رقابت بورس اوراق بهادار در یک مدل ساده از تعادل بازار سرمایه

This paper uses a simple model of mean-variance capital markets equilibrium with proportional transactions costs to analyze the competition of stock markets for investors. We assume that equity trading is costly and endogenize transactions costs as variables strategically influenced by stock exchanges. Among other things, the model predicts that increasing financial market correlation leads to a decrease of transaction costs, an increase in cross-border trading activity, and to a decrease in the home bias of international equity flows. These predictions are consistent with the recent evolution of international stock markets.

The objective of this paper is to analyze the competition between stock exchanges in the framework of asset pricing theory. We do this by considering a simple mean-variance capital market equilibrium model with transactions costs and by endogenizing the transactions costs as variables strategically influenced by stock exchanges. This perspective integrates insights from the asset pricing and the industrial organization literature and thus brings together two approaches to the study of stock exchanges that have evolved largely independently up to now. We use this framework to investigate the determinants of transactions costs and trading volume for competing stock exchanges. Starting in the mid-1980s with the London Stock Exchange, European stock exchanges began a process of liberalization, which led to more profit-oriented organizations and strategies across Europe, and ultimately to serious competition between European stock markets. With the advent of cross-listings of European firms on the NYSE and Nasdaq and the continuing debate of the optimal trading structure of the American exchanges, this competition went global in the 1990s.1 Up to now, the literature has analyzed competition between stock exchanges as competition for the listing of firms (prominent examples of this literature are Chemmanur and Fulghieri (2006), Foucault and Parlour (2004), and Huddart, Hughes, and Brunnermeier (1999)). This type of competition has indeed become more important since the 1990s, in particular for large firms (see Pagano, Röell, and Zechner, 2002). However, at least as important is stock exchange competition for investors. Transactions fees, market liquidity, disclosure rules, and the characteristics of the firms listed on the exchange are all important determinants of the attractiveness of a stock exchange to investors. Stock exchanges are therefore in principle subject to two-sided competition in the sense of Rochet and Tirole (2004): the more attractive it is for firms to list on the exchange, the more attractive it is for investors to trade on this exchange, and vice versa. As a first step towards a fuller analysis of such two-sided competition, the present paper analyzes stock exchange competition for investors, taking the listing decisions of firms as given. Interestingly, Table 1 shows that, at least until recently, the vast majority of listed firms around the globe has listed on a local stock exchange. In fact, in 2002 the only major European stock exchange with large foreign turnover was London. Table 1 also shows that while the share of foreign firms listed on some stock exchange can reach 35% of total listings in numbers (in Switzerland with 140 foreign listings out of 398), the total value of foreign share trading on all exchanges (except London) is negligible. Table 1. Value of shares traded and number of companies listed for selected stock exchanges Note: Data for 2002, main and parallel markets. Remaining percentages are investment funds. Source: World Federation of Exchanges. Total Value of Trading Number of Listed Comp. Domestic (%) Foreign (%) Domestic Foreign Euronext 98 1 1114 N.A. Frankfurt 92 8 715 219 Hong Kong 100 0 968 10 Milan 91 9 288 7 London 47 53 1890 382 Nasdaq 96 3 3268 381 NYSE 91 7 1894 472 Madrid 99 1 2986 29 Tokyo 99 0 2119 34 Zurich 97 2 258 140 Table options In line with the figures in Table 1, we therefore model stock exchanges as trading platforms for local assets and analyze their competition for investors who wish to diversify their portfolios across those assets. While our abstract model is a priori more general, it is particularly interesting to use it to investigate the determinants of international stock exchange competition for two reasons. First, global cross-border portfolio investment has increased substantially since the late 1980s.2 As documented by Tesar and Werner (1998) and the IMF's Coordinated Portfolio Investment Surveys (see in Appendix A), the percentage equity holdings of investors in domestic equity (the home bias) decreased on average from well above 90% in the late 1980s to below 70% in 2002. Second, almost all countries have witnessed a process of concentration of stock exchanges towards one national exchange, and sometimes (as in the case of Euronext) even a supranational exchange. Therefore, the trading of foreign equity has typically been channeled through the respective national exchanges, who have been forced to compete vigorously for this order flow. In our model, stock exchanges charge fees and commissions to profit from this trading. High fees benefit stock exchanges directly, but hurt them indirectly because they distort investors’ portfolio choices away from the assets traded on that exchange. The optimal fee size balances these two effects, just as in standard oligopoly theory. What is new in our work is that we explicitly derive the demand for stock exchange services, namely the intermediation of market transactions, in a fully-fledged capital markets model with proportional transactions costs.3 Because of the relative simplicity of the model, we obtain an explicit solution, which nevertheless is non-trivial and has some surprising features. One such feature is that in equilibrium those investors who in a world without transactions costs would reduce their exposure to an asset, can be net buyers of this asset. This result is surprising and, as we show, cannot happen in a model with only one single risky asset. In the context of international portfolio allocation, this means that the home bias of local investors may be reinforced by trading under transactions costs. However, as mentioned above, the recent experience in international capital markets has been a systematic erosion of the home bias. Our analysis allows to identify the conditions on the variance–covariance structure of asset returns and endowments that are consistent with this development. Under these conditions, we find that in the unique subgame-perfect Nash equilibrium of the competition game between stock exchanges, stronger market integration, as measured by an increase in the correlation of local asset payoffs, leads to a decrease in transactions costs. This effect mainly stems from the decreasing demand for international diversification by investors, which erodes foreign exchanges’ market power, and is consistent with the recent trend in Europe away from cross-country allocation strategies and towards industry-based allocation strategies.4 Similarly, we predict that stock exchanges of markets that are less well integrated with the rest of the world should have higher transactions costs, which is consistent with the international comparative data provided by Domowitz, Glenn, and Madhavan (2001). We further find that equilibrium fees depend negatively on exogenous trading costs (trading costs that cannot be directly controlled by the stock exchange). Hence, exchanges have an interest in setting rules and using technology that lower these costs. This is, of course, exactly what has happened in the last 10–20 years in stock exchanges around the world: exchanges have adopted automated trading mechanisms, improved clearing and settlement procedures, and implemented trading rules that reduce trading costs. This has made these exchanges more attractive and allowed them to reduce trading fees less than they would have otherwise been forced to.5 Our work also yields predictions on international equity flows. While an increase in international payoff correlations has a direct negative impact on trading volume because of reduced hedging demand from investors, it also has an indirect positive effect through reduced endogenous stock market fees. The model predicts that transactions costs adjust to accommodate the decreased hedging demand of investors, which in turn stimulates cross-border portfolio investment. As we show, this indirect effect dominates the direct effect, leading to an overall increase in trading volumes and to an erosion of the home bias, without, however, fully eliminating it. This has exactly been the trend in Europe since the 1990s: increasing stock market correlation together with increasing cross-border trading volumes has led to a reduction in the home bias. While this may also be due to factors outside our model, such as increased spillovers in real activity or increased stock market participation, our model is consistent with this observation. Two branches of the literature are related to this paper: general equilibrium models of asset pricing under transaction costs and models of exchange competition. As mentioned above, the latter literature mainly studies competition for the listing of firms or the trading of securities between different exchanges and thus has a different focus than our work. Relevant issues in that context are economies of scale in trading (Demsetz, 1968), liquidity effects (Pagano, 1989), transportation costs (Gehrig, 1998), economies of scope (Pirrong, 1999, and network externalities (Di Noia, 2001). Steil (2002) and Domowitz and Steil (2002) have argued that improvements in trading technology in the 1990s, most notably the advent of electronic trading, have facilitated and increased competition between stock exchanges, thus increasing entry and reducing transactions costs. Our work is consistent with this argument, but goes beyond it in at least two respects. First, as stock market transaction costs have a first-order effect on stock market trading, it is important to analyze this impact explicitly. We show that the mechanics of this impact are non-trivial, characterize them, and use the results to evaluate the incentives of stock exchanges to adjust transactions costs. An example of a prediction of our theory that demonstrates the need for a careful analysis is that decreasing transactions costs can lead to decreasing or increasing stock prices.6 Second, we consider other determinants of market activity and stock exchange competition beyond intermediation costs, such as market correlation, volatility, or the distribution of asset holdings. These factors are at least as important as cost factors and are particularly relevant for general equilibrium considerations. It is also worth noting that increased entry has not necessarily been a dominant factor in international stock market activity, as the opposite, namely stock exchange consolidation, has played an important role in several key markets (such as the creation of Euronext). In the asset pricing literature, a key contribution has been Vayanos’ (1998) mean-variance general equilibrium model of several risky assets with proportional transactions costs in continuous time. In his model, agents are born without assets, buy them when they are young, and sell them off gradually when getting older in order to finance consumption. Hence, at any point in time, there are two groups of agents ready to trade, one with no assets at all and the other with a full portfolio. This structure is not well suited to study questions such as ours, where investors with differently composed non-trivial portfolios want to rebalance their portfolios. By abstracting from life-cycle and similar questions, our simpler one-period model is more flexible and may also be useful as a work-horse for other applications. Models without life-cycle considerations up to now have mostly focused on settings with one risky asset and one riskless asset. Building on the continuous-time analyses of portfolio choice of Constantinides (1979), Constantinides (1986) has analyzed equilibrium under proportional transactions costs and finds that while the impact of transactions costs on trading behavior (characterized by a “no-trade region” in endowment space) can be substantial, the impact on asset returns is small, due to adjustments in dynamic trading strategies. Basak and Cuoco (1998) have analyzed equilibrium in a market in which one group of investors is excluded from trading the (one) risky asset, which can be viewed as the limiting case of infinite transactions costs. Recently, progress has been made in the study of portfolio problems with several risky assets (see, in particular, Liu, 2004), but this work does not analyze market equilibrium. Similarly, Dybvig (2005) analyzes a one-period mean-variance portfolio rebalancing problem with proportional transactions costs and obtains instructive explicit solutions. But like Liu (2004), he does not consider market equilibrium. The few papers that study markets with several assets under transactions costs typically assume “variable proportional costs”, i.e. transactions costs that are effectively quadratic in the quantity traded.7 This has the advantage that transactions costs are a second-order effect for small trades and thus that Constantinides’ no-trade region disappears. If one is interested in the impact of transactions costs on trading activity, the full first-order effect is, however, important, because transactions costs affect each traded unit equally. The rest of the paper is organized as follows: Section 2 sets out the model. Section 3 describes the equilibrium in the asset market and Section 4 derives the optimal behavior of stock exchanges. Section 5 delivers the main comparative statics results and discusses empirical evidence. Section 6 concludes. The appendix contains some details of a longer proof and its generalization to the case of more than two risky assets and investors. The appendix also contains a table with data on the international home bias.

This paper has analyzed the competition between stock exchanges under the premise that stock exchange fees constitute revenues for the exchanges and transactions costs for the market participants. Using a standard mean-variance capital market equilibrium model with transactions costs, we have thus endogenized transactions costs as variables strategically influenced by stock exchanges. Applied studies typically take transactions costs as exogenous and try to identify their impact on trading. In their empirical study, Domowitz and Steil (2002), for example, estimate that a decrease of 10% in trading costs yields an 8% increase in trading volume and a 1.5% decrease in the cost of capital to blue-chip listed companies. These estimates show how important the effects are that we identify in this paper, but also how important it is to understand their driving forces. The present paper contributes to this task by identifying fundamentals that drive transactions costs and trading volumes simultaneously, and by shedding light on their interaction. In principle, the framework that we have adopted in this paper allows us to study the impact of stock exchange competition on stock market activity quite generally. International portfolio investment is a particularly natural application of our model, as the vast majority of listed firms still is listed on a domestic stock exchange. Hence, the portfolio of firms listed on a domestic stock exchange corresponds largely to the national index, and as a consequence, international portfolio diversification occurs largely via the choice of different national exchanges. More generally, if stocks are not cross-listed, stocks listed on different stock exchanges are only imperfect substitutes for the investors’ portfolio problem, and the competition for investors between stock exchanges takes on an element of strategic complementarity. This type of competition also exists in contexts other than that of international portfolio flows, for example between exchanges specializing in different types of stock, such as the NYSE and the Nasdaq. In this case, the endowment differentials that drive trade in our model cannot be interpreted as international portfolio biases, but rather correspond to other, more conventional portfolio imbalances. The present paper has restricted attention to stock exchange competition for investors. This complements the existing literature that has focused on competition for firms, but still is incomplete. In fact, if stocks can be traded on several exchanges or platforms, stock exchange competition in principle takes the form of two-sided price competition, for the listing of firms on the one side and for the trading activity of investors on the other. This is an example of the more general phenomenon of two-sided markets discussed by Rochet and Tirole (2006), in which the success on one side of the market depends on that of the other and vice versa. Linking our work with the existing work on stock exchange competition for firms in the perspective of two-sided competition is a promising next step on the research agenda.