198 THEORY AND EVIDENCE ON SHORT SELLING and at-the-money). The solid line, the actual stub, goes from strongly negative at the beginning to positive $10 a share. The dotted line, the synthetic stub, is positive in all but one week. By the distribution date, the difference between the two lines is close to zero, roughly consistent with put-call parity. The pattern shows that options prices adjust to vir- tually eliminate profitable trading opportunities. Put differently, the implied cost of shorting falls as the desirability of shorting falls. Thus we have three ways of inferring Palm’s true value: the embed- ded value reflected in 3Com’s share price, the value reflected in options prices, and the actual price. The market for November options and the shareholders in 3Com seemed to agree: Palm was worth far less than its market price. The direction of the deviation from put call parity is con- sistent with the difficulty of shorting Palm. To profit from the difference between the synthetic security and the underlying security, one would need to short Palm and buy the synthetic long. If shorting is costly, then EXHIBIT 7.4 Palm Options on 3/17/00 Options Prices Note: May options expire 5/20/00. August options expire 08/19/00, November op- tions expire 11/18/00. A synthetic short position buys a put (at the ask price), sells a call (at the bid price), and borrows the present value of the strike price. A synthetic long position sells a put (at the bid price), buys a call (at the ask price), and lends the present value of the strike price. We discount May cash flows by 3-month LIBOR and August and November cash flows by 6-month LIBOR. Source of options price data: CBOE. Source of LIBOR: Datastream. LIBOR 3-month 6.21 6-month 6.41 Stock Prices Palm 55.25 3Com 68 Call Put Synthetic Short Percent Deviation Synthetic Long Percent DeviationBid Ask Bid Ask May 55 5.75 7.25 10.625 12.625 47.55 –14 51.05 –8 August 55 9.25 10.75 17.25 19.25 43.57 –21 47.07 –15 November 55 10 11.5 21.625 23.625 39.12 –29 42.62 –23 7-Lamont-Short Constraints Page 198 Thursday, August 5, 2004 11:12 AM Short Sale Constraints and Overpricing 199 the deviation can be interpreted as the cost of borrowing (shorting) Palm shares. Again, although the prices here are consistent with very high short- ing costs, one can turn the inequality around and ask why anyone would ever buy Palm (without lending it). On March 17 one can create a synthetic long Palm by buying a call and selling a put, and this syn- thetic long is 23% cheaper than buying an actual share of Palm and holding until November. Arguments that the planned spin-off may not occur are irrelevant to the synthetic long constructed using options. Why are investors who buy Palm shares directly willing to pay much more than they could pay using the options market? One plausible explanation is that the type of investor buying Palm is ignorant about the options market and unaware of the cheaper alternative. It is worth noting that the 3Com/Palm case is very unusual. In most cases, put-call parity holds. Ofek, Richardson, and Whitelaw study options prices during the tech stock mania period (a period where we would expect to find the most extreme cases of mispricing, such as 3Com/Palm). They find the average deviation between actual prices and synthetic prices to be very small. For a handful of firms, though, there are extreme violations. Confirming the 3Com/Pam results, for this handful of firms, Ofek, Richardson, and Whitelaw (forthcoming) find abnormal returns of about –2% per month for the period 1999–2002. The 3Com/Palm case reflect several elements of the Harrison and Kreps story. First, Lamont and Thaler find that volume on the over- priced subsidiaries (such as Palm) to be far higher than volume on the underpriced parents (such as 3Com). Volume is key part of the story. Second, the story predicts that otherwise identical securities which can- not be traded at date 1 should have lower prices. Puts and calls are illiq- uid assets (especially compared to the highly traded Palm) with high bid/ask spreads. Thus, the difference between the price of Palm and the synthetic shares of Palm constructed from November options can be interpreted as a measure of the “speculative premium” of Harrison and Kreps. Third, Palm was a young company with a short operating his- tory, and great uncertainty about its future. Thus it is easier to disagree about the true value of Palm than about 3Com, a mature company with less uncertainty. The case of 3Com and Palm, while special, is interesting because it is a situation in which it is particularly easy for the market to get things right. To price Palm correctly versus 3Com requires investors to merely multiply by 1.5. If the market is flunking these no-brainers, what else is it getting wrong? 7-Lamont-Short Constraints Page 199 Thursday, August 5, 2004 11:12 AM 200 THEORY AND EVIDENCE ON SHORT SELLING TECH STOCK MANIA AND SHORT SALE CONSTRAINTS Can short sale constraints explain the amazing gyrations of stock prices in recent years? Prices seemed absurdly high in the period 1999–2000, espe- cially for technology-related stocks. The Palm example shows that for some specific stocks, short sale constraints relating to mechanical prob- lems in stock lending are surely the answer. More generally though, diffi- culty in borrowing stock cannot be the answer. Although Ofek and Richardson report that Internet stocks had higher average short interest and were more expensive to short than non-Internet stocks in this period, the average difference in cost was only 1% per year. 18 And one can always easily short NASDAQ or the S&P using futures or exchange-traded funds. So if short sale constraints do play a wider role, it is not because of the stock lending difficulties, but because of more generic short sale con- straints. It must be that investors are unwilling to establish short posi- tions because of risk (such as fundamental risk or noise trader risk) or institutional constraints (such as the fact that mutual funds are mostly long only). Perhaps many investors thought that Internet stocks were overpriced during the mania, but only a small minority were willing to take a short position, and these short sellers were not enough to drive prices down to rational valuations. Looking now at the aggregate market instead of individual stocks, there is a variety of evidence that is consistent with the short sale con- straints story. Many of the factors leading to differences of opinion and thus to overpricing were present in this period. Reading Miller, it is hard not be impressed with the eerie similarities between his descriptions and the events of 1998–2000. The first factor that creates differences of opinion is that the firm has a short track record, or has intangible pros- pects: “The divergence of opinion about a new issue are greatest when the stock is issued. Frequently the company has not started operations, or these is uncertainty about the success of new products or the profit- ability of a major business expansion.” 19 The second is that the company has high visibility, so that there are many optimists: “Some companies are naturally well known because their products are widely advertised and widely consumed…Of course, the awareness of a security may be increased if the issuing company receives much publicity. For instance, new products and technological breakthroughs are news so that companies producing such products receive more publicity.” 20 18 Eli Ofek and Matthew Richardson, “DotCom Mania: The Rise and Fall of Internet Stock Prices,” Journal of Finance (June 2003), pp. 1113–1138. 19 Miller, “Risk, Uncertainty, and Divergence of Opinion,” p. 1156. 20 Miller, “Risk, Uncertainty, and Divergence of Opinion,” p. 1165. 7-Lamont-Short Constraints Page 200 Thursday, August 5, 2004 11:12 AM Short Sale Constraints and Overpricing 201 Tech stocks certainly fit both of these criteria. Stocks like Amazon or AOL were familiar to the investing classes who used them, but unlike other familiar products (such as Coca-Cola) had a short operating history, so that optimists could construct castles in the sky without fear of contra- diction by fact. Vissing-Jorgensen reports survey data on Internet use that seems to fit in with this story. 21 Investors who had actually used the Inter- net thought Internet stocks had higher expected returns than other stocks, and were more likely to include Internet stocks in their portfolio. Recall in the Harrison and Kreps model, overpricing is associated with high volume, high dispersion of opinion, and widespread agree- ment that the market is overpriced in the long run but is unlikely to decline in the short run. Each one of these predictions is borne out in the data. First, volume on NASDAQ more than doubled between Janu- ary 1999 and its peak in January 2001. Second, Vissing-Jorgensen finds that measures of investor disagreement with each other peaked in early 2000 around when stock prices peaked. Third, Exhibit 7.5, from a con- 21 Annette Vissing-Jorgensen, “Perspectives on Behavioral Finance: Does Irrational- ity Disappear with Wealth? Evidence from Expectations and Actions,” in Mark Gertler and Kenneth Rogoff (eds.), NBER Macroeconomics Annual 2003 (Cam- bridge, MA: MIT Press, 2004). EXHIBIT 7.5 Yale School of Management Stock Market Confidence Indexes™ The Percent of the Population Who Think that the Market Is Not Too High. 7-Lamont-Short Constraints Page 201 Thursday, August 5, 2004 11:12 AM 202 THEORY AND EVIDENCE ON SHORT SELLING tinuing survey conducted by the Yale School of Management, shows that about 70% of those surveyed thought the market was overvalued in early 2000. Remarkably, Exhibit 7.6 shows that simultaneously, 70% of those surveyed also thought market would continue to go up. If every- one agrees the market is overvalued, but expects it to continue to go up amid high volume—this is the essence of the greater fool theory, and in particular the Harrison and Kreps version. Another fact explained by the overpricing hypothesis is the very high level of stock issuance that occurred from 1998 to 2000. One inter- pretation is that issuers and underwriters knew that stocks were over- priced and so rushed to issue. Evidence arising out of subsequent legal action against underwriters (such as emails sent by investment bank employees) is certainly consistent with the hypothesis that the under- writers thought the market was putting too high a value on new issues. One way to think about issuance is as a mechanism for overcoming short sale constraints. Both short selling and issuance have the effect of increasing the amount of stock that the optimists can buy; both are examples of supply increasing in response to high prices. Suppose you think Lamont.com is overpriced in 1999. One way to take advantage of this fact is to short the stock. In doing this, you are selling overpriced EXHIBIT 7.6 The Percent of the Population Expecting an increase in the Dow in the Coming Year. 7-Lamont-Short Constraints Page 202 Thursday, August 5, 2004 11:12 AM Short Sale Constraints and Overpricing 203 shares to optimists. This action is very risky, however, as Lamont.com might well double in price. A safer alternative action is for you to start a new company that competes with Lamont.com, call it Lamont2.com, and issue stock. This IPO is another way to sell overpriced shares to optimists. SUMMARY The overpricing hypothesis says stocks can be overpriced when some- thing constrains pessimists from shorting. In addition to short sale con- straints, there also needs to be either irrational investors, or investors with differences of opinion. This chapter has shown a variety of evi- dence consistent with the overpricing hypothesis. First, I have discussed three studies of extreme overpricing leading to extremely low subse- quent returns. Second, I have discussed some suggestive evidence that the tech stock mania period that peaked in March 2000 may also have been overpricing due to the reluctance of pessimists to go short. 7-Lamont-Short Constraints Page 203 Thursday, August 5, 2004 11:12 AM 7-Lamont-Short Constraints Page 204 Thursday, August 5, 2004 11:12 AM CHAPTER 8 205 How Short Selling Expands the Investment Opportunity Set and Improves Upon Potential Portfolio Efficiency Steven L. Jones, Ph.D. Associate Professor of Finance Indiana University, Kelley School of Business–Indianapolis Glen Larsen, Ph.D., CFA Professor of Finance Indiana University, Kelley School of Business–Indianapolis arry Markowitz’s seminal work on mean-variance portfolio optimi- zation did not allow for short sales of risky securities. 1 Professional money managers who use portfolio analysis have traditionally ignored this opportunity as well, due either to institutional constraints or the difficulties involved with short selling. 2 Yet, short selling clearly repre- 1 Harry M. Markowitz, “Portfolio Selection,” Journal of Finance (March 1952), pp. 77–91; and Harry M. Markowitz, Portfolio Selection: Efficient Diversification of In- vestments (Somerset, NJ: John Wiley and Sons, 1959). 2 Harry M. Markowitz, “Nonnegative or Not Nonnegative: A Question about CAPMs,” Journal of Finance (May 1983), pp. 283–295. Markowitz notes that his assumption of no short selling is generally consistent with institutional practice. He is particularly critical of portfolio optimization models that allow short sales but ig- nore escrow and margin requirements and thus tend to give solutions with extreme positive and negative weights that cannot be implemented in practice. H 8-Jones/Larsen-ExpandInvest Page 205 Thursday, August 5, 2004 11:13 AM 206 THEORY AND EVIDENCE ON SHORT SELLING sents an opportunity to expand upon the long-only investment set, and there are several reasons to believe that this offers the potential to improve upon realized (ex post) mean-variance portfolio efficiency. First, as several of this book’s chapters point out, there is considerable evidence of transitory overpricing in stocks that are expensive to short sell as well as in stocks with high short interest. Thus, short selling such stocks, when they are thought to overpriced, has the potential to improve upon mean portfolio returns. Second, the opportunity to short sell effectively doubles the number of assets, from N to 2N. This clearly offers the poten- tial to reduce portfolio variance since the covariances of the second set of N stocks (potentially held short) have the opposite sign from the respective covariances in the first set of N stocks (potentially held long). It is important to recognize, however, that while short selling offers the potential to improve realized portfolio efficiency, there is no guarantee without perfect foresight (ex ante). That is, if one can be certain of the forecasted means and covariances, then short selling improves mean-vari- ance efficiency as a simple matter of portfolio mathematics. Recent empir- ical research, however, suggests that covariance forecasts are so fraught with error that realized portfolio efficiency might actually be improved by restricting or even prohibiting short positions. In addition, very little work has been done on how best to reflect the margin requirements of short selling in the portfolio optimization model. For example, the so- called “full-investment constraint” is usually defined such that the portfo- lio weights are constrained only in that they must sum to one, with nega- tive weights assigned to short positions, and without any constraint on the magnitudes of the weights. This assumes there are no escrow and margin requirements, which implies that all of the proceeds from short selling are available to finance additional investment in long positions. We begin the next section by explaining the predictions of mean- variance portfolio theory and its logical extension, the Capital Asset Pricing Model (CAPM). In theory, short selling is not needed to optimize portfolio efficiency as long as market prices reflect equilibrium required returns. But despite this result, we do not dismiss short selling as unnec- essary; instead, the result serves to emphasize the importance of distin- guishing between investors based on their information set. We assume that active investors trade based on some informational advantage, while investors lacking any such advantages are logically passive. Thus, indexing, rather than short selling, is probably the best way for passive investors to optimize their potential portfolio efficiency. Other practical implications emerge from considering the theoretical predictions in light of the actual requirements of short selling. Although we focus on the effects of margin requirements and escrowed short sale proceeds, we also point out that the risk of recall and the transitory nature of over- 8-Jones/Larsen-ExpandInvest Page 206 Thursday, August 5, 2004 11:13 AM How Short Selling Expands the Investment Opportunity Set 207 pricing means that short positions must be actively managed. We then consider the evidence on whether short selling improves realized portfo- lio efficiency, which is mixed, as was mentioned above. We close by summarizing the practical implications of the theory and evidence. SHORT SELLING IN EFFICIENT PORTFOLIOS: THE THEORY AND ITS PRACTICAL IMPLICATIONS We first consider the role of short selling in mean-variance portfolio theory and the CAPM. While the theory predicts a minimal role for short selling in a passive investor’s portfolio, the analysis provides a useful framework for thinking about the conditions necessary for short positions to appear in efficient portfolios. This framework provides the basis for later consid- eration of (1) how active investors can improve expected portfolio effi- ciency, ex ante, by short selling, and (2) how margin requirements and the escrowing of short sales proceeds affect the feasible asset allocation. Short Holdings in a Passive Investor’s Efficient Portfolio Passive management has become almost synonymous with indexing, but this definition omits any description of passive or active investors. Active investors believe they can identify and profit from mispriced securities, either through their own analysis or by paying for active management. Active management is usually associated with a goal of improving mean returns by trading on transitory advantages. Passive investors remain so because they lack the time or the skill to identify mispriced securities, and they do not believe active management is worth the higher fees, so their goal is adequate diversification. Although both types of investors may short sell, the important distinction is that only active investors can short sell with the expectation of improving mean returns; passive investors will short sell only for the purpose of diversification. Mean-Variance Portfolio Theory and the CAPM Markowitz’s mean-variance portfolio theory is a prescription for how to choose and construct efficient portfolios. The resulting frontier shown in Exhibit 8.1, in terms of expected mean returns (Er) and standard deviations ( σ, the square root of the variance), represents the minimum variance attainable at every level of return based on estimates of the expected returns for individual securities and the return covariances for pairs of securities. The positively sloped portion of this minimum-vari- ance frontier, above the unique minimum-variance portfolio (MV), is referred to as the efficient frontier of risky assets. Note that it would be 8-Jones/Larsen-ExpandInvest Page 207 Thursday, August 5, 2004 11:13 AM [...]... Levy, and David Starer, “On the Optimality of Long -Short Strategies, Financial Analysts Journal (March/April 1998), pp 40–51 2 16 THEORY AND EVIDENCE ON SHORT SELLING Enhanced Indexing with Short Selling As several other chapters in this book point out, a considerable amount of evidence indicates that individual stocks may occasionally become overpriced, and short interest or the costs of short selling. .. = $6, 000/$10,000 = 0 .6, W SO C = –$2,000/$10,000 = –0.2, and W Lending = $6, 000/$10,000 = 0 .6 C C Adjusted Weights in the Complete Portfolio: W L = $6, 000/$14,000 = 0.43, W SO C =$2,000/$14,000 = 0.14, and W Lending = $6, 000/$14,000 = 0.43 Total Equity from long + Short positions = $10,000; Total lending = $6, 000 = Escrowed short sale proceeds + Short margin requirement + Lending at rf 223 How Short. .. and that margin requirements severely limit borrowing when short selling 218 THEORY AND EVIDENCE ON SHORT SELLING Interpreting Exhibit 8 .6 in terms of enhanced indexing implies that the market portfolio (MP) is the desired long-only index, while the short position (SH) can be thought of as a short- only portfolio in one or more stocks Since the long-only index is passive, the line between passive and. .. Long-plus -Short Portfolios 17 The less exaggerated convexity of the frontier between portfolios SO and L in Exhibit 8.7, when compared to that between portfolios SH and MP in Exhibit 8 .6, indicates that the return correlation between portfolios SO and L is higher (less negative) than that between portfolios SH and MP 220 THEORY AND EVIDENCE ON SHORT SELLING Effects of Margin Requirements and Escrowing... long and short margin.) Next, we consider how risk-averse investors can lend or borrow to achieve their own optimal complete portfolio (over the risk-free and risky assets) 18 We consider the margin requirements in a manner similar to Gordon J Alexander, Short Selling and Efficient Sets,” Journal of Finance (September, 1993), pp 1497– 15 06 In addition to addressing portfolio optimization with short selling. .. Conditions of Risk,” Journal of Finance (September 1 964 ), pp 425–442 John Lintner, “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,” Review of Economics and Statistics (February 1 965 ), pp 13–37 How Short Selling Expands the Investment Opportunity Set EXHIBIT 8.2 209 Standard CAPM with Risk-Free Lending and Borrowing portfolio of risky assets that... Frontier,” Journal of Finance (December 19 86) , pp 1051–1 068 How Short Selling Expands the Investment Opportunity Set 215 position in the same asset Thus, short selling an asset with an expected return of zero and positive correlations (with all other assets) will not change the expected return, but it will reduce the variance of any longonly portfolio (as a result of the short position’s negative correlation... taking an active strategy in both the short- only portfolio and the long-only portfolio We refer to this as an active long-plus -short strategy, where the long and short positions are held in separate portfolios, just as with enhanced indexing Long-Plus -Short Portfolios There are two reasons why long-plus -short portfolios might beat enhanced indexing with short selling First, the investor may be adept... that short selling has little to offer passive investors The question is how should active investors, who have some prospects of identifying overpriced stocks, go about short selling so as to improve potential portfolio efficiency We analyze the theoretical justifications for three specific strategies: (1) enhanced indexing with short selling, (2) long-plusshort portfolios, and (3) integrated long -short. .. their long positions, rather than continue to sell short This outcome is more realistic than that of the above zero-beta model, which assumed unlimited short selling such that the sellers had full use of the sale proceeds Note that unlimited 212 EXHIBIT 8.4 THEORY AND EVIDENCE ON SHORT SELLING CAPM with Differential Lending and Borrowing Rates short selling is implied when the full-investment constraint . Datastream. LIBOR 3-month 6. 21 6- month 6. 41 Stock Prices Palm 55.25 3Com 68 Call Put Synthetic Short Percent Deviation Synthetic Long Percent DeviationBid Ask Bid Ask May 55 5.75 7.25 10 .62 5 12 .62 5 47.55 –14. getting wrong? 7-Lamont -Short Constraints Page 199 Thursday, August 5, 2004 11:12 AM 200 THEORY AND EVIDENCE ON SHORT SELLING TECH STOCK MANIA AND SHORT SALE CONSTRAINTS Can short sale constraints. H 8-Jones/Larsen-ExpandInvest Page 205 Thursday, August 5, 2004 11:13 AM 2 06 THEORY AND EVIDENCE ON SHORT SELLING sents an opportunity to expand upon the long-only investment set, and there are several