biases exist. Unbiased expectations means that if all the opinions were averaged, the average would be the correct value. Incidentally, it may even be true that each investor is on average correct when his estimates are averaged over all the stocks he follows, even though he is sometimes high and sometimes low. Finally, the implications of divergence of opinion for value additivity, closed-end funds, and spin-offs will be developed. INTERACTION OF DIVERGENCE OF OPINION AND SHORT SELLING RESTRICTIONS A distribution can be represented in either probability density form or cumulative form. The first bell-shaped curve in Exhibit 6.1 shows the distribution of investors’ opinions about the security’s maximum value. This is the price at which the security just enters into their portfolios. At lower prices they may hold more of the security, although this effect cannot easily be shown in the exhibit (since it has only two dimensions). EXHIBIT 6.1 Number of Investors with Various Estimates of Value 6-Miller-Implications Page 119 Thursday, August 5, 2004 11:11 AM 120 THEORY AND EVIDENCE ON SHORT SELLING The same information can also be shown as a cumulative distribu- tion as shown in Exhibit 6.2. The vertical axis is the price and the hori- zontal axis shows the number of investors whose willingness to pay for a security is at, or below, that level. For expositional convenience, imagine that investors buy one share if they decide to include a security in their portfolios and no shares oth- erwise. (The argument can easily be generalized to where each investor buys a certain number of shares depending on his wealth and diversifi- cation requirements.) The vertical line in Exhibit 6.2 shows the number of investors needed to absorb the total quantity of the stock in existence (which at one share per investor is also the number of shares issued). The equilibrium price is at the intersection of the cumulative probability distribution and the vertical line. If the price was higher, investors who thought the stock was worth at least that price would not be willing to hold all of the stock that exists. The excess stock would be offered for sale, causing the price to drop. If the price was below the point of intersection, there would be more investors who thought the stock was worth at least that amount. Some inves- tors who thought the stock was worth including in their portfolio would find EXHIBIT 6.2 Cumulative Distribution of Investor’s Valuations 6-Miller-Implications Page 120 Thursday, August 5, 2004 11:11 AM Implications of Short Selling and Divergence of Opinion for Investment Strategy 121 none to purchase at the prevailing prices. These disappointed investors would bid the price up until it reached the equilibrium price. Exhibit 6.2 is actually a demand/supply diagram. The demand curve is simply the cumulative valuation curve as long as each investor pur- chases one share. The supply curve is simply the number of shares out- standing, a number determined by the company. The theory of price determination offered is that the price is set at the level where demand equals supply. In a more general formulation the demand curve is the summation of all investors’ demand curves. In the exhibit the supply curve was shown as simply the quantity of stock issued by the company. A short sale is essentially the issuance of new stock by the short seller. The volume of short sales increases with the price causing the total quantity of shares to increase. Thus the supply curve has a slightly upward slope. However, since the volume of shares issued by short sellers is just a small fraction of the number issued by the firm itself, the argument is little altered if realistic amounts of short selling occur. Boehme, Danielson, and Sorensen, as part of a larger study (discussed later), report that the mean short interest as of July 1, 1999, was only 1.454% of the number of shares held. 2 Even looking at the top 1% of firms, the short interest was only 15.6%. One would expect much higher ratio if there were not obstacles to short selling, whether institutional or psychological. Equilibrium Prices Do Not Equal Consensus Value Estimates Several simple points emerge from the above analysis. Probably most important is that there is nothing to insure that the demand and supply curves intersect at a price representing the consensus valuation of all investors. The consensus is at point A, the value where half of the inves- tors think the stock is worth more and half think it is worth less. Only by coincidence would this consensus value be the market determined price. Normally only a small fraction of investors can absorb a security’s total floating supply. Consider a small company with ten million shares outstanding. Suppose each investor purchases 1,000 shares. Only 10,000 investors need think the stock is worth holding to absorb the whole sup- ply of the stock. The stock will be priced at the level that is just adequate to induce the marginal investor, the ten thousandth investor, to hold it. Normally, much less than half of the investors can absorb the float- ing supply of a stock, with the result that the marginal investor’s evalua- tion is far above the valuation of the median investor or the average investor. An alternative way to express the argument so far is that the 2 Rodney D. Boehme, Bartley R. Danielson, and Sorin M. Sorescu, “Short Sale Con- straints and Overvaluation,” working paper, American Finance Association 2003 Annual Conference, January 2003. 6-Miller-Implications Page 121 Thursday, August 5, 2004 11:11 AM [...]... studies (Aggarwal and Rivoli,33 Aggarwal, Leal, and Hernandez, 34 Brav and Gompers,35 Carter, Dark, and Singh,36 Dawson,37 Finn and Higham,38 Ibbotson,39 Kunz and Aggarwal ,40 Levis ,41 Loughran ,42 Loughran and Ritter ,43 Loughran, Ritter, and Rydqvist ,44 Ritter ,45 Stern 33 Reena Aggarwal and Pietra Rivoli, “Fads in the Initial Public Offering Market?” Financial Management (1990), pp 45 –57 34 Reena Aggarwal,... (December 2001), pp 45 1 48 4 Implications of Short Selling and Divergence of Opinion for Investment Strategy 141 result in short selling as option dealers and others make short sales in the course of placing hedges The professional dealers can often make short sales easier and at lower costs than can individuals or institutions They can get use of at least part of the proceeds of short sales and are often... 165–199 45 Jay R Ritter, “The Long-Run Performance of Initial Public Offerings,” Journal of Finance (1991), pp 3–27  144 THEORY AND EVIDENCE ON SHORT SELLING and Bernstein ,46 Stoll and Curley ,47 and Uhlir48) have shown that IPOs do worse than the general markets, in spite of their higher risks Ritter examined the returns from 1,526 initial public offerings from 1975 to 19 84. 49 The three-year return was 34. 47%... with restricted short selling implies that when divergence of opinion changes, prices should change In particular, when divergence of opinion declines, prices should decline 32 Douglas W Diamond and Robert E Verrecchia, “Constraints on Short- Selling and Asset Price Adjustment to Private Information,” Journal of Financial Economics (1987), pp 277–311  142 THEORY AND EVIDENCE ON SHORT SELLING This should... the presence of restrictions on short selling One is to see if constraints on short selling affect returns The other is to see if high divergence of opinion stocks have lower returns Evidence on Short Sales Constraints The level of short interest can be interpreted in several ways If short sales are observed, some short selling is possible Since the major reason for short sales is because one expects... of its wealth in the stock they think will do best A short selling restriction prevents them from making short sales of the less preferred stock and using the proceeds to purchase the more preferred stock In the theoretical model with full short selling, the first group would sell short B and use the funds to buy A The other group would short sell A and use the funds to buy B (this provides the buying... of high short costs and low returns is predicted by the divergence of opinion, restricted short selling model Early studies showed an inconsistent relationship between short interests and future returns Desai et al suggest that this was because of the small numbers of stocks studied and the fact that only a minority of stocks have large short interests, introducing much noise into the studies. 24 For... that 40 ,000 individual observations were manually checked in comparing the various 27 Desai, Ramesh, Thiagarajan, and Balachandran, “An Investigation of the Informational Role of Short Interest in the NASDAQ Market.” 28 Paul Asquith and Lisa Meulbroek, “An Empirical Investigation of Short Interest,” working paper, Harvard Business School, Harvard University, 1995 138 THEORY AND EVIDENCE ON SHORT SELLING. .. 1–2% per month Even after paying the fees, shorting 23 Charles M Jones and Owen A Lamont, Short- Sale Constraints and Stock Returns,” Journal of Financial Economics (2002), pp 207–239 See also Chapter 7 in this book 136 THEORY AND EVIDENCE ON SHORT SELLING these stocks would have been profitable Because addition to the short borrowing list was observable and the fees charged were reported, the possibility... slope of the demand curve The steeper the demand curve, the more price fluctuates with random buying and selling Thus price and return volatility can serve as surrogates for divergence of opinion Carter, Dark, and Singh have found that the standard deviation, calculated over the first 225 days commencing 6 days after the offer, of 2,292 (1979– 1981) IPOs predicts 3-year underperformance. 54 As the story . 113 Thursday, August 5, 20 04 11:10 AM 1 14 THEORY AND EVIDENCE ON SHORT SELLING favor of a larger budget. The larger budget implies higher fees for out- side managers, and more staff for inside. Ownership and Stock Returns.” EXHIBIT 6.3 Effect of Changing the Divergence of Opinion 6-Miller-Implications Page 123 Thursday, August 5, 20 04 11:11 AM 1 24 THEORY AND EVIDENCE ON SHORT SELLING in. effects of divergence of opinion with short selling restricted. 6-Miller-Implications Page 130 Thursday, August 5, 20 04 11:11 AM Implications of Short Selling and Divergence of Opinion for Investment