The Common Lender Effect : Are Banking Centers Crisis Carriers?

Transcription

1 The Common Lender Effect : Are Banking Centers Crisis Carriers? May 1, 008 Saranwut Takapong Economics Undergraduate Stanford University Stanford, CA saranwut@stanford.edu Under the direction of Prof. John B. Taylor ABSTRACT During the late 0 th and the beginning of 1 st century, a number of emerging countries, which depended on external financing, experienced a series of financial crises. The common lender effect, first proposed by Kaminsky and Reinhart (1999), asserts that a country that shares the same lender as a crisis-stricken country is more likely to also experience a financial crisis. This study adds to the literature of the common lender effect by investigating if the effect is operational despite a lack of correlation between economic fundamentals of the affected countries. The theoretical section of this paper finds that a financial shock abroad can induce investors to decrease their exposure in another country despite the lack of fundamental correlation between the two countries. By improving upon current methods proposed in Van Rijckeghem and Weder (003) and Caramazza et al. (004), the empirical section addresses a possible bias from endogeneity problem and provides empirical evidence in support of the common lender effect. Keywords: Financial Crisis, Crisis Transmission, Debt Financing Acknowledgement: I am immensely grateful to a remarkable group of people: Prof. John B. Taylor for providing me the inspiration and heartfelt support to pursue advanced studies in Economics, and, in particular, his thoughtful comments and advice on this paper. Prof. Geoffrey Rothwell for his support and commitment. Prof. Robert Hall for his helpful advice throughout my study at Stanford. Khanh Do for helping me articulate my ideas and polish this paper. And above all, my family for their incessant love and support.

2 Section I The Common Lender Effect and Financial Crisis Transmission: An Introduction The miraculous economic growth of developing countries was significantly interrupted when a wave of currency and financial crises swept the emerging market countries the Mexican crisis in 1995, the Asian crisis in 1997, the Russian crisis in 1998, and financial crises in Turkey and South America at the beginning of the 1 st century. Some of these crises crossed national borders, creating disturbances in international financial markets and the financial sectors of developing countries. After the outbreak of the crises, most of the countries affected experienced sharp currency devaluation, stock market slumps, and capital outflows. However, the magnitude of the repercussions varied among countries, with some proven to be more vulnerable to external shocks than others. Over the last 0 years, a number of economic studies have attempted to explain and understand how a financial crisis arises and spreads. While the majority of the earlier research focused on trade links among countries, more recent ones have focused on financial links among countries. Late 0 th century researchers argued that trade links among countries contribute to the propagation of financial crises across borders. Frankel and Rose (1996), Eichengreen et al. (1996), and Glick and Rose (1999) assert that countries may suffer from a crisis in another country due to the income effect, wherein a crisis country reduces its imports from its trading partners. In addition, the devaluation of the crisis country s currency increases the price competitiveness of the crisis country and suppresses the price competitiveness of other countries. As a result, on the international market, the crisis country gains competitiveness at the expense of its competitors. Eichengreen et al. (003) found that the probability a country experiencing a crisis increases if the country is a major trading partner with a crisis country. Likewise,

3 Kaminsky and Reinhart (000) reveal that a country is more likely to experience a crisis if its exports and target markets are the same as those of a crisis country. Although earlier findings indicated that trade linkages help promulgate crises among countries, the absence of these linkages among the affected countries in later crises, such as Thailand and Indonesia during the Asian crisis, has led economists to focus on financial linkage as a channel of contagion. Recent literature suggests that financial crises can be transmitted through financial linkages in the international financial market. However, in one of the earliest works on financial linkage as a channel of financial turmoil in developing countries, Krugman (1979) argues that financial crises stem from speculative attacks on pegged currencies, which may occur when governments do not adhere to the currency peg and pursue expansionary fiscal policy. Successful speculation causes the central banks to stop adhering to the peg after they have depleted foreign reserves and raised domestic interest rates, leading the country to experience a financial crisis. Speculation continues in countries that have similar monetary and fiscal policies. Krugman s model suggests that financial crises can be predicted by focusing on economic fundamentals, such as budget deficits, expansionary monetary policies, and real exchange-rate overvaluation. However, a series of rather unforeseen contagious financial crises in the mid- to late-1990s prompted economists to reassess the existing models and examine the possibility of crisis transmission. The more recent models, especially those constructed after the financial crises of the 1990s, emphasize the unpredictable characteristics of a crisis due to external financing and investor activities. Heavily relying upon the assumption of market imperfection in the world financial market, these models suggest that a financial system, including the currency valuation, in a debtor country is vulnerable to portfolio rebalancing by major lenders and international 3

4 investors. One of the earliest models of financial crisis is the herding model, which asserts that crises result from the high cost of and/or unavailability of data. According to this model, uninformed investors who cannot afford the cost of information withdraw their financial investments after observing the credit retrenchment of a few supposedly informed investors. Another model, the self-fulfilling crisis model, resembles the classic bank-run scenario, as suggested in Goldstein and Pauzner (004). The model argues that investors who fear that their investments will be lost compete to sell off their assets in a financially crisis-stricken country, despite the fact that no investment would be lost if only a small number of creditors/investors retrenched their credit. Another set of models is based on arguments that do not rely on the concept of market imperfection. One such argument is the wake-up-call argument, which posits that a financial crisis in one country may serve as a wake-up call that leads international investors to interpret the crisis as an international shock, prompting them to reassess the country s macroeconomic fundamentals. Especially during asset price bubbles, a sudden shift in their expected returns and risk exposure induces investors to retrench their credit lines, causing liquidity shock and financial crisis. Kaminsky and Reinhart (000) found that a country s fundamental economic similarity to a crisis country may increase its probability of experiencing its own crisis. Using absolute differences between economic fundamentals between those of a country and a crisis-hit country, Eichengreen et al. (003) reports a similar finding. However, Sbracia and Zaghini (003) argue that the economic variables used to capture the effect are simply the proxies of general vulnerability. Despite their differences, both the self-fulfilling crisis model and the wakeup-call argument fail to explain why investors choose to update their expectations of and risk aversion for some countries and not others. 4

5 Kaminsky and Reinhart (1999) were the first to observe that the countries affected during the last three contagious crises heavily depended upon the same banking centers as the countries experiencing the financial crises. This observation sheds light on the reason for which the Philippines, similar to Latin American countries, depends on U.S. banks and was the only Asian country affected during the Mexican financial crisis. This observation has also led economists to believe that the level to which a foreign country shares a source of financing with a crisis country is related to its vulnerability to external shock, which may explain the pattern of contagion. Thus, financial linkages between countries, especially those that resulted through the lender to crisis countries, helped manifest the patterns of the financial crises of the 1990s. Graph 1: The Decomposition of Capital Inflow to Crisis-Stricken Countries in Each Crisis by Source of Funds Data collected by the Bank of International Settlement (BIS), which documents capital inflow into emerging markets by the nationality of the investors or location of the financial institution, also supports Kaminsky and Reinhart s (1999) observation. The data suggest that a 5

6 domestic currency devaluation and disturbance in a country s financial system are induced by a crisis in a foreign country that borrows from the same banking center as the affected country. Graph 1 presents the composition of capital inflow to crisis-stricken countries during each crisis episode. It shows that during the Mexican, Asian, and Russian crises, approximately 35 to 40 percent of the affected countries liabilities were due to the same lender. By contrast, developing countries borrowed only from 10 to 15 percent, on average, from those banking centers. A correlation also exists between the severity of a crisis and the extent to which a country borrowed from the major lender to the crisis countries. For example, during the Asian financial crisis, 65 percent of Thailand s and 57 percent of Indonesia s capital inflow were from Japanese banks, whereas only 3 percent of Sri Lanka s external borrowing originated in Japan. These observations have led economists to formalize the common lender effect, which is believed to shed light on the extent to which countries were vulnerable to external shock and financial contagion during the financial crises of the 1990s. These observations are in support of Kaminsky and Reinhart s argument, which is later called the common lender effect. The common lender effect argues that a country that relies on the same source of financing as a crisis-hit country is more likely to experience a financial turmoil, as it might face creditor s retrenchment of credit line induced by a crisis in that foreign country. An increase in non-performing loans or a loss in a country in crisis induces international creditors to reduce the amount of the loan and withdraw their financial assets form other countries. Schinasi and Smith (000) demonstrate that a financial crisis leads the investors to reduce their loss and risk exposure by selling the assets of countries whose returns are positively correlated with that of a crisis country rather than those of a country in crisis. These adjustments lead to unanticipated 6

7 credit retrenchments in other debtor countries, suggesting that countries that depend on a lender exposed to a crisis country are vulnerable to liquidity shock and financial crisis. The risk of experiencing a financial crisis due to the common lender effect, as argued by Sbracia and Zaghini (003), is greatest when the first country experiencing a financial crisis is the most important debtor to a particular lender. Creditors adjustments cause other debtor countries to face unanticipated currency and maturity mismatches, which eventually lead to a financial crisis. According to the common lender effect, an increase in non-performing loans or losses in the portfolio values of international creditors that are induced by a crisis in one of their debtor countries prompts them to reduce the amount of the loan and sell off their assets in other countries. Despite their sound financial systems and debt structures, the affected countries are vulnerable to such credit retrenchment and mismatches, which lead them to experience sharp currency devaluation, stock market slumps, and capital outflows after the outbreak of the crisis. More recent financial models, which focus on the sudden retrenchment of financial capital in a market, demonstrate the way in which a sudden capital outflow can lead to a financial crisis in a borrowing country that relies heavily upon external financing. Adjustments in investors and creditors portfolios may lead to liquidity shock or financial crisis in their debtor countries even if these countries economies and financial sectors are robust. Krugman (1999) and Eichengreen (1999) argue that the vulnerability of an economy to such crises, unlike the crises in the 1980s and early 1990s, rests on two forms of mismatch that between the maturity of debt and the period when real investments become productive and that between the currency denomination of debts and collaterals. By relying on external financing to fund domestic investments, financial intermediaries in developing countries are exposed to bank runs and, thus, financial crises through portfolio 7

8 rebalancing. Chang and Velasco (1999) apply a traditional bank-run model to three financial crises in the 1990s. Emerging countries depend on external financing to fund long-term projects, which, if completed, yield high returns; however, if terminated prematurely, such projects may yield considerably lower returns. Broner et al. (004) shows that emerging economies borrow in the short term because of the high-risk premium charged by international investors on long-term debt. Thus, financial intermediation in a developing country creates a maturity mismatch that exposes domestic banks to sudden shifts in creditors expectations and, thus, bank-runs. Consequently, a sudden credit retrenchment or selling of assets can lead to liquidity shock, whose magnitude is magnified because of the presence of long-term investments in an emerging market country. In other words, a sudden credit constraint is sufficient to create a financial crisis in which a fundamentally sound economy and banking system are at risk of crisis due to their vulnerability to bank runs. When a sudden selling of assets takes the form of a flight from a country, a debtor country suffers from a currency mismatch between debt and collateral. The liabilities of firms and banks in developing countries are denominated in major currencies, whereas their collateral is denominated in local currencies. Basic economic reasoning suggests that the value of assets plummet when the domestic currency devalues, worsening the position of firms and a country s central bank on the balance sheets. Krugman (1999) and Calvo (1999) argued that although devaluing the currency improves an affected country s competitiveness in the world market, the balance sheet problems outweigh the positive effects and create an economic contraction that also depresses other fundamentals. Based on the currency mismatch between debt and collateral, the theoretical models and empirical research have attributed a disturbance in the domestic financial system to the sudden portfolio rebalancing of international financial creditors and 8

9 investors. However, a transmission of a financial disturbance from one market to others through the influence of major lenders remains not completely understood. This paper defines contagion as an increase in the likelihood of a crisis in a home country due to the existence of a financial crisis abroad. Though economists have not agreed on a definition of contagion, two common versions exist. The first version, as defined by Eichengreen et al. (1996), denotes an increase in the odds of a financial crisis in a country as a result of a financial crisis abroad, whereas the second version refers to an increase in the cross-market correlation of return from stock markets and the volatility of the currency exchange rate. However, according to Forbes and Rigobon (001), an increase in correlation may result from an increase in volatility in each market. Therefore, most of the recent literature, including this paper, uses the former definition of contagion. This paper derives the common lender effect through the mathematical models displayed in Section II, which shows that a financial crisis abroad induces investors to sell off their assets in a home country despite the lack of a fundamental correlation between two markets, which leads to a financial crisis. Section III investigates the empirical implications derived from the theoretical section and provides empirical evidence for the existence of the common lender effect. Section IV summarizes the results of the previous sections and provides policy implications as well as suggestions for future research into the topic. 9

10 Section II A Model of the Common Lender Effect This section attempts to show the existence of the common lender effect among rational investors through a portfolio balance model. Financial contagion literature has described the transmission of financial shock across assets markets through various models. Some of these models have explored the phenomenon through a single investor s decision making, and others studied the impact of portfolio rebalancing in the general equilibrium framework. Schinasi and Smith (000) and Calvo and Mendosa (000) have analyzed the behavior of fund managers through the partial equilibrium context. In addition, the literature has investigated transmission through the general equilibrium framework. Papers by Calvo (1999), Kyle and Xiong (001), Kodres and Pritsker (00), Danielson, Shin, and Zigrand (004), and Goldstein and Pauzner (004) study portfolio rebalancing by different types of investors under various institutional settings in price dynamic general equilibrium. Some of these authors based their analyses on market information, such as data unavailability and the payment scheme of the fund managers. On the other hand, other studies have assumed that all of the investors have access to information and that they behave rationally. The literature review for the theoretical section will focus on two papers that employed a partial equilibrium framework, which is closely related to the framework presented in this paper. A paper by Schinasi and Smith (000) analyzes the behavior of fund managers through the two-country framework in the event of two shocks from a foreign market an increase in volatility in the return of an asset (a volatility event) and a decrease in managers capital (a capital event). The authors explore the rebalancing through various models that reflect the managers interests, such as the portfolio balance model, Value at Risk model (VaR), and others. 10

11 Without placing restrictions on the managers (no short sale and borrowing constraints) or correlation of the returns of the two assets, the authors find that all of the three portfolio management rules suggest that a volatility event in one country can induce the managers to readjust their holdings of the other asset. However, the condition is true only when both markets exhibit a positive correlation, which Schinasi and Smith argue is the relevant case, as asset returns in emerging markets are generally correlated. Moreover, they investigate the behaviors of leveraged and unleveraged investors. The authors contend that leveraged investors reduce their exposures in both types of risky assets when the cost of funding exceeds the return of the portfolio. Calvo and Mendoza (000) study the transmission in an imperfect market setting, in which information is costly and only available to informed investors. The authors argue that this characteristic encourages uninformed investors to follow the informed one. It is too costly for those investors to acquire private information, hence, creating a herding behavior. Furthermore, the study incorporates institutional restrictions, such as the short-selling and noborrowing conditions, which the managers face in the international financial market in their analyses. That is, managers cannot short-sell an asset in a crisis market and borrow at a risk-free rate during the financial crisis. Calvo and Mendoza have found that the benefit from acquiring private information decreases with the presence of short-selling constraints. Similarly, the fund managers incentives to follow the benchmark positions are higher when they cannot borrow during the crisis. These restrictions allow a more realistic analysis of the impact of portfolio rebalancing. To investigate the common lender effect, this paper studies the current-period portfolio allocation, which captures the situations portfolio and fund managers face during financial 11

12 turmoil. Specifically, this paper relies on an analysis of the portfolio balance model suggested in Schinasi and Smith (004). The implications of this model capture the nature of portfolio allocation higher return and lower risks. Not only is this model mathematically tractable, but it is also flexible enough to allow experimentation with various correlations between countries, fund managers levels of risk aversion, as well as institutional restrictions in the financial market. The previous literature on the common lender effect that investigates the topic through the portfolio rebalancing relies on the analyses on the two-country model. The papers find that the increase in the volatility shock in one country affects the optimal investment in another country. However, these models have the limitation in which they do not permit an analysis when two assets are uncorrelated. Therefore, even though these analyses imply the existence of the common lender effect, they do not prove the effect when the assets are uncorrelated; that is, a country is affected by a crisis in a foreign country even if they are not fundamentally related. To derive the common lender effect, this paper relies on a three-risky-asset and one-risk-free asset model, which allows an analysis when two of the risky assets are not fundamentally correlated. Thus, addition adds to the literature of the common lender effect by showing the existence of the effect regardless of the correlations between two risky assets. This study adapts the portfolio balance model from Schinasi and Smith (000) in order to derive the analysis of the common lender effect. In this paper, the model features three risky assets and one risk-free asset, which respectively denote the assets in different markets and bonds issued by central banks in developed countries. Examinations allow comparisons of the impact of a volatility shock in one asset market on the two other asset markets. With three assets, the paper is able to explore the impact of portfolio rebalancing when two of the asset returns in the portfolios are not fundamentally correlated. In addition, this paper also considers the relative 1

13 payment scheme, which permits fund managers to deviate from the benchmark index according to their levels of risk aversion or private information. Motivated by Calvo and Mendoza s paper in 000, the model incorporates short-selling and no-borrowing constraints. These features permit formal analyses of the common lender effect in a financial contagion, which argues that a financial shock in one country can transmit to another country through foreign investors and fund managers, despite no correlations between the two markets. In addition, by including the realistic institutional settings, this paper presents a comprehensive analysis of the impact, which will shed light on the results in the empirical section. In this study, the financial crisis in an asset market or country is defined to be an increase in the variance of the return of that asset. The literature has illustrated two types of financial shock volatility shock and the wealth effect. The literature on the financial spillover that has used the definition of wealth effect has usually analyzed the role of the margin call in financial crisis transmission. On the other hand, analysis of the spillover through the portfolio balance model does not rely on the assumption of the margin call, as the analysis only takes into account a higher volatility of one of the assets in the portfolio. It is interesting to include the wealth effect within the further analysis because the market value of the portfolio, or the assets of the fund manager, may decrease due to the increase in variance of their portfolio returns. However, as this analysis concerns the case that fund managers may reduce their optimal proportion of the portfolios of a specific asset, a decrease in overall wealth also leads to the same effect. Thus, this paper does not formally take into account the wealth effect in the analysis. The Model According to the portfolio balance model in Schinasi and Smith (000), the specification of the portfolio balance model is shown below: 13

14 maximize µ p! 1 "# p, in which! denotes the risk tolerance parameter, and µ p and! p respectively denote the expected return of the portfolio and its volatility. The return and volatility of the portfolio are equivalent to those in the mean-variance framework. To study the problem of countries that rely on the same source of financing, this paper considers the case in which three risky assets and a risk-free one are available. A risky asset may represent the financial asset in both emerging and developed countries and a developed market, and the risk-free asset serves as bonds issued by central banks in developed countries. In this specification, the portfolio balance model can be written as: maximize 3 "! i µ i + r # 1 3 i=1 $ '! )" i % i + "! i! j % ij,, (1) ( i=1 i& j + where! i is the proportion of wealth invested in asset i, µ i = µ i! r is the return of asset i less that of the risk-free asset (r),! i is the variance of the return of asset I,! ij is the covariance 1 of the returns of assets i and j, and! is the level of risk aversion of the fund managers (! > 0). In the simplest case where there is neither correlation between each market! ij = 0 nor institutional restrictions, the fund manager s optimal choices are: for all i s.! i = µ i "# i, 1 The covariance! ij can also be written as! ij =! i! j " ij, where! i is the standard deviation of asset i, and! ij is the correlation coefficient between the return of assets i and j. 14

15 It is evident from the choice of! i that a higher volatility in the market induces managers to reduce their exposure to that market. The risk tolerance parameter exhibits the same relationship. In addition, the formula above suggests that there exists no evidence of crisis transmission or contagion, as an increase in volatility in other markets does not affect the optimal proportion of investments allocated to other countries. Nonetheless, the returns of assets in emerging country markets are correlated, even though the magnitude of this correlation varies according to the characteristics of each country. However, to study the common lender effect through the portfolio balance model, this paper does not assume that the pair-wise correlation between the markets is zero so that it is more compatible with the common lender argument. Supposing that the returns of assets from different markets exhibit some correlation among themselves, the portfolio and fund manager solve the problem (1). Proposition 1: Consider risky assets i, j, and k and the risk-free asset. The optimal choices,! i, are: 1 " #! jk, i = $% i (1 " # ij " # ik " # jk + # ij # ik # jk ) µ & i " µ j% i % k (# ij " # ik # jk ) + µ k % i % j (# ik " # ij # jk )) /. ( ' % j % k (1 " # jk ) 01 1 " #,! j = ik $% j (1 " # ij " # ik " # jk + # ij # ik # jk ) µ & " µ i% j % k (# ij " # ik # jk ) + µ k % i % j (# jk " # ij # ik )) /. ( ' % i % k (1 " # ik ) 01 1" #! ij, k = $% k (1" # ij " # ik " # jk + # ij # ik # jk ) µ & 3 " µ i% j % k (# ik " # ij # jk ) + µ j % i % k (# jk " # ij # ik )) /. ( ' % i % j (1" # ij ) 01, and the optimal proportion allocated to risk-free assets,!, is given as:! = 1 " # 1 " # " # 3. 15

16 Thus, the increase in volatility of the return of an asset reduces its proportion in the portfolio, and that higher risk aversion (higher! ) also leads to lower holding of risky assets. On the other hand, the higher level of either of the parameters increases the optimal proportion allocated to the risk-free asset. The model also suggests that the optimal portfolio choice of asset i depends on the pair-wise correlation between the three assets. This result leads to an interesting comparative static, which sheds light on the role of investors in transmitting a financial crisis, as well as the phenomenon of the common lender effect. Corollary 1.1: Consider three risky assets, i, j, and k, and a risk-free asset (r). A volatility shock in the return of asset k gives rise to a spillover in a market for asset i, even if the correlation between the two assets is zero. The managers decisions to sell off or buy asset i depends on the correlation between assets i and j and that between j and k; that is, for! ij +! jk < 1, and for! ij +! jk > 1, sign d! # & i % ( $ d" = sign # $ ) ij jk & ', k ' sign d! # & i % ( $ d" = sign # $ ) ij) jk & '. k ' Even though two cases arise from the analysis, the empirical evidence suggests that only the first case in Corollary 1.1 is warranted. This paper collects the correlation between the weekly returns of the stock markets of countries in the region where a financial crisis took place over the span of 5 years before the start of the financial crisis. In all of the three crises, the Mexican, Asian, and Russian crises, the pair-wise sum of the second moment of the correlation The negative holding of a risky and risk-free asset means that the managers are in the short position, or they borrow with risk-free interest rates, respectively. 16

17 coefficient between countries in the same region, as the data suggests, is higher than that across the region; however, it is less than 1. For example, during the Mexican crisis, the returns of stock markets in Mexico and Argentina are most correlated, and the coefficient is Any combination of the pair-wise correlation coefficients sums up to be less than 1. Likewise, the most correlation between the stock market returns during the Asian crisis is that between Hong Kong and Singapore, which is This trend has persisted throughout the early 1 st century. The data set for the Russian crisis witnesses less correlation of asset returns between affected countries than the first two crises, even though those between affected and unaffected countries have increased. None of the pair-wise sum exceeds 1. Hence, the evidence from the stock returns suggests that only the first case of Corollary 1.1 is empirically warranted, which agrees with the finding in the argument and regression results of the common lender effect. Hence, later discussions of Corollary 1.1 assume that! ij +! jk < 1. In addition, the correlations of asset returns between the markets are usually positive, as in the sample return, the all of the returns are positively correlated with the least positive correlation coefficient is that between Columbia and Mexico at during the early 1990s. The paper disregards the case where the correlation coefficient between assets i and j and that of j and k are both negative. To illustrate the consequence of Corollary 1.1, assume that no correlation exists between assets i and k (! ik = 0 ). From proposition 1, the optimal proportion of the portfolio allocated to asset 1,! 1 can be simplified as: 1 " #! jk & i = ( $% i (1" # ij " # jk ) µ " µ i k '( % i # ij % j (1 " # jk ) + µ k % i # ij # jk % k (1" # jk ) )

18 Suppose that asset i represents the asset in the home country, and assets j and k are assets in managers portfolios in other foreign countries. According to the formula above, increased volatility in a foreign market can affect the manager s optimal level of a domestic market, d! 1 $ = #µ 1$ 3 3 d" 3 %" 3 " 1 (1 # $ 1 # $ 3 ). Thus, it is clear that: sign d! # & 1 % ( $ d" = sign #$ ) 1 3 & '. 3 ' Assuming that the return from asset i is higher than that of the risk-free asset, whether portfolio managers decide to increase or decrease their exposure in the home country (asset i), depends on the correlation between the return of assets in countries i and j, as well as that between countries j and k. Evidently, the managers will optimally sell off domestic assets in response to a volatility shock in a foreign market (asset k), provided that the return of asset j exhibits a positive or negative correlation between both the return of the domestic asset i and that of the country experiencing an increase in volatility k. The consequences of Corollary 1.1 suggest that a country that relies on the same lender as a country in a financial crisis might encounter a spillover through portfolio rebalancing of rational fund managers who hold assets in the three markets. In the case of a financial crisis in emerging market countries, the managers portfolios are composed of assets in the same region, which show the positive pair-wise correlation between countries. Thus, as argued in the literature of the common lender effect, an increase in volatility in that foreign country leads managers to reduce their exposure in the home country, even though no fundamental correlation exists between the return of the domestic asset and that of a foreign country experiencing a financial turmoil. Not only do these correlation coefficients determine the decision to buy or sell the domestic asset, but they also play a role in determining the volume of the transactions. Evidently, 18

19 the higher correlation between the two pairs of assets causes the managers to lower their optimal exposure in the domestic country. The model also suggests that financial contagion can arise from rational behaviors of fund managers who behave according to the portfolio balance rule. It is also interesting to point out that the risk tolerance parameters do not influence the managers decisions to sell off or buy the asset but, rather, the optimal amount of investment allocated to the asset. Corollary 1.1 points to the existence of financial spillover, which provides theoretical evidence in support the existence of the common lender effect. In addition, this paper also investigates the relative impact of the volatility shock of the return of an asset on the optimal holding of assets in two other countries, according to their characteristics. Corollary 1.: Consider three risky assets, i, j, and k, and a risk-free asset, r. In response to a volatility shock of the return of asset k, the fund managers readjust their optimal holdings of assets i and j, and the relative volume of the transactions follows the relationship below: For! ij +! ik +! jk "! ij! ik! jk < 1, then d! i # d! j, if the following condition holds: d" k d" k! ik "! ij! jk # i $! jk "! ij! ik # j. Otherwise, (! ij +! ik +! jk "! ij! ik! jk > 1), then d! i # d! j, if this condition holds: d" k d" k! 13 "! 1! 3 # 1 $! 3 "! 1! 13 #. Similarly, only the first case from Corollary 1.,! ij +! ik +! jk "! ij! ik! jk < 1, is empirically warranted in the study of the common lender effect in the 1990s financial crisis. Based on the same set of correlation coefficients between the stock market returns in Corollary 1.1, none of these correlation coefficients, whether within or across the region, satisfy the second 19

20 inequality of Corollary 1., hence, suggesting that the analysis of the Corollary should attend to the case of positive correlations among returns of assets. According to Proposition 1, the change of the optimal proportion of the portfolio allocated to asset i in the event of an increase in the volatility of asset k can be written as: d! i (# = µ $ # ik ij# ) jk k. It is clear that Corollary 1. holds. The managers d" k " k " i (1 $ # ij $ # ik $ # jk + # ij # ik # jk ) will sell off asset i, if! ik "! ij! jk < 0 ; otherwise, they will buy the asset. If the following equation holds,! ik =! ij! jk, the volatility shock does not affect the optimal proportion invested in asset i. In the context of portfolio rebalancing, provided that the managers are in the long position in assets i and j, Corollary 1. provides two interesting implications. First, it implies that the fund managers usually flee to the less volatile asset. Second, it suggests that the managers tend to replace the increasingly volatile asset with an asset that exhibits a positive correlation with the asset. For example, suppose the variance of the return of asset k increases, and its correlations with the other two assets are equal. Then, according to Corollary 1., the managers will increase their exposure in asset i more than in asset k, if asset i is the less volatile. Likewise, given that the other two assets are equally volatile, the managers will opt for the one that is most correlated with asset k. Although the first implication makes intuitive sense, the second one raises a question that requires further explanation. One would imagine that the managers should replace asset k with the less correlated asset of the other two. It is crucial to note that in this analysis, the paper assumes that the volatility shock of the return of asset k does not influence other characteristics of other assets, for example, their expected returns less that of a risk-free asset, µ i, their variances,! i, or their correlations with asset k,! jk. Thus, it is reasonable to 0

21 replace the volatile asset with its most similar or correlated counterpart. Furthermore, even though the expected returns of asset i and j influence the optimal investment in the market, they do not influence either the decision to sell the asset or the volume of the transaction. Corollary 1. provides an additional explanation as to why some countries that rely on the same lender as the country encountering financial crisis are not affected, or less so than their other counterparts. During the Asian financial crisis in 1997, China 3 and India experienced less financial turmoil than other Asian countries, even though, along with the affected countries, they relied on the Japanese banks as fund providers. The statistics show that the returns of assets in both China and India, as measured by the variance of returns of the stock market and JPMorgan s EMBI bond spread, are relatively low compared to other countries [insert citation]. In addition, the returns in both countries are as correlated to those of crisis countries (for example, Thailand and Indonesia) as those of affected countries, such as Malaysia, which would suggest similar sell-offs in these markets. Therefore, this condition suggests that the low volatilities of returns in China and India counteracted the effects of their correlations, according to Corollary 1.. (Note that the dominator is relatively small, so the magnitude may be dominated by the variances, the denominators.) The previous model assumes that the managers earn their absolute returns from their portfolios; however, the portfolios and fund managers performance are usually benchmarked to that of the index portfolio, µ!. To take the possible impact of this arrangement into account, the paper modifies the portfolio balance model in Problem (1) by developing a relative portfolio balance model to capture this real-world characteristic. In this analysis, this paper assumes that 3 Another explanation in China s case is that the government more heavily controlled and intervened in its financial system during the crisis than governments of other Asian countries. However, this control might be reflected in the low volatility. 1

22 the market portfolio is known to every fund managers and fixed for the period. Consequently, the expected relative return and its volatility can be written as: 3 E(µ i! µ " ) = ( $ # i µ i + r)!( $ " i µ i + r) i=1 3 $ = (# i! " i )µ i i=1 3 $ Var(µ i! µ " ) = (# i! " i ) % i + (# i! " i )(# j! " j )% ij The portfolio balance model is reformulated as: i=1 3 i=1 $ i& j maximize 3 $ (! i " # i )µ i " 1 3 i=1 % ( (! " # + $ i i ) & i + $ (! i " # i )(! j " # j )& ij -, () ) i=1 i' j, where! i denotes the proportion of the market portfolio invested in asset i, and r denotes the return of the risk-free asset. Proposition : For risky assets i, j, and k, the optimal proportion of portfolio allocated to asset i is given as: 1 # $! jk - i = " i + %& i (1# $ ij # $ ik # $ jk + $ ij $ ik $ jk ) µ ' i # µ j& i & k ($ ij # $ ik $ jk ) + µ k & i & j ($ ik # $ ij $ jk ) 0 / ) ( & j & k (1# $,./ jk ) + 1, and the optimal proportion allocated to a risk-free asset,!, is given as:! = 1 " # i " # j " # k. According to the formula above, it is clear that the sensitivity analysis from the absolute return case also applies to the relative return case. Consequently, the model suggests that the investors whose returns are benchmarked to the index will behave similarly as the managers whose performances are not benchmarked during the crisis, even though their optimal rebalanced investments are different. Another intriguing implication from this proposition shows that their portfolio readjustments do not depend on! i. According to Corollary 1.1 and 1., this implication

23 suggests that even though the fund managers performances are benchmarked to different indices, for example, different! i, they would still make the same transactions. For example, institutional investors and hedge fund managers would all sell-off a specific asset, though their returns are indexed to different benchmarks. Moreover, the model gives insights into the behaviors of relative-return investors. A higher level of risk aversion and the asset s volatility both reduce the proportion of risky assets. The relative-return investors respond to either higher risk aversion or the increased volatility of asset k by readjusting the optimal proportion of their investments in the asset (! i ) to be closer to that of the benchmark index. The analysis suggests the existence of rational herding, where rational investors with perfect information optimally follow the same investment strategies. On the other hand, the increased volatility of other assets does not necessarily imply that investors will shift their investment schemes closer to that of the index portfolio. According to Corollary 1., the investors move closer to the benchmark index if equation (i) holds; otherwise, they move away from the benchmark index. Therefore, even when the returns of portfolio managers are benchmarked to the index portfolio, an increase in volatility of the return of asset k may cause a spillover to other assets, hence, causing rational investors to reduce their proportions allocated to assets i and j. For example, suppose a financial turmoil causes higher volatility of the return of asset k; the portfolio managers prefer to reduce their exposure in that asset. In addition, they may reduce the proportion of the portfolio invested in asset i, given the positive correlation of the return of assets i and j, as well as that of j and k, even though there exists no correlation between assets i and k, regardless of whether or not their performances are benchmarked to the market index. Even though the previous analysis provides theoretical support of financial spillover through the major investors (for example, the common lenders) in a region, it is 3

24 preferable to incorporate possible institutional restrictions on investors in order to gain a more comprehensive analysis of the subject. The previous model does not impose any constraints on the managers; that is, they can freely buy or short-sell any assets. However, during a crisis, managers are usually unable to short-sell assets, especially the ones with volatility shocks or to borrow freely. Thus, it is worthwhile to impose these conditions on the portfolio balance model. Suppose that fund managers follow an investment scheme aligned with the portfolio balance rule and face shortselling and borrowing constraints. In addition, as demonstrated in Proposition that relativereturn investors behave similarly to absolute-return ones, for simplicity, the paper considers only the absolute-return managers in the constrained case. The managers solve the problem, which can be formulated as follows: maximize 3 "! i µ i # 1 3 i=1 $ '! )" i % i + "! i! j % ij, subject to ( i=1 i& j +! 1,!,! 3 " 0 3 #! i " 1. i=1 Proposition 3: Considering the constrained optimization described above, the fund managers optimal proportions of the portfolios allocated in assets i, j, and k can be written as: 3.1 Positive Investment in Risk-free asset ("! i < 1): 1 " #! jk, i = $% i (1 " # ij " # ik " # jk + # ij # ik # jk ) µ & i " µ j% i % k (# ij " # ik # jk ) + µ k % i % j (# ik " # ij # jk )) /. ( ' % j % k (1 " # jk ) No Investment in Risk-free asset ("! i = 1): 3 i=1 3 i=1 4

25 1" #! jk - i = $% i (1 " # ij " # ik " # jk + # ij # ik # jk ) µ " & ' i 4 " µ j% i % k (# ij " # ik # jk ) + µ k % i % j (# ik " # ij # jk ) 0 / ) ( % j % k (1 " #,./ jk ) + 1, where! 4 = ' { } p,q% i, j,k p&q " i " j " k " p " q (1 # $ pq ) + - ((1 # $ ij # $ ik # $ jk + $ ij $ ik $ jk ) + )(p) # - ' p% { i, j,k},- 3 ' { } p,q% i, j,k p&q. (p,q) 0, 0 / 0!(i) = (1 " # jk )µ i, and! (i, j) = (µ + µ )(" # " i j ij ik" ) jk. $ i $ i $ j It is evident that if the managers invest in a risk-free asset, their responses to a volatility shock of the return of an asset in another market will be the same as those in the unrestricted scenario, except that they cannot short-sell an asset (for example, the optimal holding of an asset is non-negative) When the optimal proportions are positive, the comparative static results for Problem (1) also apply to case 3.1. That is, the evidence points to the existence of financial spillover, despite no correlation between affected markets. The managers tend to reduce their investments in domestic markets in response to an increase in volatility in a foreign market, given that these two markets are not correlated. In addition, the managers prefer to replace the asset in a crisis market with the more correlated asset and the less volatile of the other two assets. However, the fund managers may behave differently if they invest in the risk-free asset, which can be described in Corollary 3.1. Corollary 3.1: Consider risky assets i, j, and k, and no correlation exists between assets i and k. Given that the managers do not invest in the risk-free asset after portfolio rebalancing, an increase in volatility of the return of asset k induces the managers to reduce their optimal 5

26 positions in asset i if d! i # d$ 4, where! i is the optimal investment in Proposition 1, and! 4 is d" k d" k the optimal Lagrange multiplier of the borrowing constraints. Corollary 3.1, along with the empirical evidence demonstrated in Corollary 1.1, suggests that the managers tend to reduce their exposure in the home country by selling off asset i in the case of a volatility shock of asset k in a foreign country. The empirical evidence suggests that d! i is negative, but it is shown that d! 4 is always positive. Thus, the rebalancing scheme, d" k d" k d! i d" k, can be written as: d! i = d! i # d$ 4 d" k d" k d" k % 0 The Corollary implies that the fund managers are more likely to reduce their holdings of other assets when they face short-selling and borrowing constraints. In addition, the volume of the rebalancing transaction to reduce their investments in asset i under these restrictions is equal, if not greater, in the unrestricted scenario. Interestingly, similar to the results in the unconstrained scenario, the risk aversion parameter does not affect the decision to sell off or buy asset i but the magnitude. However, in this case, the higher risk aversion leads to the bigger reduction in the managers holdings of asset i, cerebus paribus. The finding from Proposition 3 confirms that an increase in volatility in a foreign country can result in financial turmoil in the domestic country as a result of the selling-off of the asset in the market, even if the returns of these two markets are independent. From the formula of d! 4 d" k, it is evident that when managers 6

27 are able to borrow at the risk-free rate, their optimal holdings of the asset i would be higher. Hence, the fund managers would be led to sell off their assets for less than they would otherwise receive with the borrowing constraint. The comparison of the impacts of the volatility shock on asset k under the institutional restrictions on the markets of assets i and k is identical 4 to that of the unconstrained case. Therefore, according to Corollary 1.3, the volatile asset is more likely to be affected by a volatility shock in an asset market aboard. Conclusion The analysis of the impact of portfolio rebalancing from the three-country portfolio balance model points to the existence of the common lender effect: The financial crisis can be transmitted through the fund managers, despite no fundamental correlation between two markets. The fund managers always sell off an asset in a country in response to a volatility shock in a foreign market; even though, these two assets are not fundamentally correlated if the correlations of the assets in the rest of the portfolio are positive. In addition, if the fund managers encounter the borrowing constraint, the volume of rebalancing is greater than usual, hence, suggesting a more severe financial turmoil in the affected country. The volatility of each asset return also plays a role in determining the volume of the rebalancing; however, its expected return does not influence the decision to sell off that asset. This finding agrees with previous empirical works in the literature, such as Van Rijckeghem and Weder (003) and Kaminsky and Reinhart (1999), which have shown that an asset market experiences a greater capital outflow if it relies on the same sources of financing as a crisis country. The next section of the paper uses empirical analysis to test the results from this 4 Please see the proofs in Appendix A. 7