Journal of Financial Economics 18(1987)277-311.North-Holland CONSTRAINTS ON SHORT-SELLING AND ASSET PRICE ADJUSTMENT TO PRIVATE INFORMATION* Douglas W.DIAMOND University of Chicago.Chicago.IL 60637.USA Robert E.VERRECCHIA University of Pennsylvania,Philadelphia,PA 19104.USA Received September 1985,final version received May 1986 This paper models effects of short-sale constraints on the speed of adjustment (to private information)of security prices.Constraints eliminate some informative trades,but do not bias prices upward.Prohibiting traders from shorting reduces the adjustment speed of prices to private information,especially to bad news.Non-prohibitive costs can have the reverse effect,but this is unlikely.Implications are developed about return distributions on information announcement dates.Periods of inactive trade are shown to impart a downward bias to measured returns.An unexpected increase in the short-interest of a stock is shown to be bad news. 1.Introduction This paper models the effects of constraints on short-sales on the distribu- tion and speed of adjustment (to private information)of security prices.A very simple rational expectations model of trade with bid and ask prices posted by a specialist is used to clarify the informational effects of these constraints.The model yields results concerning the effects of constraints on short-sales on the distribution of security prices,the absolute speed of adjust- ment of prices to private information,and the relative speed of adjustment to (private)good,versus bad,news.This,in turn,has implications for the 'informational efficiency'of security prices that are subject to constraints on short-selling.When combined with the notation that introducing traded put and call options can reduce the cost of establishing what is effectively a short position,these implications have empirical content.In particular,the model .We are grateful for useful comments from the referee.Haim Mendelson,Jennifer Conrad. Kenneth French,Robert Holthausen,Richard Leftwich,Robert Vishny and workshop par- ticipants at Carnegie-Mellon.Chicago,Columbia,Duke.UCLA,University of Pennsylvania and Yale.Diamond is grateful to acknowledge financial support from a Batterymarch Fellowship and the Center for Research in Security Prices at the University of Chicago.Verrecchia is grateful to acknowledge financial support from the Arthur Young Foundation. 0304-405X/87/$3.501987,Elsevier Science Publishers B.V.(North-Holland)
Journal of Financial Economics 18 (1987) 277-311. North-Holland CONSTRAINTS ON SHORT-SELLING AND ASSET PRICE ADJUSTMENT TO PRIVATE INFORMATION* Douglas W. DIAMOND Universiry of Chicago, Chicago, IL 60637, USA Robert E. VERRECCHIA Unlversir) o/Pennsylvania, Philadelphia, PA 19104, USA Received September 1985. final version received May 1986 This paper models effects of short-sale constraints on the speed of adjustment (to private information) of security prices. Constraints eliminate some informative trades, but do not bias prices upward. Prohibiting traders from shorting reduces the adjustment speed of prices to private information, especially to bad news. Non-prohibitive costs can have the reverse effect, but this is unlikely. Implications are developed about return distributions on information announcement dates. Periods of inactive trade are shown to impart a downward bias to measured returns. An unexpected increase in the short-interest of a stock is shown to be bad news. 1. Introduction This paper models the effects of constraints on short-sales on the distribution and speed of adjustment (to private information) of security prices. A very simple rational expectations model of trade with bid and ask prices posted by a specialist is used to clarify the informational effects of these constraints. The model yields results concerning the effects of constraints on short-sales on the distribution of security prices, the absolute speed of adjustment of prices to private information, and the relative speed of adjustment to (private) good, versus bad, news. This, in turn, has implications for the ‘informational efficiency’ of security prices that are subject to constraints on short-selling. When combined with the notation that introducing traded put and call options can reduce the cost of establishing what is effectively a short position, these implications have empirical content. In particular, the model ‘We are grateful for useful comments from the referee, Haim Mendelson. Jennifer Conrad, Kenneth French, Robert Holthausen, Richard Leftwich, Robert Vishny and workshop participants at Carnegie-Mellon, Chicago, Columbia, Duke, UCLA, University of Pennsylvania and Yale. Diamond is grateful to acknowledge financial support from a Batterymarch Fellowship and the Center for Research in Security Prices at the University of Chicago. Verrecchia is grateful to acknowledge financial support from the Arthur Young Foundation. 0304-405X/87/$3.500 1987, Elsevier Science Publishers B.V. (North-Holland)
278 D.W.Diamond and R.E.Verrecchia,Price adjustment to private information predicts how introducing these options influences the magnitude of price adjustments to public information,such as earnings announcements.A second set of empirical implications is contained in a characterization of the impact on prices of the announcement each month of the short-interest in a stock:we show that an unexpected increase in the short-interest is bad news.We analyze the relation between these announcement effects and the speed of adjustment to private information,producing joint empirical predictions.A final im- portant implication of short-constraints is identified:the last transaction price is an upward biased measure of the value of a stock during periods when no trade is observed. Existing studies of short-sales constraints stress that it is pessimists who would want to sell short [e.g.,Miller (1977),Figlewski (1981)].This approach concludes that constraining pessimists without constraining optimists imparts an upward bias to stock prices.An analogy with voting on a referendum illustrates this point.In an 'unconstrained'vote,voters may choose yes or no, and the motion passes if subtracting no votes from yes votes yields a positive number.If the voters were constrained to choose between voting yes or abstaining and the election rule were unchanged,the results would be biased in favor of the yes voters.Changing the election rule at the same time as the voting constraint could remove the bias.One example of a new rule is to require a fixed number of yes votes for the referendum to pass.This paper analyzes the ways that market forces change the 'election rules'in a security market when short-sale constraints are imposed.Previous work assumes that these 'rules'are unchanged.We show that unchanged 'rules'are inconsistent with common knowledge that short-selling is constrained(since no one would argue that this constraint is a secret),when the differences in votes(security trades)is due to information differences rather than to differences in tastes. Rational expectation formation changes the election rules and removes any upward bias to prices,but there remain important implications of short-con- straints that we identify. The model is structured to examine the observable effects of constraints on short-selling.Our approach is to assume that not all traders face the same cost of short-selling a stock (although our model can analyze situations where all face the same cost).Some traders and market makers can sell short at no cost and immediately obtain the sale proceeds for reinvestment,others cannot sell short at all,and a third group can sell short but cannot immediately receive the sale proceeds. We model a market with a competitive market maker who sets bid and ask prices at each instant of time.The basic structure of the model is based on Glosten and Milgrom (1985),though the logic goes back to Bagehot (1971) 1Jarrow (1980)shows that the 'bias'can be cither positive,negative or zero.None of these papers have investors with rational expectations
278 D. W. Dtamond and R. E. Verrecchia. Price adjustment to pricate tnformation predicts how introducing these options influences the magnitude of price adjustments to public information, such as earnings announcements. A second set of empirical implications is contained in a characterization of the impact on prices of the announcement each month of the short-interest in a stock: we show that an unexpected increase in the short-interest is bad news. We analyze the relation between these announcement effects and the speed of adjustment to private information, producing joint empirical predictions. A final important implication of short-constraints is identified: the last transaction price is an upward biased measure of the value of a stock during periods when no trade is observed. Existing studies of short-sales constraints stress that it is pessimists who would want to sell short [e.g., Miller (1977) Figlewski (1981)]. This approach concludes that constraining pessimists without constraining optimists imparts an upward bias to stock prices.’ An analogy with voting on a referendum illustrates this point. In an ‘unconstrained’ vote, voters may choose yes or no, and the motion passes if subtracting no votes from yes votes yields a positive number. If the voters were constrained to choose between voting yes or abstaining and the election rule were unchanged, the results would be biased in favor of the yes voters. Changing the election rule at the same time as the voting constraint could remove the bias. One example of a new rule is to require a fixed number of yes votes for the referendum to pass. This paper analyzes the ways that market forces change the ‘election rules’ in a security market when short-sale constraints are imposed. Previous work assumes that these ‘rules’ are unchanged. We show that unchanged ‘rules’ are inconsistent with common knowledge that short-selling is constrained (since no one would argue that this constraint is a secret), when the differences in votes (security trades) is due to information differences rather than to differences in tastes. Rational expectation formation changes the election rules and removes any upward bias to prices, but there remain important implications of short-constraints that we identify. The model is structured to examine the observable effects of constraints on short-selling. Our approach is to assume that not all traders face the same cost of short-selling a stock (although our model can analyze situations where all face the same cost). Some traders and market makers can sell short at no cost and immediately obtain the sale proceeds for reinvestment, others cannot sell short at all, and a third group can sell short but cannot immediately receive the sale proceeds, We model a market with a competitive market maker who sets bid and ask prices at each instant of tune. The basic structure of the model is based on Glosten and Milgrom (1985), though the logic goes back to Bagehot (1971) ‘Jarrow (1980) shows that the ‘bias’ can be either positive, negative or zero. None of these papers have investors with rational expectations
D.W.Diamond and R.E.Verrecchia.Price adjustment to pricate information 279 and Copeland and Galai (1983).The information structure is the simplest other than perfect information:there are informed traders who observe identical private information and uninformed traders who observe only public information.The competitive,risk-neutral market maker does not observe the private information,but does observe all trades as they take place.Potential competition implies that a risk-neutral market maker will earn a zero expected profit on each transaction.He sets a bid-ask spread such that,on average,his losses from transacting with informed traders are equal to his profits from transacting with uninformed traders.This requires that each bid and ask price be set equal to the conditional expectation of the value of the asset given all past trades,and given the information of the current trade(e.g.,a buy at the ask,or a sale or short-sale at the bid).Changing the constraints on short-sell- ing affects the information content of observed transactions.Rational market makers and investors take this into account when formulating their demand and pricing decisions. Imposing a cost on short-selling obviously makes it less attractive,and one expects that those willing to pay the cost are the ones with the greatest anticipated benefits from selling short.This implies that imposing a cost on short-selling both reduces the number of short-sales and influences the mix of relatively informed and relatively uninformed traders who remain in the pool of short-sellers.To examine the implications of both effects,we specify two types of short-selling costs,each of which has only one of the two effects.In practice,most costs would have both effects(we discuss the empirical implica- tions of this in section 5). The first effect arises from the prohibition,or elimination,of short-sales.We refer to this as the short-prohibition effect.Here,we assume there exists a cost that prevents investors who want to short from so doing.This eliminates short-sales by informed and uninformed traders alike.Examples include legal or contractual prohibitions of shorting by certain institutional investors and corporate insiders,the inability to borrow stock to short,and (in the short run) the 'no short-sale on a down-tick'rule,which prohibits short-sales at prices below the last differing price. The second effect arises from the restriction of short-sales through the imposition of additional costs.We refer to this as the short-restriction effect.If sale proceeds cannot be reinvested,or there is an additional cost of borrowing securities to short,only investors who have strong beliefs that a significant price decline will soon occur will choose to short.Thus,the restriction of short-sales due to costs changes the composition of the remaining pool of short-sellers.In contrast to the prohibition of short-sales,a restriction drives relatively uninformed traders out of the pool of shorts more so than it drives out relatively informed traders.We specify a cost that drives out only the uninformed traders.Observed changes in the costs of establishing short-posi- tions probably contain elements of both effects,driving out some informed
D. W. Diamond and R. E. Verrecchla. Pnce adjurment to pricate information 279 and Copeland and Galai (1983). The information structure is the simplest other than perfect information: there are informed traders who observe identical private information and uninformed traders who observe only public information. The competitive, risk-neutral market maker does not observe the private information, but does observe all trades as they take place. Potential competition implies that a risk-neutral market maker will earn a zero expected profit on each transaction. He sets a bid-ask spread such that, on average, his losses from transacting with informed traders are equal to his profits from transacting with uninformed traders. This requires that each bid and ask price be set equal to the conditional expectation of the value of the asset given all past trades, and given the information of the current trade (e.g., a buy at the ask, or a sale or short-sale at the bid). Changing the constraints on short-selling affects the information content of observed ,transactions. Rational market makers and investors take this into account when formulating their demand and pricing decisions. Imposing a cost on short-selling obviously makes it less attractive, and one expects that those willing to pay the cost are the ones with the greatest anticipated benefits from selling short. This implies that imposing a cost on short-selling both reduces the number of short-sales and influences the mix of relatively informed and relatively uninformed traders who remain in the pool of short-sellers. To examine the implications of both effects, we specify two types of short-selling costs, each of which has only one of the two effects. In practice, most costs would have both effects (we discuss the empirical implications of this in section 5). The first effect arises from the prohibition, or elimination, of short-sales. We refer to this as the shorr-prohibition effect. Here, we assume there exists a cost that prevents investors who want to short from so doing. This eliminates short-sales by informed and uninformed traders alike. Examples include legal or contractual prohibitions of shorting by certain institutional investors and corporate insiders, the inability to borrow stock to short, and (in the short run) the ‘no short-sale on a down-tick’ rule, which prohibits short-sales at prices below the last differing price. The second effect arises from the restriction of short-sales through the imposition of additional costs. We refer to this as the short-restriction effect. If sale proceeds cannot be reinvested, or there is an additional cost of borrowing securities to short, only investors who have strong beliefs that a significant price decline will soon occur will choose to short. Thus, the restriction of short-sales due to costs changes the composition of the remaining pool of short-sellers. In contrast to the prohibition of short-sales, a restriction drives relatively uninformed traders out of the pool of shorts more so than it drives out relatively informed traders. We specify a cost that drives out only the uninformed traders. Observed changes in the costs of establishing short-positions probably contain elements of both effects, driving out some informed
280 D.W.Diamond and R.E.Verrecchia,Price adjustment to pricate information and some relatively uninformed traders.Therefore,our strategy is to identify the implications of each effect,and identify predictions we can make without directly knowing which one dominates. The balance of the paper proceeds as follows.Section 2 develops the model. Section 3 examines the effect of prohibiting short-selling on the speed of adjustment of prices to private information,on the magnitude of price adjustments to announcements of public information,and on the bid-ask spread.Section 4 presents analogous results on the effect of restricting the receipt and reinvestment of the proceeds of a short-sale,rather than prohibit- ing such sales.Section 5 presents empirical implications of the model's results on informational efficiency,on short-interest announcements,and on the implications for measuring returns after periods of inactive trade.Section 6 concludes the paper. 2.The model The basic structure of the model is based on Glosten and Milgrom(1985): market makers are risk-neutral,face no inventory costs or constraints,and earn zero expected profits from each trade.Traders are also risk-neutral and are either informed or uninformed.There is an infinite number of each type of trader.Informed traders know (privately)the true liquidating value of the risky.asset,while uninformed traders make an inference about its value based on all public information.The prior distribution of the risky asset's value is Bernoulli:its liquidating value is one with probability one-half,and zero with probability one-half.The liquidating value is paid in the distant future,but we abstract from discounting in determining market prices.Apart from short-sale constraints,an informed trader buys the asset if it is underpriced and sells if it is overpriced.A share is underpriced if its ask price is less than the trader's conditional expectation of the liquidating value,and overpriced if its bid price is above the trader's conditional expectation. An informed trader makes a particular trade on the basis of his information and the current price of the stock.If the market maker traded only with informed traders,he would lose money because informed traders would buy when the price was too low and sell only when the price was too high.Absent a motive for trade other than speculative profit,there would exist no prices that allow the specialist to break even and the market would break down. Therefore,we introduce another motive to trade by considering the role of 'liquidity trading'.Liquidity trading occurs for reasons exogenous to our model,and involves the need to buy or sell at a particular time.The reasons might include immediate consumption needs,tax planning,and alternative outside investment opportunities.With liquidity trading,voluntary trade is possible because the specialist can earn enough profit on non-informational trades to offset losses from transactions with informed traders
280 D. W. Diamond and R. E. Verrecchia, Price arijustment to pncate information and some relatively uninformed traders. Therefore, our strategy is to identify the implications of each effect, and identify predictions we can make without directly knowing which one dominates. The balance of the paper proceeds as follows. Section 2 develops the model. Section 3 examines the effect of prohibiting short-selling on the speed of adjustment of prices to private information, on the magnitude of price adjustments to announcements of public information. and on the bid-ask spread. Section 4 presents analogous results on the effect of restricting the receipt and reinvestment of the proceeds of a short-sale, rather than prohibiting such sales. Section 5 presents empirical implications of the model’s results on informational efficiency, on short-interest announcements, and on the implications for measuring returns after periods of inactive trade. Section 6 concludes the paper. 2. The model The basic structure of the model is based on Glosten and Milgrom (1985): market makers are risk-neutral, face no inventory costs or constraints, and earn zero expected profits from each trade. Traders are also risk-neutral and are either informed or uninformed. There is an infinite number of each type of trader. Informed traders know (privately) the true liquidating value of the risky. asset, while uninformed traders make an inference about its value based on all public information. The prior distribution of the risky asset’s value is Bernoulli: its liquidating value is one with probability one-half, and zero with probability one-half. The liquidating value is paid in the distant future, but we abstract from discounting in determining market prices. Apart from short-sale constraints, an informed trader buys the asset if it is underpriced and sells if it is overpriced. A share is underpriced if its ask price is less than the trader’s conditional expectation of the liquidating value, and overpriced if its bid price is above the trader’s conditional expectation. An informed trader makes a particular trade on the basis of his information and the current price of the stock. If the market maker traded only with informed traders, he would lose money because informed traders would buy when the price was too low and sell only when the price was too high. Absent a motive for trade other than speculative profit, there would exist no prices that allow the specialist to break even and the market would break down. Therefore, we introduce another motive to trade by considering the role, of ‘liquidity trading’. Liquidity trading occurs for reasons exogenous to our model, and involves the need to buy or sell at a particular time. The reasons might include immediate consumption needs, tax planning, and alternative outside investment opportunities. With liquidity trading, voluntary trade is possible because the specialist can earn enough profit on non-informational trades to offset losses from transactions with informed traders
D.W.Diamond and R.E.Verrecchia,Price adjustment to private information 281 Formally,we model liquidity trading as a shock to an individual's time preference.All traders discount future consumption by the factor p,so the present utility value of consumption,Cr,on the date of the liquidating dividend,is p x Cr.We assume that absent a shock,p equals one.Unin- formed traders (but no one else)receive one of two possible shocks:either p =0,which implies that one sells the asset to satisfy consumption today,or p=+oo,which implies that one buys the asset as a means of deferring consumption indefinitely.Modeling preference shocks as we do is a'reduced form'for many possibilities.We use extreme values purely for simplicity of interpretation.The Glosten-Milgrom (1985)model is consistent with more general shocks and types of private information.Some motive for trade other than speculative profit is necessary to construct a model of trade by unin- formed individuals:unless they have some potential gains from trade,they will be unwilling to pay the bid-ask spread.Nothing of substance depends on the assumption that only uninformed traders are subject to liquidity shocks. To offer the simplest setting for the role of information and liquidity shocks toward generating observable trades,we abstract from the possible variations in the size of trades established by traders.Specifically,a trader is allowed to buy a single share,sell a single share,short-sell a single share,or do nothing. For example,if a trader is informed and observes that the stock is underpriced at the ask price,he then buys one share and holds it (because under our assumptions,it will never subsequently become overpriced at the bid).Simi- larly,if a trader receives a liquidity shock and has a desire to invest (i.e.. p=+co),he buys one share.If a trader who already owns the stock finds it overpriced at the bid price or receives a liquidity shock and must sell (i.e., p=0).he sells one share. A trader's willingness to short-sell is influenced by the cost associated with this transaction.We assume a simple cost function that is independent of a trader's level of information or type of liquidity shock.The cost associated with selling short falls into one of three categories:no-cost,proceeds-restric- tions,and short-prohibitions.The no-cost scenario allows full reinvestment or consumption of short-sale proceeds,implying that a short-sale generates funds on its initiation date.The proceeds-restrictions scenario delays receipt of proceeds.In this circumstance a short-sale generates no funds today but does allow one to profit if the price falls.Finally,short-prohibitions eliminate any opportunity to short-sell,either because an individual trader is prohibited from engaging in this activity,or the cost is so high that no trader would avail himself of the opportunity regardless of what he knows.We represent that fraction of the population which encounters no cost associated with short-sell- ing by c,that fraction which faces proceeds-restrictions by c2,and that fraction which is essentially prohibited from this activity by c3.All traders, independent of whether they are informed or uninformed,fall into one of these three categories,i.e.,c+c2+c3=1 at all times.Under the assumption
D. W. Diamond and R. E. Verrecchia. Puce adjustment roprioate information 281 Formally, we model liquidity trading as a shock to an individual’s time preference. All traders discount future consumption by the factor p, so the present utility value of consumption, Cr. on the date of the liquidating dividend, is p X Cr. We assume that absent a shock, p equals one. Uninformed traders (but no one else) receive one of two possible shocks: either p = 0, which implies that one sells the asset to satisfy consumption today, or p = + cc, which implies that one buys the asset as a means of deferring consumption indefinitely. Modeling preference shocks as we do is a ‘reduced form’ for many possibilities. We use extreme values purely for simplicity of interpretation. The Glosten-Milgrom (1985) model is consistent with more general shocks and types of private information. Some motive for trade other than speculative profit is necessary to construct a model of trade by uninformed individuals: unless they have some potential gains from trade, they will be unwilling to pay the bid-ask spread. Nothing of substance depends on the assumption that only uninformed traders are subject to liquidity shocks. To offer the simplest setting for the role of information and liquidity shocks toward generating observable trades, we abstract from the possible variations in the size of trades established by traders. Specifically, a trader is allowed to buy a single share, sell a single share, short-sell a single share, or do nothing. For example, if a trader is informed and observes that the stock is underpriced at the ask price, he then buys one share and holds it (because under our assumptions, it will never subsequently become overpriced at the bid). Similarly, if a trader receives a liquidity shock and has a desire to invest (i.e., p = + co), he buys one share. If a trader who already owns the stock finds it overpriced at the bid price or receives a liquidity shock and must sell (i.e., p = 0), he sells one share. A trader’s willingness to short-sell is influenced by the cost associated with this transaction. We assume a simple cost function that is independent of a trader’s level of information or type of liquidity shock. The cost associated with selling short falls into one of three categories: no-cost, proceeds-restrictions, and short-prohibitions. The no-cost scenario allows full reinvestment or consumption of short-sale proceeds, implying that a short-sale generates funds on its initiation date. The proceeds-restrictions scenario delays receipt of proceeds. In this circumstance a short-sale generates no funds today but does allow one to profit if the price falls. Finally, short-prohibitions eliminate any opportunity to short-sell, either because an individual trader is prohibited from engaging in this activity, or the cost is so high that no trader would avail himself of the opportunity regardless of what he knows. We represent that fraction of the population which encounters no cost associated with short-selling by ct, that fraction which faces proceeds-restrictions by c2, and that fraction which is essentially prohibited from this activity by cs. All traders, independent of whether they are informed or uninformed, fall into one of these three categories, i.e., ci + c2 + cj = 1 at all times. Under the assumption