Optimal government policy in emerging financial markets

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Master’s Thesis

Optimal Government Policy in Emerging

Financial Markets

Author: Marc van Houdt

Student number: 6036996

Date of final version: August 29, 2015 Master’s programme: Econometrics

Specialisation: Financial Econometrics Supervisor: Prof. dr. J. Tuinstra Second reader: Dr. M.J. van der Leij

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Statement of Originality

This document is written by Student Marc van Houdt who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this docu-ment is original and that no sources other than those docu-mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Introduction

In recent years, financial markets have developed further. However, there still are many un-derdeveloped economies. These economies/markets are often referred to as emerging markets, since there is a large potential growth to be realised. Often the countries that correspond to these economies belong to the third world countries, and also have underdeveloped financial systems and there might be trade restrictions for foreign investors. In financial markets, in-vestors will always seek ways to make a profit. To accomplish this, inin-vestors are also active in emerging markets. Emerging markets in general have high volatility, but the expected re-turn is also high (Harvey, 1995). Since emerging market rere-turns are also not largely correlated to developed market returns, trading in these markets may be a good way of diversifying a portfolio that mainly consists of assets in developed markets (Harvey, 1995).

As increasing welfare to a country’s population is an important policy aspect for govern-ments, it is important to know which policy actions will increase or decrease economic growth. Different policies that have been used in the past include more/less openness to foreign invest-ment. An advantage in closing the economy for foreign investment is that indigenous investors are protected from foreign investors. A disadvantage is that this protective policy decreases foreign investments in the economy. It will be interesting to investigate which of these policies actually improves welfare of investors (the most). Therefore in this thesis I will study the effect of trade restrictions for foreign investors on emerging market investors.

In the past, many economies, countries and markets have been characterized as emerging. For example, O’Neill (2001) defined the BRIC countries (Brazil, Russia, India and China) be-cause these countries would surpass the G7 economies1by 2050 as the richest countries in the world. Other countries that were defined emerging in the past were for example the Asian Tigers (Singapore, Hong Kong, South Korea and Taiwan), these countries don’t fall under the emerging countries anymore since they have developed so much in the past years. BBVA Re-search (2015) has done reRe-search in the past years to identify the emerging countries in the world. Their methodology makes a difference in EAGLEs, countries that will contribute more

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to world growth than the average of G6 economies2in the next ten years, and Nest, countries contributing to world growth more than the average of non-G7 developed economies which have GDP of over $ 100 billion but fall below the EAGLEs threshold3. In 2015, BBVA defined 14 EAGLE countries and 16 Nest countries. It is interesting which policies are used by these countries to achieve this growth.

It is generally accepted that free trade increases efficiency in financial markets (Bhagwati, 2003), so it would seem that for long term growth this is the best policy. However, countries like the Asian Tigers have been able to become developed countries by using different govern-ment policies. For example, according to Frankel et al. (1996) in Singapore and Hong Kong openness to trade has provided a large part of GDP growth, while in South Korea and Taiwan the GDP growth was less based on openness to trade. This follows from the policies of the respective governments, as Singapore and Hong Kong were among the most free economies in the world and South Korea and Taiwan took a more protectionist approach. As both ap-proaches have obviously proved their use, it is interesting to look how economic growth has been pursued in the past.

In the 1990s, many countries adopted a new view about how to achieve economic growth. Williamson (1990) named this the Washington Consensus as in his opinion, this was the view of the United States government and the international financial institutions in Washington. He discusses ten topics, of which trade policy is one. The view on trade policy is that restric-tions on trade to protect domestic industries lead to costs for the domestic country. Many countries adopted this view of liberalization and this led to very positive growth perspectives. Mexico, as Krugman (1995) mentions, was a prime example for other countries as it changed from being a protectionist country to signing a free trade agreement with the United States in 1994. However, in December 1994 the Peso crisis hit and the once so positive economic outlooks disappeared. Krugman (1995) states that the Mexican crisis was ”an accident waiting to happen”, because the recommendations in the Washington Consensus were based more on positive expectations than on solid achievements. He also states that the ideas were not neces-sarily wrong but people, fueled by optimistic expectations, expected too much. This led to a speculative bubble that burst after the Peso crisis.

To model markets with possibilities for trade restrictions, different methods have been used in previous research. Tuinstra et al. (2014) investigate the welfare effect of trade restrictions and find scenarios in which it is optimal to have a positive import tariff. Henry (2000) finds that stock market liberalization leads private investment booms. With this liberalization it is meant that it becomes easier for foreigners to invest in the country that is liberalizing its stock market. Private investment booms are positively related to GDP growth, so Henry (2000) states that stock market liberalization drives GDP growth.

Historically, in economic modelling it was assumed that all agents could be described by rational representative agents. After the financial crisis of 2008, many have challenged this

2_{Due to its size, the United States is dropped from the benchmark.}

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idea of rationality of financial agents. As the prices of e.g. the S&P 500 fell with around fifty percent in 2008, it seems that the assets were previously overpriced. The behavioural finance literature explains this by showing that not all irrational investors can always be driven out of the market, see e.g. Barberis and Thaler (2003). When investors with irrational behaviour are active on a market, supply and demand mechanics can be distorted and deviations from the rational price can be seen. More recent behavioural finance research has been done by Avgouleas (2009) about the behavioural impact of regulations and Adam and Marcet (2011) and Adam et al. (2014) about the impact of subjective beliefs on booms and busts in the S&P 500 price-dividend ratio.

To investigate the dynamics of emerging markets, with a possibility for trade restrictions, in this thesis the heterogeneous agents model by Brock and Hommes (1998) will be used as framework to model interaction between emerging and developed market assets. These mod-els have also been used to model exchange rates, option prices and oil prices. In the model as proposed by Brock and Hommes (1998), every period agents have a choice between being fun-damentalist and chartist. Funfun-damentalists believe in mean-reversion of prices, so their belief of the price is the fundamental value (which would be obtained if all agents were rational). Chartists believe that the existing trend will continue. Heterogeneous agents models have been used to model stock prices, as e.g. Boswijk et al. (2007), Chiarella et al. (2014) and Lof (2014) have done. Westerhoff and Dieci (2006) have used a heterogeneous agents model using two speculative markets, where agents can trade on both markets, to investigate the effect of transaction taxes on price variability.

This thesis contributes to the literature in the following ways. First, I will expand on the model by Brock and Hommes (1998) to investigate two markets simultaneously, where one of the markets is an emerging market and the other is a developed market. On both markets, agents can choose between being fundamentalist or being chartist. The agents that are trading on the developed market can also trade on the emerging market, but I assume that agents in the emerging market cannot trade on the developed market. Second, I will also include a possibility for the government of the emerging market to impose a trade restriction for foreign traders. Third, the agents do not only form beliefs about prices, but also about dividends. Fourth, the analysis of different models leads to the result that a trade ban for foreigners leads to highest profits for emerging market investors. However, the profits in this scenario are decreasing, and optimal policy would be to switch to free trade in the long run.

The rest of this thesis will be structured as follows. In section 2, the heterogeneous agents model with its extensions will be described. In section 3, the dynamics of the different sys-tems will be analysed, and section 4 will conclude. Proofs and other results are found in the Appendices.

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Chapter 2

Modeling asset prices in developed and

emerging markets

In this chapter I will explain the model that is used to model the interaction between a devel-oped and an emerging market. In the first section the baseline model is introduced, whereafter restrictions on foreign investors in the emerging market are introduced.

2.1 Model without restrictions

In this thesis the model by Brock and Hommes (1998) will be expanded to incorporate mul-tiple assets, where I make a difference between assets in emerging markets and in developed markets.

Following an earlier expansion by Verhoeven (2014) to the model by Brock and Hommes (1998), I will denote the model in vector and matrix notation. Verhoeven (2014) has gener-alized the heterogeneous agents model to multiple risky assets, and I will build upon this to make a difference between markets.

As I consider k asset markets, the vectors of prices and dividends at time t will be given by

p_t= (p_1t, .., p_kt)

dt= (d1t, .., dkt).

Similar to Brock and Hommes, I will assume heterogeneous expectations of prices among in-vestors, but homogeneous beliefs about conditional variance. In the next sections I will de-scribe the model for the different markets, starting with rational expectations and then ex-tending to heterogeneous expectations.

2.1.1 Rational Expectations

As stated previously, let p_t be the k-dimensional vector of prices at time t and let d_t be a k-dimensional vector of stochastic dividends at time t. I assume that across the k markets, a

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riskless asset is perfectly elastically supplied with gross return R = 1 + r, where r is a constant return. All investors thus have access to the same riskless asset. At every time period t the different agents h choose the number of assets that they include in their portfolio, such that their wealth evolves as follows:

Wh,t+1= RWt+ z

0

ht(pt+1+ dt+1−Rpt). (2.1)

Here z_ht0 is a k-dimensional excess demand vector of the number of shares of each asset of an agent h at time t. Again following Verhoeven, a CARA-utility function is assumed for all agents, with constant absolute risk aversion a_h:

uh(W ) = −exp(−ahW ).

The optimal portfolio of shares at time t is defined by maximizing the expected CARA-utility of wealth at time t + 1,

max

zht

E(−exp(−ahWh,t+1)).

Ang (2014) showed that optimizing a CARA-utility function is equivalent to solving the fol-lowing myopic mean-variance problem:

max

zht

Eht(Wh,t+1−

ah

2V arht(Wh,t+1)).

By the definition of wealth in equation (2.1) this is equivalent to solving max zht z0ht[Eht(pt+1+ dt+1) − Rpt] − ah 2z 0 htV arht(pt+1+ dt+1)zht. (2.2)

In this model, I will assume constant and homogeneous beliefs about volatility of the risky assets across investors. As Verhoeven (2014) and Gaunersdorfer (2000) argue, if agents are updating their beliefs about conditional means, it makes sense that they update their beliefs about conditional variance as well. However, as Nelson and Foster (1995) have showed, it is much easier to estimate conditional variances than conditional means. According to this, the assumption of homogeneous beliefs about conditional variance across agents seems reason-able.

The framework by Verhoeven (2014) allows for possible correlations between the di ffer-ent risky assets in the following homogeneous variance-covariance matrix: Ωt = V arht(pt+1+

dt+1) =        σ_1,t2 ρ12,tσ1,tσ2,t ρ12,tσ1,tσ2,t σ2,t2       

. The resulting individual excess demand at time t now

equals

zht=

1

ah

Ω−_t1[Eht(pt+1+ dt+1) − Rpt]. (2.3)

Assume now that there exists an equilibrium between supply and demand of shares, and let

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k-dimensional vector of fractions of agents at the k different markets, that use strategy h at time

t. There is a vector of fractions, since these fractions are different on both markets because

of the absence of emerging market investors on the developed market. On both markets, the fractions sum to 1. Then equilibrium of supply and demand can be written as

H X h=1 1 ah Ω−_t1[E_ht(p_t+1+ d_t+1) − Rp_t] ◦ n_ht= s. (2.4) Following Brock and Hommes (1998), I will assume that risk aversion is constant across in-vestors, such that a_h= a, ∀h.

In this thesis I assume that the investors that trade on the developed market can also invest in the emerging market asset, while the investors on the emerging market can only trade in that market. This assumption is made to make a difference in the types of traders on both markets, and it seems realistic that investors in developed markets have easier access to other markets. From this point onwards I will assume that n = 2 for investors on the developed market and n = 1 for investors on the emerging market.

Rational expectations in the developed market

For the developed market I assume dividends to follow the martingale process:

d1t+1= d1t+ σξ1ξ1,t+1,

where d1t is the dividend for the risky asset in the developed market at time t, ξ1,t+1 is an independently and identically distributed standard normal random variable with E(ξ1,t) = 0 and V ar(ξ_1,t) = 1 and σ_ξ1is a parameter.

Brock and Hommes assume that agents have correct and homogeneous beliefs about div-idends. However, this assumption seems limiting since agents observe past dividends and might assume a trend in the dividend process. Therefore I will expand on Brock and Hommes (1998) by assuming that agents form expectations about dividends like they do about prices.

Under these assumptions, the equilibrium equation can be solved for the price of the asset in the developed market p1t at time t:

p1t= 1 R[ H X h=1 Eht(p1t+1+ d1t+t)n1,ht−aΩ1,ts]. (2.5) Here, Ω_1,t = (σ_1,t2 ρ12,tσ1,tσ2,t) is the upper line of the variance-covariance matrix Ωt. n1,htis the fraction of agents of type h at time t at market 1.

Under rational expectations, there would be only one type of agent, so E_ht(p_1t+ d_1t) =

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and dividends are constant leads to Ωt = Ω0. Then the previous equation simplifies to

p_1t= 1

R[Et(p1t+1+ d1t+1) − aΩ1,0s].

This equation typically has infinitely many solutions, but only one of them satisfies the transver-sality condition limt→∞E_Rtt = 0. This is the following solution:

p_1t∗ =d1t−aΩ1,0s

R − 1 . (2.6)

Let p∗_1tbe thefundamental solution for the risky asset in the developed market. For the case of s = 0 this reduces to the discounted expected dividend model.

Rational expectations in the emerging market

For the emerging market, I assume that dividends grow over time. This follows among others Bekaert and Harvey (2000). Bekaert and Harvey (2000) assume that dividend growth follows an AR(1) process and finds that this fits their data reasonably well. However, for computa-tional purposes I will use a simpler model, namely with a constant growth rate.

The dividend then follows the following process:

d2t+1= (1 + g)d2t+ σξ2ξ2t+1, for a parameter g, a parameter σξ2and for ξ2,t∼N (0, 1).

As for the developed market, we would like to have a notion of a fundamental solution for the emerging market. The equivalent of (2.5) in the developed market becomes the following in the emerging market:

p2t= 1 R[ H X h=1 Eht(p2t+1+ d2t+1)n2,ht−aΩ2,ts]. (2.7) Here, Ω2,t= (ρ12,tσ1,tσ2,t σ2,t2 ) is the bottom line of the variance-covariance matrix Ωt. Under

rational expectations, there would be only one type of agent, so Eht(p2t+ d2t) = Et(p2t+ d2t). Using this leads to:

p2t= 1

R[Et(p2t+1+ d2t+1) − aΩ2,0s].

This equation again typically has infinitely many solutions. As one step ahead dividends will be taken into account perfectly by rational agents, we can find a solution using the same steps as in the developed market:

p∗_2t=(1 + g)d2t−aΩ2,0s

R − 1 (2.8)

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s = 0 this reduces to the discounted expected dividend model.

2.1.2 Heterogeneous expectations

In this section I will consider boundedly rational agents, that have heterogeneous expecta-tions about future prices of risky assets. Following for example Brock and Hommes (1998), Menkhoff et al. (2009) and Ter Ellen and Zwinkels (2010), I assume two types of agents. The first type arefundamentalists. Fundamentalist agents have perfect knowledge about the

damental price, and believe that in the long run the price of an asset will return to this fun-damental price. The second type of agents are namedchartists. These agents believe that the

future price will be an extrapolation of past prices. They are thus trend following. As knowl-edge is needed about the fundamental price to be a fundamentalist, choosing this strategy comes at a cost.

I consider two markets, where the investors on the developed market can invest in both the developed and the emerging market asset. There are thus four types of investors on the developed market, since (following Verhoeven (2014)) they choose between being fundamen-talist and chartist on both markets. As I assume that investors in the emerging market can only invest in their own market asset, there are two types of investors in the emerging market. The total of types of investors is thus six.

An explanation of these assumptions is as follows. It is more difficult for investors in emerging markets to invest in foreign assets than for investors on developed markets. In a more developed economy there will be more demand for foreign assets, as investors there will in general look further than their own country to create a diversified portfolio. This demand will be provided by e.g. investment banks. In an emerging market, the economy will be less developed and there will be less opportunity to invest in foreign markets.

For the developed market investors, it might seem strange that investors would have a different type on different markets. However, investors are generally looking for foreign assets to either make more profit because of higher returns, or to further diversify their portfolio. It makes sense for individual investors to have an expert that gives them advice on their assets. It might be that they have different experts on the two markets, where these experts have different investment types.

I will now make assumptions about the beliefs of agents about future prices and dividends: Assumption 2.1The beliefs of agents about prices have the following form:

Eht:= fht=

f1h(p1,t−1, ..., p1,t−L)

f2h(p2,t−1, ..., p2,t−L) !

.

Assumption 2.2The beliefs of agents about dividends have the following form: Eht:= ght=

g1h(d1,t−1, ..., d1,t−L)

g2h(d2,t−1, ..., d2,t−L) !

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where fihand gih are autonomous functions that describe the beliefs of agent h about

respec-tively the price and dividend of asset i in period t + 1, based on past prices and dividends. Under these assumptions, the price equation can be written as follows:

p_t= 1 R[ H X h=1 (f_ht+ g_ht)nht−aΩts]. (2.9)

The system described above leads to six different types, with respect to the beliefs of agents about prices, distinguished in the model. Type FF are fundamentalists on both markets, type

FC are fundamentalist on the developed market and chartist on the emerging market, type CF

are chartist on the developed market and fundamentalist on the emerging market and type

CC are chartists on both markets. Additionally, type xF are fundamentalists on the emerging

market and type xC are chartist on the emerging market. These types do not trade on the developed market.

The strategies as followed by the agents are characterised as follows:

f_FFt= p∗_t+ α(p_t−1− p∗_t) f_FCt= p∗_t+ α1(p1t−1−p ∗ 1t) γ₂(p_2t−1−_p∗ 2t) ! f_CFt= p∗_t+ γ1(p1t−1−p ∗ 1t) α2(p2t−1−p2t∗ ) ! f_CCt= p∗_t+ γ(p_t−1− p∗_t) fxFt= p ∗ 2t+ α3(p2t−1−p ∗ 2t) fxCt= p ∗ 2t+ γ3(p2t−1−p ∗ 2t).

γ =diag(γ1, γ2) and γ3 here stands for the level of extrapolation by the chartist agents with

γj> 1 and α = diag(α1, α2), αj∈[0, 1] stands for the speed at which fundamentalists believe the

price will return to its fundamental value. The level of extrapolation and the speed of return to the fundamental value could differ between markets, but not between traders that are based in the same market. For the special cases of α_j = 0 the fundamentalists believe that the prices will return to the fundamental value immediately, and for αj = 1 the fundamentalists believe

that prices will remain constant.

I will assume that agents also form beliefs about future dividends. It makes sense to make a difference in some sort of fundamentalist strategy and a chartist strategy, and to make a difference across markets. As Bekaert and Harvey (2000) claim, there is evidence for growing dividends in emerging markets. However, this is not the case in developed markets. Therefore it seems reasonable that both fundamentalist and chartist agents assume a growing dividend in the emerging market, as this is suggested by economic theory. As fundamentalist agents hire experts, I assume that they form correct beliefs about the growth rate of dividends.

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fair that chartist agents, who believe in a trend in prices, also believe that a trend exists in dividends. In contrast, agents that are fundamentalist on the developed market don’t believe in a trend in dividends. These belief strategies are the following in formula form:

g_FFt= dt−1◦ 1 1 + g ! g_FCt= d_t−1◦ 1 γ4(d_d2t−1_2t−2) ! g_CFt= d_t−1◦ (γ5 d1t−1 d1t−2) (1 + g) ! g_CCt= d_t−1◦ (γ6 d1t−1 d1t−2) (γ6d_d2t−1_2t−2) ! gxFt= d2t−1∗(1 + g) gxCt= d2t−1∗( d2t−1 d2t−2 ) ∗ γ7.

In these equations γi represents the level of extrapolation of the trend. As stated in the text

before, an agent of e.g. type FF will have belief gFFtabout dividends.

2.1.3 Time-varying variance

As stated in section 2.1.1, I assume that agents have homogeneous beliefs about conditional variance. Following Verhoeven (2014), I will let the variance-covariance matrix depend on time. This is an expansion on Brock and Hommes, as they assume a fixed variance-covariance matrix over time. As stock market volatility changes over time, the assumption of time-varying variance is more realistic.

Now, I will make the following assumption about the beliefs of agents about conditional variance:

Assumption 2.3The beliefs of agents about conditional variance are of the following form: V arht(pt+ dt) := Ωt= (1 − λ)Ω0+ λVt−1.

In this equation, λ ∈ [0, 1] is the importance of last period’s variance for the beliefs of next periods variance. V_t−1is the estimated variance at period t−1. For the estimate of the variance-covariance matrix, I use an Exponentially Weighted Moving Average (EWMA), as this measure is commonly used in risk management. This results in

ut= δut−1+ (1 − δ)pt (2.10)

Vt= δVt−1+ (1 − δ)(pt− ut−1)(pt− ut−1)

0

. (2.11)

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weighted moving average of prices is based.

2.1.4 Evolutionary learning

One of the main strengths of the original model by Brock and Hommes is that agents observe the performance of the different strategies, and are able to switch between strategies. This phenomenon is namedevolutionary learning.

We first have to specify a performance measure. Brock and Hommes take the realized prof-its as performance measure, but by doing this they stimulate taking higher risks. Gaunersdor-fer et al. (2008) use therisk adjusted profits, this measure is also considered here. Using this

measure makes sense, since agents optimize over the mean and variance as well.

πht= z 0 ht−1(pt+ dt−Rpt−1) − a 2z 0 ht−1Ωt−1zht−1.

Additionally to this measure, there are certain costs involved with the different types. These costs can be thought of as costs to obtain expert advice, and can differ between markets and investors. In general, there will be no costs involved in being chartist, since it is assumed that past prices and dividends are publicly available. There is a cost in being fundamentalist, as agents have to hire experts. Following Brock and Hommes, a memory parameter η is also introduced, so past performance is also taken into account by investors. The performance measure then equals:

Uht= (1 − η)(πht−Ch) + ηUht−1.

The evolutionary learning works as follows. Agents choose a type for period t and later re-ceive information about the performance of all types in this period t. For period t + 1, agents again choose a type, but now this choice is based on the performance of all types in period t. Every period, on both markets the fraction of agents that choose type h is calculated using the following formula:

ni,ht= exp(βUht−1)/Ni,t,

where N_i,t is the total number of investors on market i, so N_i,t=

Hi

P

h=1

exp(βU_ht−1), where H = 4 in the developed market and H = 6 in the emerging market, and β is the intensity of choice meaning how quick investors tend to switch strategies. When this β goes to infinity, investors will choose the strategy with highest performance, while for β that goes to zero, investors will be indifferent and distribute themselves evenly among the strategies.

As is seen from the fact that U_ht−1is used for determining the fractions at time t, the choice of agents depends on performance in theprevious period. The choice is made at the start of

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2.1.5 Dynamical model

The equations as specified in the previous sections lead to the following demand functions for agent type h, h ∈{1,2,3,4} zht= 1 aΩ −₁ t [fht+ ght−Rpt]

and for the following demand functions for h ∈ {5, 6}:

zht=

1

aσ_2t2 [f2ht+ g2ht

−_Rp_2t_]. The price equations in (2.5) and (2.7) become the following:

p_t= 1 R[ H X h=1 (f_ht+ g_ht) ◦ nht−aΩts], (2.12)

where n_ht= (n_1,ht n_2,ht)0. This gives the dynamical system:

p∗₁=d1t−aΩ1,ts R − 1 p ∗ 2= (1 + g)d_2t−_aΩ_2,t_s R − 1 V_t= δV_t−1+ (1 − δ)(p_t− ut−1)(pt− ut−1) 0 ut = δut−1+ (1 − δ)pt n1,ht= exp(βUht−1)/N1,t h ∈ {1, .., 4} N1,t= 4 X h=1 exp(βUht−1) n2,ht= exp(βUht−1)/N2,t h ∈ {1, .., 6} N2,t= 6 X h=1 exp(βUht−1) d1t= d1t−1+ σξ1ξ1t d2t= (1 + g)d2t−1+ σξ2ξ2t With Ω_t= (1 − λ)Ω₀+ λV_t−1 Uht= (1 − η)(z 0 ht−1[pt+ dt−Rpt−1] − a 2z 0 ht−1[(1 − λ)Ω0+ λVt−2]zht−1−Ch) + ηUht−1

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f_FFt= p∗_t+ α(p_t−1− p∗_t) g_FFt= dt−1◦ 1 1 + g ! f_FCt= p∗_t+ α1(p1t−1−p ∗ 1t) γ2(p2t−1−p ∗ 2t) ! g_FCt= dt−1◦ 1 γ4(d_d2t−1_2t−2) ! f_CFt= p∗_t+ γ1(p1t−1−p ∗ 1t) α2(p2t−1−p ∗ 2t) ! g_CFt= dt−1◦ (γ5d_d1t−1_1t−2) (1 + g) ! f_CCt= p∗_t+ γ(p_t−1− p∗_t) g_CCt= dt−1◦ (γ6d_d1t−1_1t−2) (γ₆d2t−1 d2t−2) ! fxFt= p ∗ 2t+ α3(p2t−1−p ∗ 2t) gxFt= d2t−1(1 + g) f_xCt= p∗_2t+ γ3(p2t−1−p ∗ 2t) gxCt= d2t−1( d2t−1 d2t−2 ) ∗ γ7

2.2 Foreign investment restrictions

In this section I will propose a model with restrictions on foreign investments. In section 2.1 the investors from the developed market could invest in the emerging market without restrictions. However, due to government policy it could be that only a certain share of assets can be owned by foreigners. This has been the case in for example France, Sweden, India and Mexico (Eun and Janakiramanan, 1986), Brazil and South Korea (Bonser-Neal et al., 1990) and Thailand (Bailey and Jagtiani, 1994). Even in many OECD countries this is still the case (Golub, 2003).

In this section, I will first derive the restricted demand curves, and later derive the price equations in the restricted market.

2.2.1 Restricted demand curves

The restrictions that will be modeled will be for foreign investors on the emerging market. There will be both a maximum and a minimum restriction, i.e. there is a maximum amount that investors can go long or short in an asset. I will denote these values z2hand z2h. For com-putational purposes I will also model demand restrictions for the emerging market investors, however in this thesis I will set these restrictions to be respectively +∞ and −∞. The demand for the emerging market asset will then be the following for h ∈ {FF, FC, CF, CC, xF, xC}:

˜z2ht=                  z_2h if z_2ht< z_2h z2ht if z2h< z2ht< z2h z2h if z2h< z2h.

If the demand for asset 2 is between the lower and upper bound, the optimization problem in (2.2) remains unchanged. However, if one of the constraints is binding, the optimization

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problem changes. Let s be zero for simplicity from here on. The equation in (2.2) can be written as follows for the emerging market asset:

z2ht= 1

adet(Ω)(−ρ12σ1σ2[f1ht+ g1ht−Rp1t] + σ

2

2t[f2ht+ g2ht−Rp2t]). (2.13) When one of the restrictions is binding, the optimization function changes. Agents will now optimize the demand for the developed market asset, given the restricted demand for the emerging market asset. This results in the following:

z1ht(˜z2ht) = 1

aσ_1t2 (f1ht+ g1ht

−_Rp_1t−_aρ₁₂_σ_1t_σ_2t_˜z_2ht_). _(2.14) Now, there are three possible equilibrium situations for each investor h ∈ {FF, FC, CF, CC}. First, both restrictions could not be binding, second the first restriction could be binding or last the second restriction can be binding. Since the restrictions for the investors h ∈ {xF, xC} are never binding, there is only one option for these investors. To get a notion of equilibrium of supply and demand, we need to specify the demand given these restrictions. Let A ⊂ {FF, .., xF} be the subset of strategies for which in equilibrium z2ht< z2h for each h ∈ A, let B ⊂ {FF, .., xF} be the subset of strategies for which in equilibrium z2h < z2ht < z2h for each h ∈ B and let

C ⊂ {FF, .., xF} be the subset of strategies for which in equilibrium z2h < z2ht for each h ∈ C. These three sets A, B, C together form all possible situations i.e. A ∪ B ∪ C = {FF, .., xF} for all investors. This gives the equilibrium of supply and demand:

X h∈A z1(z2h) z2h ! ◦_n_ht₊X h∈B zht◦nht+ X h∈C z1(z2h) z2h ! ◦_n_ht_{= 0} _(2.15)

2.2.2 Price equations in restricted market

To derive the price equations, we need to solve (2.15). Proposition 2.1: Suppose that nA= P

h∈A

n2,ht, nB = P h∈B

n2,ht, nC = P h∈C

n2,ht. Then the equilibrium

prices that follow from (2.15) are: p_1t= 1 R(1 − ρ₁₂2 (nA+ nC)) [X h∈B (f_1ht+ g_1ht)n_1,ht+ (1 − ρ2₁₂)X h<B (f_1ht+ g_1ht)n_1,ht −_aρ₁₂_σ_1t_σ_2t_{(1 − ρ}2 12)(nAz2+ nCz2) − ρ12σ1tσ −₁ 2t (ρ12σ −₁ 1t σ2t[(nA+ nC) X h∈B (f1ht+ g1ht)n1,ht −_n_BX h<B (f_1ht+ g_1ht)n_1,ht] + a(1 − ρ₁₂2 )σ_2t2(n_Az2+ nCz2))] (2.16)

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and p_2t= 1 RnB [X h∈B (f_2ht+ g_2ht)n_2,ht−_ρ₁₂_σ−1 1t σ2t[(nA+ nC) X h∈B (f_1ht+ g_1ht)n_1ht −_n_BX h<B (f_1ht+ g_1htn_1,ht] + a(1 − ρ2₁₂)σ_2t2(n_Az₂+ n_Cz₂)] (2.17)

Proof : See Appendix A.

When the restrictions are not binding for any agent type, A∪C = ∅, and nA= nC = 0, nB= 1.

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Chapter 3

Analysis of interaction between

developed and emerging markets

In this chapter the analysis of the different models will be discussed. First, the results of the model without restrictions will be discussed and later the results of the restricted models will be discussed. There will also be a section about an investment tax for foreigners. Some further discussions about dividend beliefs and developed market size are found in Appendix B and C respectively.

3.1 Baseline model

In this section first the starting values of the different parameter values is discussed. Second, different results of the baseline model can be found.

3.1.1 Choice of parameter starting values

Some of the parameters that need to be chosen for the baseline model are straightforward, others need more explanation.

Stochastic dividends

As we are dealing with a baseline model, I choose σξ1and σξ2= 0, so the dividend process has no stochastic term.

Variance and correlation

I have chosen σ1to be 0.4 and σ2to be 0.6. The variance of the emerging market asset is higher than the variance of the developed market asset, following Harvey (1995). Also following Har-vey (1995), I have chosen ρ12to be -0.1, so that developed market investors see the emerging market as a good opportunity to diversify their asset portfolio.

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Costs

I have chosen the costs in the following way. For developed market investors, it costs 1 to be fundamentalist on a market. The investors that are fundamentalist on both markets thus have a total cost of 2. Now for emerging market investors, I have chosen the cost to be funda-mentalist as 1/2. This comes from the assumption that emerging market investors have better knowledge about their own market than foreign investors have.

Investor beliefs

A number of important parameters are αi, i ∈ {1, 2, 3} and γi, i ∈ {1, .., 7}, since these parameters

compose the investors beliefs about future prices. I choose γ₂at 1.6, higher than γ₁at 1.2, since

γ2 is used for the beliefs about the emerging market asset price, and the emerging market asset has higher variance than the developed market asset. I choose α₁, α₂, α₃ = 0.1, so all fundamentalist investors have the same level of naivity.

The investors also form expectations about future dividends, with parameters γ4 to γ7. I choose these parameters to equal 1, so beliefs about dividends are linear extrapolations of the past dividends. As there is a constant trend in the dividends in the case with deterministic dividends (1 in the developed market and (1+g) in the emerging market), the beliefs about dividends are thus the same for all agents.

Other parameter values

I have chosen λ, η, s = 0 in the baseline model, β = 3, r = 0.025 and δ = 0.98.

Summarizing, the following starting values for the input parameters are used in the base-line model: β =3, λ =0, δ =0,98, r =0.025, η =0, σξ1 = σξ2 = 0, σ1=0.4, σ2= 0.6, ρ12=-0.1, cFF = 2, c_FC= c_CF = 1, c_CC = 0, c_xF= 1/2, c_xC=0, g = 0.005, γ₁= 1.2, γ₂= γ₃= 1.6, α₁= α₂= α₃= 0.1, γ4= γ5= γ6= γ7=1 and s = 0. Some of these variables will be changed in later sections.

3.1.2 Results of the baseline model

First, the prices of the assets are presented and later other interesting variables will be dis-cussed. In all figures, results are plotted for t = 200 until 300, to give the system enough time to start up.

In figure 3.1a, p1represents the price of the developed market asset and p2represents the price of the emerging market asset. It can be seen that the emerging market fundamental price is increasing across time. This makes sense, since only the expectation about the dividend one period ahead is used in the calculation of the fundamental price. Further, it can be seen that in the developed market, the price stays steady (but not constant) below the fundamental price.

In figure 3.1b, the price differences from the fundamental price can be found. It can be seen that in the developed market, the price stays steady at around 0.3 below the fundamental price. In the emerging market however, the difference between the price and the fundamental price is higher than in the developed market and is changing. About every 4 periods, the price

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(a) Prices of both assets (b) Differences with the fundamental

Figure 3.1: Prices and price differences of both assets

drops to little over a half below the fundamental value, and rises towards the fundamental value afterwards.

(a) Fractions on the developed market (b) Fractions on the emerging market

Figure 3.2: Fractions of investors for both markets

On both markets, there is no investor type that forces the other type out of the market, but the chartist investors clearly dominate the developed market. From figure 3.1a this makes sense, as a difference with the fundamental price persists over time. On the emerging market there are frequent fluctuations in the fractions, where the fraction of fundamentalists is substantially higher than in the developed market. This makes sense from figure 3.1b, since the price rises towards the fundamental price every four periods.

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(a) Investor background on emerging market (b) Fractions of indigenous investors

It can be seen in figure 3.3a that during the entire considered time period, more than seventy percent of the investors on the emerging market are indigenous investors. About every seven periods, most of the foreign investors retract from the emerging market. In figure 3.3b, it is shown that the emerging market investors behave in a similar manner to the developed market investors. The fraction of fundamentalists is higher than for the developed market investors, this will probably be caused by lower costs to be fundamentalist.

(a) Wealth of developed market investors (b) Wealth of emerging market investors

Figure 3.4: Time series of profits

In figure 3.4, the development of wealth is shown for both markets. W1 corresponds to the investors that are fundamentalist on both markets, W₂ to fundamentalist on the developed market and chartist on the emerging market, W3 to chartist on the developed market and

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fundamentalist on the emerging market and W4 to chartist on both markets. It is seen in figure 3.4a that the investors that are fundamentalist on the emerging market in general make a profit, while the chartist investors make a loss. As W₃lies above W₂, the profits that are made on the emerging market exceed the profits that are made on the developed market. Intuitively it then makes sense that the investors that are chartist on both markets incur the heaviest loss. Of the emerging market investors, W5corresponds to the fundamentalist investors and W6 to the chartist investors. In general, for almost the entire period the fundamentalist investors make more profit than the chartist investors, so it is clear why the fraction of fundamental-ist investors is higher than the fraction of chartfundamental-ist investors. However, every four periods the chartists make more profit than the fundamentalistsis. The periods where the wealth of chartists is higher explain the frequent changes in fractions.

(a) Total wealth of developed market investors (b) Total wealth of emerging market investors

Figure 3.5: Time series of total wealth

The weighted total wealth of investors from both markets from t = 200 onwards is depicted in figure 3.5. It can be seen that on both markets, steady profits are made during the considered time period. In the considered time period, the emerging market investors make a profit of about 11, while the developed market investors make a profit of about 9.

In figure 3.6, the positions that the different investors take are shown. It can be seen that the investors that are fundamentalist take a long position on the respective markets and vice versa. Concluding, the fundamentalists thus take long positions and make a profit, but there still is a higher fraction of chartists on the developed market. This is possible because the fundamentalists will take larger positions when p1is further from p

∗

1and thus make a profit. One would expect this to lead to prices closer to the fundamental price. However, the profits that the fundamentalists make are not enough to convince the chartists to switch their investor type.

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(a) Positions in the developed market asset (b) Positions in the emerging market asset

Figure 3.6: Time series of positions

(a) Volatility and trade volume of the developed market asset

(b) Volatility and trade volume of the emerging market asset

Figure 3.7: Time series of volatilities and trade volumes

volatility on the emerging market is higher than on the developed market. The trade volumes indicate that there is also more trade on the emerging market. The trade volumes show that there never is zero trade, so there are always investors who are willing to buy and sell the assets.

3.1.3 Sensitivity to parameter changes

The results that were presented in the previous section depend on the parameter values that were chosen. In this section the effect of a change in the parameters β and η will be discussed.

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β

In the baseline model, β = 3 is chosen. As the parameter β influences if agents will switch their strategy, a different value of this parameter could lead to different results. Therefore figure 3.8a shows a bifurcation diagram, where the difference between the price and the fundamental price of the developed market asset has been evaluated after 1000 periods for different values of β. It can be seen that for low values of β, the system is stable. A low value of β corresponds to agents that are reluctant to change strategies. If β becomes higher than about 1.6, the price of the first asset decreases with β and becomes unstable. As agents will be less reluctant to switch strategies, there will be fractions of both fundamentalists and chartists present after 1000 periods. If β is chosen higher than 3.7, the system is still alternating between prices and is not yet stable. The higher β is chosen, the higher the instability in the system. What is clear from the graph is that a different value for β would lead to different results only if it would be chosen outside the region β ∈ (1.6, 3.7).

(a) Bifurcation diagram of developed market asset (b) Bifurcation diagram of emerging market asset

Figure 3.8: Bifurcation diagram for the price differences with the fundamental price In figure 3.8b the bifurcation diagram is shown for the price differences with the fundamental price for the emerging market asset. The figure shows that in the long run, the price will be close to (and below) the fundamental price for all values of β. The chosen value of β therefore seams reasonable.

η

In the baseline model, η is chosen to be zero. As η is the memory parameter of past profits, it could be that a positive value of η changes the way in which agents switch strategies and therefore it could lead to different results.

In figure 3.9, the prices of both assets are shown for η = 0.1 and 0.9. There seems to be more fluctuation on the emerging market and there is no visible difference in the developed market. In figure 3.10, the fractions for both markets are shown for η = 0.1. There is also

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slightly more flucuation in the fractions for the emerging market, the minimum amount of fundamentalists drops to under 0.1.

(a) Prices of both assets with η = 0.1

(b) Prices of both assets with η = 0.9

Figure 3.9: Prices and price differences of both assets for two values of η

Figure 3.9b shows that when η = 0.9, the patterns in the fluctuations look the same, however both prices are lower than before. It seems that if the previous period performance is less important to investors, the prices become lower. Since the patterns in both prices and fractions remain the same, there are no large differences in results expected with a different choice for the parameter value of η.

(a) Fractions for developed market asset (b) Fractions for emerging market asset

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Outside supply of shares

In the baseline model, s is chosen to be zero. However, it could be that the results are different for other values of s. The figures below show the prices for s = (0.1 0.1)’ and for s = (0.2 0.1)’.

(a) Prices with s = (0.1 0.1)’ (b) Differences with fundamental prices

Figure 3.11: Prices and differences with s = (0.1 0.1)’

It can be seen that, when s = (0.1 0.1)’, the fundamental prices both lie lower than before, this makes sense from equations (2.6) and (2.8). The dynamics of the prices however do not change from the scenario with s = 0. The following figure shows that when s = (0.2 0.1)’, the price of the developed market asset not only lies lower, but there is also more volatility. Still the differences with the baseline are marginal, so no different results will be expected with other values of s.

(a) Prices with s = (0.2 0.1)’ (b) Differences with fundamental prices

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Heterogeneous beliefs

The belief parameters γ1= 1.2, γ2= γ3= 1.6 make up an important part of the model. In this section I will reverse these values, so γ₁ = 1.6, γ₂= γ₃ = 1.2. Now the chartist investors on the developed market are more aggressive than on the emerging market and this might lead to higher volatility on the market.

(a) Prices for both assets (b) Differences with fundamental prices

Figure 3.13: Prices and differences with different values for γ1, γ2and γ3.

From figure 3.13 it indeed shows that the volatility on the emerging market is substantially reduced by the lower value for γ2 and γ3. On the developed market, the price lies at the fundamental for most of the time, but once it deviates the difference becomes larger for a number of periods. Afterwards it goes back to the fundamental price. Summarizing, the higher the level of trend extrapolation, the higher volatility becomes in the market.

Time-varying variance

The parameter λ is the importance of last period’s variance for the beliefs of next period’s variance. In this section the prices are shown for λ = 0.5. Comparing figure 3.14 to figure 3.1, the differences with the fundamental are slightly lower for a higher value of λ. However, the patterns in the price fluctuations are still the same as in the baseline model.

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(a) Prices for both assets (b) Differences with fundamental prices

Figure 3.14: Prices and differences with λ = 0.5

3.2 Restrictions for foreign investors

In this section the results of the model with restrictions for developed market investors are shown. The parameter values that are used are the same as in the baseline model, but restric-tions are introduced for foreign investors on the emerging market. I will first introduce the restrictions zh = -1 and zh = 1 for h ∈ {FF, .., CC} and later introduce an investment ban for

foreign investors. In this section, all restrictions will be equal for all foreign investors h, so from now onwards we will use z and z for the restrictions.

3.2.1 Long and Short restriction

From figure 3.15a there are multiple obvious differences with the prices without restrictions in figure 3.1a. First, the price of the developed market asset now lies above the fundamental price. Second, the price of the emerging market asset stays closer to the fundamental price.

In the developed market, the price now varies more and it comes close to the fundamental price on multiple occasions. It makes sense that the price now is higher than without restric-tions, since limited investing possibilities in the emerging market leads to a higher demand in the developed market.

Figure 3.15b shows that the restrictions on the emerging market lead to smaller deviations from the fundamental price, but there is no clear difference in the frequency of price drops.

Comparing figure 3.16a with figure 3.2a, there are more fundamentalists on the developed market in the restricted case and the change in fractions is not as predictable as in the unre-stricted case. On the emerging market, there still are frequent changes, but there seem to be more chartists than fundamentalists.

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the model with restrictions. In the unrestricted case, the fraction of foreign investors never came above 30 percent, while this does happen multiple times in the restricted case. This might seem counterintuitive, but since the restrictions are per investor and not for all foreign investors together, it is possible that a higher fraction of investors is active in the emerging market. Combining figure 3.17a and figure 3.20b, the total investments by foreign investors on the emerging market decrease. Figure 3.17b shows that the fractions of the indigenous investors are changing more frequently, but the fundamentalists still seem to have the upper hand.

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(a) Profit of developed market investors (b) Profit of emerging market investors

Figure 3.18: Time series of profit

clear which investor type makes the most profit. It is also not clear which investor type makes the least profit. On the emerging market, the profits are now closer to zero for both the funda-mentalists and the chartists. The fundafunda-mentalists still earn higher profits than the chartists.

The total wealth of the different investors is found in figure 3.19. The wealth of both de-veloped and emerging market investors is increasing, but there now are a number of periods where the investors make a (small) loss. Also, in the unrestricted model the emerging market investors made profits of around 11 in the considered time period. This has dropped signif-icantly to around 2.5. This suggests that the restrictions of z = -1 and z = 1 make it more difficult for the emerging market investors to earn a profit.

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As seen in figure 3.20, the positions of the developed market investors are now reversed. In the unrestricted case, the fundamentalists where taking long positions in the developed market asset, while they are now taking short positions. The same holds for the chartists, they were taking short positions and are now taking long positions. This corresponds to the price as seen in figure 3.8a, it makes sense that fundamentalists take short positions, as they believe that next period’s price will be lower.

In the emerging market, it is clear that the chartists take a short position and the funda-mentalists take a long position. An interesting difference with the unrestricted case is that not only the restricted investors have smaller positions, but also the unrestricted investors take

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smaller positions than in the unrestricted case. This is undoubtedly part of the reason why the emerging market investors make a smaller profit than in the unrestricted case.

The figure above shows the volatilities and trade volumes for both markets. Comparing figure 3.21a to 3.7a, we see that the volatility on the developed market went up after restrictions were introduced. When we compare figure 3.21b to 3.7b, we see lower volatilities and lower trade volumes. As we have seen in figure 3.20, this corresponds with the smaller positions that all investors take in the restricted case. However, an important difference in figure 3.21b with respect to figure 3.7b is that the minimum trade volume lies higher in the restricted case. It therefore would be easier to buy or sell the asset, so liquidity is higher in the restricted market. Figure 3.22 makes a comparison of total wealth, earned from t= 200 onwards. It is clear to see that the total profit of all investors is higher when there are no trade restrictions.

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(a) Total wealth without restrictions (b) Total wealth in restricted case

3.2.2 Investment ban for foreign investors

In this section, the foreign investors are completely restricted from investing in the emerging market. The restrictions are thus zh= zh= 0 for h ∈ {FF, .., CC}.

Figure 3.23 shows the prices, and the differences from the fundamental. It is interesting that there seems to be a trend in the deviation from the fundamental price of the emerging market asset. Especially from figure 3.23b, it seems that this deviation converges to around 0.5. This might be positive for the emerging market government, as steady price growth is desirable. However, at first there are large price fluctuations. Also interesting is that the price of the

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developed market asset is below the fundamental price again.

While figure 3.24a shows that the fractions on the developed market alternate for the entire considered period, figure 3.24b shows that the emerging market seems to go to an equilibrium where all investors are fundamentalist. This makes sense as in figure 3.23a the price kept going towards the fundamental price.

Figure 3.25a shows that, as expected, the fraction of indigenous investors on the emerging market is one. Therefore figure 3.25b is the same as figure 3.24b.

As expected, figure 3.26a shows that both fundamentalist types have the same wealth and both chartist types also have the same wealth. On the emerging market, it seems that the profit

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(a) Profit of developed market investors (b) Profit of emerging market investors

Figure 3.26: Time series of profit

goes to zero in the long run.

Figure 3.27a shows that the developed market make steady profits during the entire consid-ered period. Interestingly, these profits lie higher than in the unrestricted scenario. This result comes as a surprise, as the investors could also take these positions in the unrestricted sce-nario. However, in Appendix D the results of a simulation over 100 different realizations of the stochastic dividend process are shown. When comparing the average profits from the un-restricted scenario and the trade ban scenario, the profits for developed market investors are higher when they are not restricted.

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profits decrease. Since we have seen in figure 3.26b that emerging market profits go to zero, the case where foreign investors are banned from the market seems to only work for a limited period of time.

In figure 3.28a we see that the fundamentalists take a long position and the chartists take a short position in both markets. All investors except the chartists on the developed market take larger absolute positions than in the other cases.

Figure 3.29 shows the same as figure 3.28, namely that the trading volumes and volatilities on both markets are significantly higher than in the other two cases. However, the trade volume

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on the emerging market does become very small at some points in time. At those moments, the market therefore is not as liquid as the restricted market.

3.2.3 Optimal level of restrictions?

In the sections before three cases have been considered, namely one case without restrictions, one case with z = -1, z =1 and one case with z = z = 0.

There are many ways in which a government could determine which policy is optimal, of which one is maximizing the domestic investors profit. If we take into account the previously considered cases, the one that maximizes domestic investors profit the most over the consid-ered time period is the case where all foreign investors are banned from the emerging market. However, it seems that this policy will only work for a limited time. Therefore the second best case, namely the case without restrictions, could also be implemented after a period of foreign investment bans.

So far we have considered only three cases. In the table below, the values of the total profit made by emerging market investors during the considered time period is shown for different values of z and z.

z z Profit Emerging Market

-30 1 3.039 -1.5 1 3.039 -1.4 1 3.039 -1.3 1 3.039 -1.2 1 2.625 -1.1 1 2.625 -1 1 2.656 -0.9 1 2.538 -0.8 1 0.832 -0.7 1 0.437 -0.6 1 -0.389 -0.5 1 -1.350

(a) Varying minimum restrictions

z z Profit Emerging Market

-1 30 20.183 -1 1.5 6.422 -1 1.4 3.314 -1 1.3 2.477 -1 1.2 2.301 -1 1.1 3.238 -1 1 2.656 -1 0.9 1.164 -1 0.8 0.222 -1 0.7 -0.742 -1 0.6 -1.013 -1 0.5 -1.076

(b) Varying maximum restrictions

Table 3.1: Emerging market profit for different values of restrictions

In table 3.1, total emerging market profit is shown, subject to restrictions. In 3.1a, z = 1 and

z is shown for -0.5 to -1.5. In 3.1b, z = -1 and z is shown for 0.5 to 1.5. Both tables show

that more restricted markets will in general lead to smaller profits for the emerging market investors.

Considering table 3.1, the emerging market government has no trigger to set investment restrictions for foreign investors. However, we know from figure 3.23b that a total invest-ment ban for foreigners does lead to significantly higher profits for emerging market investors. Therefore, to optimize domestic investor profit the emerging market government should either put a total investment ban in place or refrain from any investment restrictions.

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be to have a normal behaving asset price. A volatile price in general has a positive effect on investor welfare (Newbery et al., 1990), but not all citizens gain from this. Many people think that central banks should stimulate price stability (Benigno and Benigno, 2003), so this is another policy that might be pursued by the government. Looking at figures 3.1b, 3.10b and 3.18b, the case with the most stable price seems to be the case with the long and short restrictions.

An important property of asset markets is the liquidity. Government policy could therefore focus on creating the most liquid asset market possible. If we compare figures 3.7b, 3.17b and 3.25b, the trade volume is highest when the foreign investors are banned from the emerging market. However, the restricted market has the highest minimum trade volume over time. It would therefore be easier to buy or sell assets at those moments in time on the restricted market. The restricted market is therefore the most liquid market.

3.3 Stochastic dividends

In this section I will relax the assumption that σξ1 and σξ2are zero, and I will now set both at 0.005. Now not only will the fundamental prices fluctuate through time by the stochastic part, but also the beliefs that investors form about dividends will have impact on the prices.

Taking a different approach than in the previous section, I will now compare relevant fig-ures for the cases without foreign investment restrictions and with either restrictions of z = -1 and z = 1 or z = z = 0.

In this section results are shown for a specific realization of the stochastic dividend process. However, it could be that this realization is atypical. Therefore Appendix D shows results of a simulation over 100 of these realizations.

3.3.1 Prices for three scenarios

The prices of both assets in the different cases are shown in figure 3.30. There are a number of interesting differences with the previous sections. First, the stochastic term in the dividends makes the fundamental prices fluctuate in a more random manner. This is also reflected in the prices, it can be seen from all three figures 3.30a to (c) that during the considered time period the price of the developed market asset both becomes higher and lower than the fun-damental price. The same holds for the emerging market asset in figure 3.30a and b. Second, in figure 3.30b it can be seen that now the price of the emerging market asset lies above the fundamental a number of times during the considered time period. In all the cases where this happens, it seems that a speculative bubble is created. The prices build up for a short period and afterwards return to the fundamental.

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(a) Prices of both assets with-out restrictions

(b) Prices of both assets with restrictions

(c) Prices of both assets with foreign trade ban

Figure 3.30: Prices and fundamental prices of both assets

3.3.2 Profits for three scenarios

The total profits for the emerging market can be seen in figure 3.31, and the total profits for all investors in figure 3.32. As in the case without stochastic dividends, the total profit for emerging market investors is highest when all foreign investors are banned from the emerging market. The profits are more than twice as high as in the unrestricted case. In the restricted case the emerging market investors make a loss, compared to profits of over 50 in the unre-stricted case and over 100 in the case with a trade ban. There is thus a strong trigger for the emerging market government to put a trade ban in place.

(a) Total profits without re-strictions

(b) Total profits with restric-tions

(c) Total profits with foreign trade ban

Figure 3.31: Total profits of emerging market investors

From figure 3.32 it shows that for all investors together, the investment ban is optimal for profits.

3.3.3 Liquidity for three scenarios

To assess the liquidity in the emerging market, we again look at the trading volume in the three cases. The trade volume, along with the volatility is found in figure 3.33.

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(a) Total profits without re-strictions

(b) Total profits with restric-tions

(c) Total profits with foreign trade ban

Figure 3.32: Total profits

(a) Trading volume without re-strictions

(b) Trading volume with re-strictions

(c) Trading volume with for-eign trade ban

Figure 3.33: Trading volume of the emerging market asset

The trade volumes all lie substantially above the trade volumes in the case with a deterministic dividend process. It is however not clear which policy is best for liquidity. In the unrestricted case the peaks are higher than in the scenario with an investment ban, but there are also numerous periods with trade volumes close to zero. Since this does not happen in the case with the investment ban, the market seems to be more liquid when a foreign investment ban is in place.

3.4 Taxes on foreign investors

The emerging market government could also restrict the foreign investors by setting invest-ment taxes for foreign investors. This section shows a figure with total profits in this scenario, depending on the height of the tax.

In the figure, the purple line is the total profit of developed market investors in the consid-ered time period t = 200 to t = 300, depending on the tax level for foreign investors. The blue line is the total profit of emerging market investors, the orange line the total profit of emerg-ing market investors plus the collected taxes and the grey line is the total profit of all investors

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0 5 10 15 20 25 -0,3-0,2-0,1 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 Pr o fi t

Tax for foreign investors

Emerging Market Profit Including Taxes Total Profit Including Taxes

Profit Emerging Market Investors

Profit Developed Market Investors

Figure 3.34: Profits depending on the tax level

plus the collected taxes. It can be seen that a tax for foreign investors of 0.2 is optimal for emerging market profit (including collected taxes). The total profit including taxes is highest when the emerging market government sets a negative investment tax for foreigners, so the whole market would be better off when the government would support foreigners investing in its asset market. Emerging market profit (including taxes) however is highest when the tax level is 0.2. Since this situation is not optimal for total profits, this might lead to political issues between the two countries.

Optimal government policy in emerging financial markets

Master’s Thesis