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Regulatory Responses to Short Selling

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Abstract

It is commonly believed that secondary market prices is not just a sideshow because they contain information that facilitates the efficient allocation of resources. The feedback loop to a real investment decisions allows a short seller to make a profit even in the absence of a fundamental information. This paper analyzes the regulation of manipulative short selling is to impose a cost on short sales. Through setting the short selling cost at an appropriate level, regulators may be able to drive the uninformed speculator, but not the negatively informed speculator, out of the market, and, thus improve the investment efficiency.

One of the most fundamental roles of prices is to facilitate the efficient allocation of scarce resouces (Hayek, 1945). A financial market is a place where many speculators with different pieces of infomation meet to trade, attempting to profit from their information. Prices aggregate there diverse pieces of information and ultimately reflect an accurate assessment of firm value. Real decision makers (such as managers, capital providers, directors, customers, regulators, employees, etc.) will learn from this information and use it to guide their decisions, in turn affecting firm cash flows and values (Baumol 1965). In an efficient market, at any point in time market prices of securities provide accurate signals for resource allocation; that is, firms can make production-investment decisions according to stock price (Fama & Miller 1972).

Unlike the traditional models where prices only reflect expected cash flows, in the new models that incorporate feedback effect prices both affect and reflect firm cash flow. The feedback effect can explain this by two ways, several papers in the literature generate related implication based on models with exogenous feedback, i.e., where firm value or firms' investment decison is assumed to be mechanically tied to the price (Khanna & Sonti 2004 and Ozdenoren & Yuan 2008). However, our focus here is on models that exhibit endogenous feedback, i.e, via learning or incentives. The latter one is through which financail markets may have real effects is by affecting a decision maker's incentives to take real decisions, this is most relevant for firm managers, whose compensation is tied to the firm's share price, in some sense is a way to discourage “agency problem”. Particularly, the former one is what we interested here, real decision makers learn from stock price and use it to affect real decision.

The theoretical research on financial markets traditionally treats the real side of the firm as exogenous. Milgrom & Stokey (1982) consider that if cash flows are exogenous, the only way to generate trade is to introduce noise traders in the model. Grossman & Stiglitz (1980); Hellwig (1980) developed rational expectations equilibrium models of financial market, in which prices preform a well-articulated role in conveying information from the informed to the uninformed. Kyle (1985) developed a model that is closer to a game-theoretic approch, where the equilibrium concept is similar to the Bayesian-Nash Equilibrium, the information of speculator gets partially reflected in the stock price. However, Fishman & Hagerty (1992); Leland (1992); Khanna, Slezak & Bradley (1994); and Bernhardt, Hollifield & Hughson (1995) present models where different types of speculators-insiders and outsiders-trade on their information, in these models, real decison makers learn from price, but, there is a conflict between limiting insider trading reduces price efficiency and encouraging outsider trading reduces adverse selection. Similarly, Boot & Thakor (1997) and Subrahmanyam & Titman (1999) use the feedback effect to rationalize a firm's choice to issue publicly traded securities, rather than receving private financing (e.g., from a bank).

The traditional view of financial market is stock price has no real effect, thus speculator cannot manipulate stock price to get profit. It is often hard to generate manipulation as an equilibrium phenomennon, given that price impact will cause a manpulator to sell at a low price and buy at a high price and hence lose money overall (Jarrow 1992). Goldstein & Guembel (2008) consider a model where the manager of firm learns from the stock price about the profitability of an investment project, thus, manipulation arise as an equilibrium phenomenon. Even the speculator has no information, she can drriven the price down to make the manager belive that there exist negative information, and led to cancel the investment, thus, she can get profit from her short position. Edmans, Goldstein & Jiang (2014) extent their model to show that informed speculators are less likely to trade on bad news rather than good news. Consider a speculator who has negative information, if she short sell to lower the stock price, the manager will learn from it to take corrective action such as reducing investment, downsizing the firm makes it efficient and improve the firm's fundamental value, but this reducing the profitability of speculator's short position. Thus, the informed speculator must consider this and refrain her short selling in the first place.

The feedback effect has also some empirical supports. Luo (2005) show the companies seem to learn from the market during M&A. Companies are more likely to learn in pre-agreement deals than in agreement deals. Companies are more likely to learn in non-high-tech deals than in high-tech deals. Smaller bidders are more likely to learn than are larger bidders. Kau, Linck & Rubin (2008) extend his analysis and show that such learning is more likely when governance mechanisms are in place to reduce the agency problem between manager and the shareholders. Chen, Goldstein & Jiang (2007) show that the sensitivity of investment to price is stronger when there is more private information incorporate into price.

Our paper is continue the research question raised by Goldstein & Guembel (2008), they provid an asymmetric model to explaine the uninformed speculator can manipulate the stock price to make profit and they suggest by impose a cost on short sales may eliminate this phenomenon, but they didn't anaysis the impact of short selling cost. Conditional the speculator being uninformed, the speculator can make profit for two reasons. First, he knows that the market will not improve the allocation of resources. Thus, he can sell at a price that is higher than the expected value. Second, the speculator can profit by establishing a short position in the stock and subsequently driving down the firm's stock price by further short sales. In our analysis of short selling cost can deter the second sources of the uninformed speculator's profit.

The remainder of the paper is structured as follows. Section 2 gives a brief summary of regulatory response to short selling during the financial crises of 2007-2009 and the European sovereign debt crisis of 2011. Section 3 present the model set-up. Section 4 we derive the benchmark equilibrium when absent the feedback. Section 5 derive the equilibrium when the feedback present. Section 6 concludes. All proofs are in the Appendix.

2 Recent regulatory response to short selling

As a result of the financial market turmoil in 2008, the SEC and a number of international financial market regulators put in effect a number of new rules regarding short selling. In July the SEC issued an emergency order banning so-called “naked” short sellingIn a naked short-sale transaction, the short seller does not borrow the share before entering the short position. In our model, we can consider the short selling cost is zero is a naked short-sale. in the securities of Fannie Mae, Freddie Mac, and primary dealers at commercial and investment banks. In total 18 stocks were included in the ban, which took effect on Monday July 21 and was in effect until August 12.

On September 19 2008, the SEC banned all short selling of stocks of financial companies. This much broader ban initially included a total of 799 firms, and more firms were added to this list over time. In a statement regarding the ban, SEC Chairman Christopher Cox said, “The Commission is committed to using every weapon in its arsenal to combat market manipulation that threatens investors and capital markets. The emergency order temporarily banning short selling of financial stocks will restore equilibrium to markets. This action, which would not be necessary in a well-functioning market, is temporary in nature and part of the comprehensive set of steps being taken by the Federal Reserve, the Treasury, and the Congress.” This broad ban of all short selling in financial institutions was initially set to expire on October 2, but was extended until Wednesday October 9, i.e., three days after the emergency legislation (the bailout package) was passed.

In addition to measures taken by the SEC, a number of international financial regulators also acted in response to short selling. On September 21 2008, Australia temporarily banned all forms of short selling, with only market makers in options markets allowed to take covered short positions to hedge. In Great Britain, the Financial Services Authority (FSA) enacted a moratorium on short selling of 29 financial institutions from September 18 2008 until January 16 2009. Also Germany, Ireland, Switzerland and Canada banned short selling of some financial stocks, while France, the Netherlands and Belgium banned naked short selling of financial companies.

International restrictions on short selling of financial stocks reappeared in 2011. In August of 2011, market regulators in France, Spain, Italy and Belgium imposed temporary restrictions on the short selling of certain financial stocks as European banks came under increasing pressure as part of the sovereign debt crisis in Europe. For example, both Spain and Italy imposed a temporary bans on new short positions, or increases in existing short positions, for a number of financial shares. France temporarily restricted short selling for 11 companies, including Axa, BNP Paribas and Credit Agricole. On August 26, France, Italy and Spain extended their temporary bans on short selling until at least the end of September.

Of course, measures against short selling are not exclusive to these recent episodes. In response to the market crash of 1929, the SEC enacted the uptick rule, which restricts traders from selling short on a downtick. In 1940, legislation was passed that banned mutual funds from short selling. Both of these restriction were in effect until 2007. Going back even further in time, the UK banned short selling in the 1630s in response to the Dutch tulip mania.

We revisit the model in Goldstein & Guembel (2008). Consider an economy with four dates t\in\{0,1,2,3\}

and a firm whose stock is traded in the financial market. The firm's manager needs to take an investment decision. In t=0

, a risk-neutral speculator may learn private information about the state of the world \omega

that determines the profitability of the firm's investment opportunity. Trading in the financial market occurs in t=1

and t=2.

The speculator may suffers a short selling cost c\;(c>0)

when he short sales. In addition to the speculator, two other types of agents participate in the financial market: noise traders whose trades are unrelated to the realization of \omega

and a risk-neutral market maker. The latter collects the orders from the speculator and the noise traders and sets a price at which he executes the order out of his inventory. The information of the speculator may get reflected in the price via the trading process. In t=3,

the managers takes the investment decision, which may be affected by the stock price realizations. Finally, all uncertainty is realized and pay-offs are made.

Suppose that the firm has an investment opportunity that requires a fixed investment at the amount of K.

There are two possible states \omega\in\{l,h\}

that occur with equal probabilities. Firm valueTo simplifier the model, we do not include the assets in place in the expressions for the value of the firm, even including it will not affect our analysis. can be expressed as a function V(\omega,k)

of the underlying state \omega

and the investment decision k\in\{0,K\}:

There is one speculator in the model. In t=0,

with probability \alpha,

the speculator receives a perfectly informative private signal s\in\{l,h\}

regarding the state of the world \omega.

With probability 1-\alpha

he receives no signal, which we denote as s=\phi.

There are two trading dates : t=1,2.

In each trading date, the speculator submits orders u_{t}\in\{-1,0,1\}

to a market maker. There is a exogenous noise trader who submits orders n_{t}=\{-1,0,1\}

with equal probabilities. The market maker only observes total order flow Q_{t}=n_{t}+u_{t},

and therefore possible order flows are Q_{t}=\{-2,-1,0,1,2\}.

Moreover, it is assumed that a market maker faces Bertrand competition and thus sets the price for an asset equal to its expected value, given his information set: p_{1}(Q_{1})=E[V\mid Q_{1}]

and p_{2}(Q_{1},Q_{2})=E[V\mid Q_{1},Q_{2}].

In our model, the price is a function of total order flows, thus, to ease the exposition, we assume that the speculator observes Q_{1},

and therefore can directly condition his t=2

trade on Q_{1}

instead of p_{1}.

Similarly, the firm manager observes Q_{1}

and Q_{2}

, and may use them in his investment decision. The equilibrium concept we use is the Perfect Bayesian Nash equilibrium. Here, it is defined as follows:

• A trading strategy by the speculator \{u_{1}(s)

and \{u_{2}(s,Q_{1},u_{1})\}

that maximizes his expected pay-off, given the price-setting rule, the strategy of the manager, and the information he has at the time he makes the trade;

• An investment strategy by the firm that maximizes expected firm value given all other strategies;

• A price-setting strategy by the market maker \{p_{1}(Q_{1})

and p_{2}(Q_{1},Q_{2})\}

that allows him to break even in expectation, given all other strategies;

• The firm and the market maker use Bayes' rule in order to update their beliefs from the orders they observe in the financial market;

• All agents have rational expectations in the sense that each player's belief about the other players' strategies is correct in equilibrium.

As a benchmark, we consider in this section there is no feedback from the financial market to the firm's investment decision. We assume the firm manager known well the state of the world, and, thus, the investment decision in t=3

is not affect by the trading outcomes in the financial market in t=1

and t=2.

For the speculator, if s=h

, he knows that the firm's value is V^{+};

if s=l,

he knows that the firm value is 0;

and if s=\phi,

he knows the expected firm value is \frac{V^{+}}{2}

. The market maker also starts with the expectation that the firm value is \frac{V^{+}}{2}

and updates this expectation after each round of trade.

There exists multiple equilibria with no-feedback game when we impose the short selling cost c

in t=1.

Because there is no feedback and from the proof of Proposition 1., the short selling cost only affect to negatively informed speculator, in order to simplifier the model, we don't impose short selling cost at t=2 . If we impose short selling cost at t=2, we must distinguish not trade or sells in t=1 and buy in t=1 (see the feedback game). . For brevity, we do not develop a particular equilibrium here. The following lemma characterizes the strategy of the positively informed speculator in any equilibrium of the no-feedback game. Building on this lemma, the next proposition establishes an important result regarding the strategy of negatively informed speculator and uninformed speculator, which is the focus of this paper.

The trading strategy is rather intuitive. The short selling cost does not affect positively informed speculator's trading behavior, since he know the firm value is V^{+}

and the firm manager does not learn any information from the stock prices, thus, it is a game only between speculator and the market maker, in the case his information was not revealed to the market maker, the positively speculator will not choose sells in t=1

and t=2.

For the positively informed speculator, the only thing is try to hide his information to the market maker, otherwise, the price will equal to the true value of the firm V^{+}

and he makes zero profit.

The trading strategies are also rather intuitive. For the uninformed speculator, trading in t=1

without information generates losses because buying (selling) pushes the price up (down), so that the expected price is higher (lower) than the unconditional expected firm value. The uninformed speculator does not have the informational advantage over the market maker in t=1,

and thus cannot make a profit if he is trading. He may choose trade in t=2

when the market maker set the price is not equal \frac{V^{+}}{2},

in this case, he have the informational advantage, he knows each agent's trading orders in t=1

and his own trading order in t=2.

For the negatively informed speculator, if short selling cost is not too high, he may choose mixes the trading strategies like positively informed speculator in order to hide his information to the market maker; if the short selling cost is too high, he always get negative transaction profit in t=1,

in this case, he would like not trade in t=1.

In the no-feedback game, the short selling cost actually does not affect the trading behavior of the positively informed speculator and the uninformed speculator, it can only affect to the negatively informed speculator. It is worth noting that in the next section with feedback , the short selling cost will affect not only the negatively informed speculator, but also the uninformed speculator.


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