# Tobin-Tax and its Relevance for Financial Markets. Modelling a Scenario including the Transaction Tax in Financial Markets

Master's Thesis 2017 39 Pages

## Excerpt

## Table of Contents

1. DEFINITION AND EXPLANATION OF THE TOBIN-TAX AND ITS RELEVANCE FOR FINANCIAL MARKETS

2. MODELLING A SCENARIO INCLUDING THE TRANSACTION TAX IN FINANCIAL MARKETS

2.1.1 INTRODUCTION OF THE MODEL INCLUDING TWO HETEROGENEOUS AGENTS

2.2. EXTENSION OFTHE BASIC MODEL TO TWO RELEVANT MARKETS

2.3. DYNAMICSOFTHE MODELWITHOUT A TRANSACTION TAX

2.3.1.lmplication and resulting Dynamics ofa Transaction Tax in Market 1

2.3.2.lmplication and resulting Dynamics ofa Transaction Tax in two relevant Markets

2.4. BRIEF Outline of Market Liquidity and Comparison of both Markets regarding their Liquidity

2.4.1. Market 1 showing a high Level of Market Liguidity before a Tax Imposition

2.4.2. Market 2 showing a low Level of Market Liguidity before a Tax Imposition

2.4.3. Comparison of both Markets after a Tax Imposition

2.4.4. The Enforcement ofa Financial Transaction Tax in Reality

3. RESULTS

4. CRITIQUE AND FURTHER RESEARCH

5. REFERENCES

6. APPENDIX

## 1. Definition and Explanation ofthe Tobin-Tax and its Relevance for Financial Markets

„Finanzakteure müssen durch die Finanztransaktionssteuer zur Verantwortung gezogen werden" (Financial agents must be held accountable by the financial transaction tax) Referring to this quote by Angela Merkel (Neuhaus, 2014), and connecting it to the severe financial shocks the world economy had to recover from several times in the past 40 years, it becomes clear that financial agents sometimes might be responsible for economic disasters that potentiallycould have been prevented by stricterfinancial regulations.

The most recent occurrence of such a disaster was the world financial crisis that began in 2007 in the United States of America as a mortgage crisis and, by destabilizing financial markets all over the world, evolved into a debt crisis. The massive aftermaths can still be seen in countries such as Greece and Portugal (Ozturk, 2014). One thing economic analysts agree on is that there are various reasons that, in combination, created this economic mess. In fact, the financial meltdown was not inevitable contrary to the position of Ben Bernanke [former president of the Federal Reserve], who claimed the crisis as a chain reaction of unfortunate events and unpredictable events (Mildner, 2012). It was rather caused by human actions as well as by grave failures of the government and financial supervision (Financial Crisis Inquiry Commission, 2011). Besides, large capital inflows from countries like China allowed American banks to irresponsibly grant loans in an extraordinary manner. The focus also shifts to the authorities overseeing the deregulation of financial markets and therefore fuelling the already existing housing bubble (Mildner, 2012). Another contribution to the financial crisis was the possibility that companies could choose their regulation institution regarding their level of supervision which predominantly ended with the one having the weakest regulations (Financial Crisis Inquiry Commission, 2011). These poor regulations stress the trading process (sale/ purchase) of each financial product (credit default swaps - CDS - in that case) for many financial institutions without any boundaries regarding the speed of trading. The extensive system of CDSs will not be elucidated in the following due to the limited scope of this thesis, instead focus will be laid on the trading speed of financial products (Financial Crisis Inquiry Commission, 2011). According to Westerhoff (2004), short-term trading (speculative behaviour) destabilizes financial markets and effort should be made to shift incentives from mentioned high-frequency trading to long-run investments that supposedly have stabilizing effects on financial markets. One solution to mitigate this destabilizing behaviour of financial agents and a principle which has been under debate for several years is the introduction of a transaction tax (Effenberger, 2001). The basic concept of transaction taxes goes back to the American economist James Tobin who, in 1978, proposed a taxation of financial transactions particularly in foreign exchange markets (Menkhoff, 1995). Tobin's reason behind a tax burden on trading currencies was to alleviate the enormous volatility [V] generated by speculating on currency exchange rates. Thus, by taxing every currency exchange with 0.1 percent of the amount traded, the incentives of short-run currency trades should be eliminated (The Telegraph, 2009). Even though, the Tobin tax was supposed to reduce speculation regarding currency trades, it can potentially be applied to every kind of financial trade such as on stocks and derivatives. In this case, one refers to it as a financial transaction tax (Haq et al., 1996; Spiegel Online, 2016). Based on the concept of Tobin, the tax will be imposed on every kind of trade and also to every kind of trader. Not only short-term oriented traders will be affected by the introduction of a transaction tax but also long-term oriented traders. In general, short-run oriented, destabilizing traders will be pushed out ofthe markets due to increased costs of trading on a high-frequent level and a fiscal revenue will be gained in addition (Westerhoff, 2003a). This particular effect will be scrutinized in the course of the following thesis. Furthermore, it comes to mind that taxation affects trade in a negative way and that the price building process usually should not be interfered with externally. Defenders of the transaction tax however state that if the percentage with which trades should be taxed is chosen correctly, stability in the relevant market will be improved (Westerhoff, 2003a). Regarding the external interference into the price building process, it can be assumed that if one compares it [the transaction tax] to other financial reform proposals connected to this topic, the level of interfering is by far not as high as one might expect (Menkhoff, 1995). So far, the introduction of a transaction tax might sound reasonable to governments and financial supervisors, but its implementation is a complex process. One factor that hinders the agreement on a transaction tax is the fear of losing national or international competitiveness. Another one is represented by the difficulties in technical execution. (Spiegel Online, 2016; Spahn, 1996). After this brief introduction it becomes clear that the realization of a financial transaction tax would predominantly serve the goal of preventing future financial crises by reducing instability in financial markets (high volatility).

In the following thesis, the author will first set up a model displaying a financial market with two heterogeneous agents to explain to what extent their trading behaviours have an impact on the stability of the relevant market.

In a second step, the model will be extended to two relevant markets the agents can choose to trade in and the effects of an application of a transaction tax will be depicted. Due to the fact that the reaction of financial markets to a tax introduction depends on various factors the main goal of this work will be to test to what extent the market liquidity in combination with an imposed transaction tax has an impact on the price adjustment process across several periods. For this reason, the set-up model will be programmed in 'mathematica' where after the output will be interpreted. Furthermore, a possible influence of upcoming political events will be elucidated briefly before the results of the main question are stated and discussed. To represent a succinct perspective there will be a brief analysis about the odds of a tax introduction and a mentioning of possible further research.

## 2. Modelling a Scenario including theTransaction Tax in Financial Markets

In the upcoming section, the basic financial market model will be set up and explained in detail. The overall aim of the model is to show a set of stylized facts that are common to financial markets and therefore, a suitable tool to represent financial markets in a realistic way. According to Schmitt/Westerhoff (2013), excess volatility, returns that are not normally distributed (i.e. fat tails), bubbles and crashes, uncorrelated returns and volatility clustering can be understood as these stylized facts. The model aims to present the interaction of two types of traders - Chartists and Fundamentalists - whose strategies will be depicted later on. After explicating the dynamics of the basic model, a transaction tax will be introduced into the setup followed by a detailed analysis of its effects on market dynamics. The impact of a possible tax introduction on market liquidity and the resulting price adjustment processes will be exemplified afterwards.

### 2.1. Introduction of the Model including two heterogeneous Agents

For reasons of simplicity, the following model will first deal with a hypothetical financial market in which agents (also named traders) are able to freely perform speculative actions regarding their price development expectations (Westerhoff, 2003a). According to a study by Menkhoff (1997), there are two types of professional traders following two different set of rules regarding their trading strategies. Both kind of traders are considered to be bounded rational. Following Simon (1955), the available information is incomplete and agents in general are not capable of processing it perfectly. This can be further applied to financial agents as well. On the one hand, there are Chartists who give their orders following a technical analysis [named positive feedback trading (Westerhoff, 2003a)], meaning that they form their orders by relying on price trends from the past. More precisely, they [Chartists] expect prices to reflect all information needed to predict future price trends (Murphy, 1999). In general, technical traders expect the price of an asset to follow a certain trend and try to extrapolate future price developments from past trends. In other words, agents following technical trading rules buy the asset if the price has been increasing in the past because they expect a further rise. Vice versa they [Chartists] sell the asset if the price has been decreasing because they expect the price to drop further (Murphy, 1999). On the other hand, there are traders - they will be referred to as Fundamentalists in the following - expecting the asset price to drift off in the short-run, but to converge to its fundamental value in the long-run (Westerhoff, 2008). More precisely, Fundamentalists buy the asset if the current value is below its fundamental value because they assume the price will approach the fundamental value i.e. it will increase in this context. The asset will be sold by Fundamentalists if the asset price exceeds its fundamental value because the agents expect the price to drop and converge to its fundamental value (Moosa, 2000). Generally, it can be said that the asset price dynamics depend on how the agents decide to behave. If most of the agents in the market follow technical trading rules, its dynamics become less stable due to the extrapolation of trends by the Chartists. Vice versa, if the majority follows the fundamental approach, the asset price should usually range around its fundamental value and thus create a certain kind of stability in the particular market (Westerhoff, 2003). The model is built up on a basic price adjustment function stating the price adjustment process for the next period t+1 based on the current price in period t.

Pb 1 = Pî + а(^с'Чсд + <’ХД) + Yb The upper equation (the superscript 1 will become relevant and is explained later on) states that the asset price ofthe subsequent period [Pbi] evolves from the current asset price [Pj[1]] additional to the sum of the orders of the Chartists 0e'[1] multiplied with the percentage of technical traders Wtc'[1] in relation to all market participants and the orders ofthe Fundamentalists Df'[1] multiplied with the percentage of fundamental traders WtF'[1] in relation to all market participants (Wtc'[1] and WtF'[1] sum up to unity). This part of the equation can be referred to as the excess demand which, if positive, has an increasing effect on the asset price development while, if negative, has a decreasing impact on the asset price evolvement. The entire excess demand expression additionally is multiplied by a that can be understood as the price adjustment coefficient and expresses by which speed the price adjustment process takes place (Westerhoff, 2009). To stress that the model only represents a simplified version of real world financial markets a random, normally distributed [yt~N(0, σ[7])] variable yt with a mean of "0” and a standard deviation of "σΎ" is added to the price adjustment function (Westerhoff, 2008). The excess demand is highly dependent on the demand of both sorts of traders, Chartists and Fundamentalists. On the one hand, the demand of Chartists (D^’[1]) - following past price trends - can be expressed as:

Dct-[1] = KPl-PU)+r¡;·[1]

In this scenario Chartists receive a positive (buying) signal if the asset price in period t+1 exceeds the one in period t meaning Pt—i > Pl· . The price differential is additionally multiplied by a positive reaction parameter b that expresses the extent of following technical trading rules. The signal becomes negative (selling) (Westerhoff/Dieci, 2006;

Westerhoff, 2009). The added term rtc represents a random variable that tries to express the various possibilities of performing technical analysis (Murphy, 1999). According to Westerhoff/Dieci (2006), rtc'[1] follows a normal distribution process, meaning rtc'[1] is normally distributed with mean zero and standard deviation oc.

On the other hand, the demand of Fundamentalists (Df'[1]) who take advantage of mispriced assets can be formulated as:

All appearing formulas, if not stated differently, are taken from Westerhoff/ Dieci (2006) and Westerhoff (2008)

Df'[1] = с(# - Pf) + r*[1]

Thus, the Fundamentalists' demand is positive, meaning an asset purchase takes place, if the asset price Pf undercuts its fundamental (log-) value P[1], while, if the asset price exceeds its fundamental value, traders following fundamental analysis will have a negative demand which can be understood as selling the asset (Westerhoff/Dieci, 2006; Westerhoff, 2009). The term c in this case represents a positive reaction coefficient (Schmitt/Westerhoff, 2013). A random term rf'[1], which is also normally distributed [rF,[1]~W(0, σρ)], is added to express possible mistakes made by agents regarding the perception of the fundamental values (Westerhoff/Dieci, 2006). Fundamentalists buy the asset at a low price and sell if the price increases. Another important factor that determines the dynamics of financial markets is the particular proportion in the market the different agents occupy. To illustrate the weights Chartists and Fundamentalists represent in the market, the fitness/ attractiveness (denoted by A in the following) of respective strategies - technical or fundamental analysis - must be defined first: It is important to recognize that agents neither keep following the first chosen strategy nor always give their orders according to this strategy. Rather, they change their trading behaviour according to the strategies efficiency in the past (Hommes, 2001). At this point, it must be mentioned that besides following chart or fundamental analysis, a third option can be chosen - namely not trading at all, i.e. being inactive (Westerhoff/Dieci, 2006). For mathematical clarification purposes, the attractiveness of all three options will be formalized. While the fitness of following technical trading rules can be expressed by:

Act = ([exp[Pt] - exp[Pt_J)Dtc_2 + dAct_i

The fitness offundamental trading can be written as:

= ([exp[Pt] - exp[Pt-J)Df_2 + dAFt_1

To clarify the upper equations, the fitness of a strategy depends on the performance during the previous period. In this case, the orders from t-2 (Dt_2) are fulfilled at the price of period t-1 (Pt_i). The result - positive or negative profit - hinges on the asset price in the current period Pt.

The other impact factor d 0 <d < 1 represents a memory parameter and can be understood as the following: The larger d becomes, the stronger the particular attractiveness depends on the performance in the past. For instance, d=0, means that the attractiveness of a strategy matches current profits due to agents not remembering their past performances. If d=l, the attractiveness of a strategy can be understood as a total sum of all past profits (Westerhoff, 2008; Westerhoff/Dieci, 2006). Regarding the attractiveness of not giving any orders (Л°), it can be set to zero as inactiveness does not result in any profit (Westerhoff, 2008). After explaining the attractiveness of the various strategies, the percentage proportion of strategies in the market can be depicted in the following: According to Manski/McFadden (1981), the three relevant functions are illustrated following the proportions:

Traders following technical trading rules:

Abbildung in dieser eseprobe nicht enthalten

Traders performing fundamental analysis:

Abbildung in dieser eseprobe nicht enthalten

Traders being inactive:

Abbildung in dieser eseprobe nicht enthalten

The equations above state that with increasing attractiveness of a particular strategy [strategy stated in the numerator], the proportion of agents choosing this strategy increases, too. The parameter e incorporates the sensitivity into the formula with which agents choose the best option. With e increasing, more agents will choose the option with the highest attractiveness. If e = 0, the entirety of traders will be equally divided to all available strategies, meaning in this case every strategy will be chosen by - of the agents. While e = <x> can be interpreted as every single agent choosing the option involving the highest attractiveness (Westerhoff, 2008). Forthe sake ofclarification several charts illustrating the proportions of each strategy as well as log prices and returns will be added later on.

### 2.2. Extension of the basic Model to two relevant Markets

After explicating the mechanics of the model in the section above (chapter 2.1), the up- coming chapter will examine financial market dynamics with regard to two different relevant markets. Following Westerhoff/Dieci (2006), a second market will be introduced before a hypothetical transaction tax will be imposed in market 1. This second market explains the superscript "1" that is added to every term of the price adjustment function (of market 1) in section 2.1. Thus, the superscript "2" is added to the price adjustment function of market 2 and can be expressed as:

Abbildung in dieser eseprobe nicht enthalten

The upper equation can be interpreted the same way as before, only according to its affiliation to market 2.

Before continuing the process by applying a transaction tax to the second market (2) as well, the repercussions that come along with the introduction of a transaction tax in market 1 regarding the market dynamics will be depicted.

By introducing a second market, the available strategies agents are able to follow increase. Due to the opportunity of switching between the two markets, agents can now choose from five available trading strategies (Westerhoff and Dieci, 2006). While already mentioned strategies endure, Chartists and Fundamentalists can also give their orders in the second available market, too.

The formulas for technical trading:

Abbildung in dieser eseprobe nicht enthalten

and for fundamental trading:

Abbildung in dieser eseprobe nicht enthalten

are added. The upper equations state the orders of Chartists and Fundamentalists, while the superscript "2" ["l"for market 1 respectively (section 2.1)] indicates the market they are trading in. An adjustment of the price impact function is necessary as well, leading to:

Abbildung in dieser eseprobe nicht enthalten

The upper equation states the price adjustment process in market 2.

The equations representing the attractiveness of the particular strategies as well as the weights of traders (Wtc and Wf ) need to be adjusted to the new circumstances, as well (Westerhoff/Dieci, 2006). While a listing of the various attractiveness functions will be postponed to a later chapter (2.З.1.), the new equations displaying how the two sorts of traders divide themselves over both markets can be stated already:

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