Critical Discussion of the Predatory-Trading-Theory from Brunnermeier/Pedersen


Seminar Paper, 2005

28 Pages, Grade: 2,0


Excerpt

Inhaltsverzeichnis

1. Introduction

2. Model
2.1 Basics of the Model
2.2 Preliminary Analysis
2.3 The Predatory Phase
2.3.1 Exogenous Distress
2.3.1.1 Single Predator
2.3.1.2 Multiple Predators
2.4 Endogenous Distress, Systemic Risk and Risk Management
2.5 The Investment Phase
2.6 Further Implications of Predatory Trading
2.6.1 Front-running
2.6.2 Batch Auction Markets

3. Critical Discussion
3.1 Positive Aspects
3.2 Negative Aspects

4. Conclusion

1. Introduction

What were the reasons for the great crash of the Long-Term Capital Management (LTCM) of hedge funds in 1998[1] ? In short: predatory trading. But what is predatory in effect? How can predatory trading occur? What are the consequences of predatory trading? How can predatory trading be avoided? These questions will be answered in the following paper. The following description gives a first impression of predatory trading: “When you smell blood in the water, you become a shark. ... when you know that one of your number is in trouble ... you try to figure out what he owns and you start shorting those stocks ..."[2] The first part of this paper deals with the basics of the model of the predatory trading theory, the second part elaborates the advantages and disadvantages which are summed up in the last part.

2. Model

2.1 Basics of the model

First, we notice that there is a continuous-time economy, [illustration not visible in this excerpt], consisting of two assets, a riskless bond and a risky asset. To keep the model as simple as possible, the risk-free rate will be standardised to zero. Two different kinds of agents participate in the economy: large strategic traders (arbitrageurs) on the one hand, and long-term investors on the other. Large strategic traders are for instance traders of hedge funds and long-term investors are for example traders of pension funds or simply individual investors. Strategic traders are risk-neutral and want to maximise their expected earning. Because of the largeness of the trader, the equilibrium price will be influenced by its trading and therefore the trader must operate strategically because of his price impact. Every trader has a given start-up structure, [illustration not visible in this excerpt](0), of the risky asset and he can trade his asset with a certain trading intensity, [illustration not visible in this excerpt]. However, at time t the trader has the following position in the risky asset [illustration not visible in this excerpt].

The constraint for each strategic trader is given by [illustration not visible in this excerpt]. The most important thing is that a strategic trader is not allowed to take unlimited positions because, if this would be permitted, the price would be equivalent with the expected value [illustration not visible in this excerpt]. At time [illustration not visible in this excerpt] strategic traders succumb financial risk. In the following the set of distressed strategic traders will be referred to as [illustration not visible in this excerpt] and the set of unaffected trades, the so called “predators”, to [illustration not visible in this excerpt]. Likewise the number of distressed traders is [illustration not visible in this excerpt] and the number of predators is [illustration not visible in this excerpt]. In order to receive money, a cash-strapped strategic trader must sell his risky asset. The formula for this selling is listed up in the appendix. Accordingly, that means that a distressed trader must sell his assets with a minimum speed [illustration not visible in this excerpt] in order to achieve his final position [illustration not visible in this excerpt]. The most decisive matter of fact is that a distressed trader must liquidate his shares before time [illustration not visible in this excerpt]. Not only strategic traders are acting in the market, but also long-term investors which are at the same time price-takers and have an aggregate demand of [illustration not visible in this excerpt] (at each point of time and with current price [illustration not visible in this excerpt]). This formula includes two assumptions. The first one is that the demand curve is downward sloping and the second one is that the requirements of the long-term traders are dependend on current price [illustration not visible in this excerpt]. “The market clearing price [illustration not visible in this excerpt] solves [illustration not visible in this excerpt].”[3] [illustration not visible in this excerpt]is the aggregate holding of the risky asset, [illustration not visible in this excerpt]. When you combine the equation for the market clearing and the equation for the demand of the long-term traders, the price is [illustration not visible in this excerpt]. In the long run, the price will be [illustration not visible in this excerpt] and in the medium term, the demand curve will be downward sloping. But the important aspect of the short-run must also be considered about this context. In practice there is a certain speed limit with which a trader can sell his shares in illiquid markets. As a result of this constraint the strategic traders can sell their asset with a trading speed not exceeding [illustration not visible in this excerpt] at the current price [illustration not visible in this excerpt]. But if the traders overrun their limit given through [illustration not visible in this excerpt] they are afflicted with temporary impact cost, that means [illustration not visible in this excerpt]. This advancement and further effects are mathematically explained in the appendix.[4]

2.2 Preliminary Analysis

This part shows how solutions for a trader’s problem can be detected. We know from the model that the trader has to act within his trading range [illustration not visible in this excerpt] in order to buy or sell optimally. Furthermore we know that [illustration not visible in this excerpt]is valid at each time and the optimal trading strategy suffices [illustration not visible in this excerpt], if the trader [illustration not visible in this excerpt] is not in financial difficulties. A new equilibrium arises, where the trader wants to minimise his trading costs. In this model it is impossible for a trader to benefit from trades which affect the prices. In the appendix, the equilibrium and Lemma 1 are described.[5]

2.3 The Predatory Phase ([illustration not visible in this excerpt])

The predatory phase is cut into two stages. Stage one (exogenous default) is the phase where certain traders are already in financial straits (cf. part 2.3.1) and the role of the financial sound traders will be studied. Whereas stage two (endogenous default) endogenises the agents´ distress and describes how predatory trading can lead to a broad-base financial crisis (cf. section 2.3.2).

2.3.1 Exogenous Distress

2.3.1.1 Single Predator ([illustration not visible in this excerpt])

The simplest assumption is the case with only one predator. The liquidation strategy of the distressed trader is familiar with the single predator. Consequently, the holding of securities of the distressed trader, [illustration not visible in this excerpt], is declining to zero. This leads to the new equilibrium by using Lemma 1 (cf. the appendix). The main prediction of this equilibrium is that both, the distressed trader and the predator, can sell simultaneously at the same speed and in the end, the predator repurchases the shares. Because of the selling of the predator, price-overshooting arises. The reason for this appearance is quite simple: because of the liquidation of the two agents, distressed trader and predator, there is an oversupply of shares. Therefore the price falls and the opportunity is seized by the predator who waits as long as the distressed trader has finished selling. Then the predator acquires the assets very cheaply and this leads to an increase of the price again. This scenario has two advantages for the predator. First, the average selling price of the stocks of the predator is higher than the price which will be reached in the end when both agents have stopped their trading. Second, the purchase price for the predator evidently is very low. In order to illustrate this theoretical explanation, compare the appendix where you can find a numerical example.[6]

2.3.1.2 Multiple Predators ([illustration not visible in this excerpt]

The example with only one predator has shown that his ambition is to “front-run” the distressed trader while he is selling. In the case of multiple predators, this ambition remains and another fact must be added. All the predators, who are acting in the market, want to reach an arbitrage position with their capital and furthermore, their goal is to purchase their stocks sooner than other strategic traders do. The proposition about multiple predators can be read in the appendix. You can summarise that price overshooting also appears in the context of multiple predators, but with the increasing number of predators, the price overshooting effect nearly vanishes. A numerical example in the appendix shows the case of multiple predators.[7]

2.4 Endogenous Distress, Systemic Risk and Risk Management

In this part, distress will be endogenised and you learn that predatory trading has a contagious impact. In order to deal with this case you have to make certain assumptions. The first one is that a trader has to sell his shares if his wealth falls to a marginal level [illustration not visible in this excerpt]. Trader [illustration not visible in this excerpt]´s wealth at [illustration not visible in this excerpt] is composed of his asset holding, [illustration not visible in this excerpt], but also other assets [illustration not visible in this excerpt] will be held. The trader’s mark-to-market wealth is therefore [illustration not visible in this excerpt]. Usually, the value of other holdings, [illustration not visible in this excerpt], is constant, but it can tend to an exogenous shock at time [illustration not visible in this excerpt]. If the wealth shock [illustration not visible in this excerpt] at [illustration not visible in this excerpt] is so large that [illustration not visible in this excerpt], the trader is suddenly cash-strapped and consequently has to liquidate. [illustration not visible in this excerpt] is the maximum wealth at [illustration not visible in this excerpt], and in the case of [illustration not visible in this excerpt], it is the maximum wealth [illustration not visible in this excerpt] such that [illustration not visible in this excerpt], whereas [illustration not visible in this excerpt]stands for strategies of liquidation. Besides, if [illustration not visible in this excerpt], then [illustration not visible in this excerpt]. For a better understanding this definition needs an explanation. Assume that trader [illustration not visible in this excerpt] anticipates that [illustration not visible in this excerpt], other agents will sustain financial damages and thus have to liquidate their holdings. However, [illustration not visible in this excerpt] will pose as predators and because of this assumptions, trader [illustration not visible in this excerpt] will be distressed and his wealth will be less than [illustration not visible in this excerpt]. The outcome of these definitions is that every distressed trader [illustration not visible in this excerpt] owns wealth [illustration not visible in this excerpt][illustration not visible in this excerpt][illustration not visible in this excerpt], and every predator [illustration not visible in this excerpt] has wealth [illustration not visible in this excerpt]>[illustration not visible in this excerpt]. A further proposition says: “The more traders are expected to be in distress, the harder it is to survive. That is, [illustration not visible in this excerpt] is increasing in [illustration not visible in this excerpt].”[8] This proposition is helpful in order to get the idea of systemic risk. Talking about systemic risk, financial regulators always play an important role. They are of the opinion that contagion comes along with predatory trading. If one or two large investors experience financial problems the consequence can be that other sound traders also will become distressed and thus, the financial sector will be disequilibrated. In order to see this externality, take a look at figures 4A and 4B in the appendix. To reduce the systemic risk, it is useful especially for banking houses to install a successful risk management. In reality, banks like Deutsche Bank or JP Morgan have already conducted dealer exit stress tests which help a bank company to evaluate “the impact on its own book caused by a rival being forced to withdraw.”[9] And all risk managers and traders are of the opinion that the most imminent danger comes from dealer exits in highly concentrated markets. That´s why even US Federal Reserve chairman Alan Greenspan is a supporter of such stress tests because he criticises the fact “that a handful dealers account for two thirds of the US interest rate options and credit derivatives markets.”[10] And if one investment bank like JP Morgan Chase possesses one third of these positions it is quite obvious that a dealer exit would be a disaster and hence, the introduction of dealer exit stress tests are indispensable.[11] The past has shown that the risk management must also take into account that “the past empirical correlation structure”[12] overlooks potential predatory trading charges and therefore special stress tests are required to consider the danger of predatory actions.[13]

2.5 The Investment Phase [illustration not visible in this excerpt]

In this section the given position [illustration not visible in this excerpt] of the strategic traders, who want to invest before [illustration not visible in this excerpt], will be endogenised and the capacity [illustration not visible in this excerpt] will be held as a security in order to decrease their risk exposure or use an opportunity to buy shares for good value. [illustration not visible in this excerpt] is the probability that a randomly chosen trader is in distress [illustration not visible in this excerpt], and of course, no trader will suffer financial problems with probability [illustration not visible in this excerpt] [illustration not visible in this excerpt]. Additionally, it is essential that the risk of distress is exogenous and irrespective of the holding size. At time 0, the start-up position of the strategic trader is supposed to be zero. The main difference between the predatory phase and the investment phase is that the time [illustration not visible in this excerpt], where a trader can become distressed, is late enough, that means [illustration not visible in this excerpt]. The proposition in the appendix describes the investment phase more precisely. The investment phase has three potential results after [illustration not visible in this excerpt]: (i) no trader is in failure, (ii) another trader has financial problems and (iii) the trader himself is in distress. But the aspect that is not considered in this model is that the traders know that there will be a price increase after [illustration not visible in this excerpt] and thereby move into the money because of the fact that had created a larger position untimely to [illustration not visible in this excerpt].But it can be stated that in any equilibrium predatory trading comes along with positive probability. The financial reserve of the traders ([illustration not visible in this excerpt]) generates opportunity costs and these costs must be compensated by earnings during a liquidity crisis.[14]

2.6 Further Implications of Predatory Trading

2.6.1 Front-running

All previous equilibria have in common that predator and distressed trader sell simultaneously. But it also can happen that the predator is selling much earlier than the distressed trader. Then the predator is front-running. Of course, there are different motives for the distressed trader to liquidate later than the predator. One argument could be his supposition of thereby experiencing a positive wealth shock. This shock could help him to survive the financial crisis and to avoid transaction costs. Apart from that, the distressed trader does not realise that the predator is already exploiting him or that eventually, the predator could have the skill to liquidate faster than the distressed trader. Altogether, front-running causes predatory trading to become more gainful because of the price overshooting. The derivation of the equilibria with one predator and several predators is explained in the appendix. The equilibrium with only one predator is very simple. First and foremost, the predator sells his entire shares, and then he holds out for the distressed trader until the latter has finished his liquidation. Consequently, the price is low and at last, the predator rebuilds his position, the price overshoots and the liquidation is much more expensive because of predation. In the case of several predators, the equilibrium can be established as in the sections before.[15]

[...]


[1] Cp. McLaughlin, M. (1998)

[2] Cp. Cramer, J. (2002)

[3] Cp. Brunnermeier/Pedersen (2004), p. 8

[4] Cp. Brunnermeier/Pedersen (2004), p. 6-11

[5] Cp. Brunnermeier/Pedersen (2004), p. 12-13

[6] Cp. Brunnermeier/Pedersen (2004), p. 13-17

[7] Cp. Brunnermeier/Pedersen (2004), p. 17-21

[8] CP. Brunnermeier/Pedersen (2004), p. 23

[9] Cp. Jeffery, C. (2003)

[10] Cp. Jeffery, C. (2003)

[11] Cp. Jeffery, C. (2003)

[12] Cp. Brunnermeier/Pedersen (2004), p. 26

[13] Cp. Brunnermeier/Pedersen (2004), p. 21-27

[14] Cp. Brunnermeier/Pedersen (2004), p. 29-31

[15] Cp. Brunnermeier/Pedersen, p. 31-33

Excerpt out of 28 pages

Details

Title
Critical Discussion of the Predatory-Trading-Theory from Brunnermeier/Pedersen
College
University of Regensburg
Course
Empirical Capital Market Research
Grade
2,0
Author
Year
2005
Pages
28
Catalog Number
V43609
ISBN (eBook)
9783638413671
ISBN (Book)
9783656381129
File size
3426 KB
Language
English
Tags
Critical, Discussion, Predatory-Trading-Theory, Brunnermeier/Pedersen, Empirical, Capital, Market, Research
Quote paper
Christian Weiß (Author), 2005, Critical Discussion of the Predatory-Trading-Theory from Brunnermeier/Pedersen, Munich, GRIN Verlag, https://www.grin.com/document/43609

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