metadata: authors: 0: author: Escobar,Mariana
1: author: Pandolfi,Lorenzo
2: author: Pedraza Morales,Alvaro Enrique
3: author: Williams,Tomas
count: Colombia
docna: 0: docna: The Anatomy of Index Rebalancings : Evidence
            from Transaction Data
docty: Policy Research Working Paper
subtopic: International Trade and Trade Rules,Mutual Funds,Non Bank Financial Institutions,Capital Markets and Capital Flows,Capital Flows,Social Funds and Pensions,Financial Sector Policy
teratopic: Finance and Financial Sector Development,International Economics and Trade,Social Protections and Labor
abstracts: cdata!: This paper exploits a novel dataset
            covering the universe of transactions in the Colombian Stock
            Exchange to analyze episodes of additions to and deletions
            from MSCI equity indexes. The analysis finds that additions
            and deletions have large price effects: the median
            cumulative abnormal return in absolute value is 5.5 percent.
            The paper shows that these price effects are due to large
            demand shocks by different classes of international
            investors—not only passive funds and ETFs, but also active
            mutual funds, pension funds and government funds—which are
            not absorbed by arbitrageurs. Consistent with recent asset
            pricing models with limits to arbitrage, stock demand curves
            are estimated to be very inelastic: the demand elasticity
            for the median stock in the sample is −0.34, implying that a
            1 percent increase in the demand for the stock increases its
            price by 2.9 percent.
geo_reg_key: 119228,517191
repnme: repnme: The Anatomy of Index Rebalancings :
            Evidence from Transaction Data
display_title: The Anatomy of Index Rebalancings :
            Evidence from Transaction Data
listing_relative_url: /research/2021/09/33400835/anatomy-index-rebalancings-evidence-transaction-data
topicv3: Pension Funds m1326066 611,Trade m1326924 698,Mutual Funds m1326970 2180,Financial Sector Development m1327681 1920,Equity Finance m1327686 334
publishtoextweb_dt: 2021-09-09T00:00:00Z
dois: 10.1596/1813-9450-9770
historic_topic: Finance and Financial Sector Development,International Economics and Trade,Social Protections and Labor
origu: DECRG: Finance & Priv Sec Devt (DECFP)
no_of_pages: 26
author_keys: 0: author_key: 1321207
1: author_key: 1046708
model_extractions: Policy Research Working Paper 9770 The Anatomy of Index Rebalancings Evidence from Transaction Data _Mariana Escobar Lorenzo Pandolfi Alvaro Pedraza Tomas Williams_ Development Economics Development Research Group September 2021
Policy Research Working Paper 9770

# **Abstract**

This paper exploits a novel dataset covering the universe of transactions in the Colombian Stock Exchange to analyze episodes of additions to and deletions from MSCI equity indexes. The analysis finds that additions and deletions have large price effects: the median cumulative abnormal return in absolute value is 5.5 percent. The paper shows that these price effects are due to large demand shocks by different classes of international investors—not only passive funds and ETFs, but also active mutual funds, pension funds and government funds—which are not absorbed by arbitrageurs. Consistent with recent asset pricing models with limits to arbitrage, stock demand curves are estimated to be very inelastic: the demand elasticity for the median stock in the sample is −0.34, implying that a 1 percent increase in the demand for the stock increases its price by 2.9 percent.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at lescobvi@banrep.gov.co, lorenzo.pandolfi@unina.it, apedrazamorales@worldbank.org, and tomaswilliams@gwu.edu.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# The Anatomy of Index Rebalancings: Evidence from Transaction Data<sup>_∗_</sup>

## Mariana Escobar<sup>_♥_</sup> , Lorenzo Pandolfi<sup>_♠_</sup> , Alvaro Pedraza<sup>_♦_</sup> and Tomas Williams<sup>_♣_</sup>

_♥_ Banco de la Republica de Colombia

> _♠_ University of Naples Federico II and CSEF

> _♦_ The World Bank

> _♣_ George Washington University

### **JEL Classification:** F32, G11, G15

**Keywords:** index rebalancings; institutional investors; stocks demand elasticity; passive funds; arbitrage

> _~~∗~~_ This paper greatly benefited from helpful comments by seminar participants at the International Monetary Fund and Bank of Italy.
# **1 Introduction**

Index rebalancing episodes have been widely exploited to study several topics in financial economics. For instance, they have been used to measure the effects of large demand shocks on stock prices and estimate the slope of stock demand curves (e.g., Shleifer, 1986; Harris and Gurel, 1986; Kaul et al., 2000; Chang et al., 2014)<sup>1</sup> , as well as to study the consequences of institutional ownership on price informativeness, corporate financing, and governance (Boone and White, 2015; Appel et al., 2016; Crane et al., 2016; Bena et al., 2017), and the price comovements of commonly owned stocks (Barberis et al., 2005; Greenwood, 2008; Claessens and Yafeh, 2012). Index rebalancings are appealing from an empirical perspective since they entail sudden and large shocks in the demand of affected securities by investors – mostly large institutions – benchmarked against the indexes. To the extent that (at least some of) these shocks are unrelated to fundamentals, their quasi-experimental nature makes them an ideal laboratory to test several asset pricing and corporate finance theories.

Despite their extensive use in the literature and the vast evidence on the price effects of these events, little is known about the actual behavior of the population of investors in response to them. This is because traded quantities are usually hard to observe. High-frequency data on investors’ portfolios is often unavailable, and low-frequency (quarterly) data typically covers a subset of investors. This lack of data leaves many unanswered yet important questions about index rebalancings. For instance: which types of investors rebalance into (out of) affected stocks? Are these portfolio rebalancings permanent? Do investors trade when rebalancings are announced, when they are made effective, or in the interim period between these two dates? Moreover, lacking data on actual traded quantities is particularly problematic when using index inclusions and deletions to estimate the demand elasticity for stocks, which is a key parameter of interest for financial economists and policy makers.<sup>2</sup> Researchers estimating such elasticity usually infer the demand shocks implied by the rebalancings from the assets under management (AUM) of funds benchmarked against the indexes and make assumptions on the degree of _passivism_ of such funds. Depending on these assumptions, estimates can vary widely.<sup>3</sup> 1Similar studies have been conducted in exchange rate and sovereign debt markets (Hau et al., 2010; Pandolfi and Williams, 2019).

> 2In fact, this elasticity is at the heart of a new class of asset pricing models – such as those developed by Koijen and Yogo (2019) and Gabaix and Koijen (2020) – which are used to study key policy issues, such as the impact of asset purchase programs on asset prices.

> 3Wurgler and Zhuravskaya (2002) review studies estimating the demand elasticity for stocks and note that it can range between -1 and -37. Even when looking at the very same event, estimates can vary depending on the assumptions made to infer quantities. For

2
Our main contribution in this paper is to shed novel light on index rebalancings – and especially on the behavior of investors – by combining transaction-level data from the Colombian stock market with episodes of additions into and deletions of Colombian stocks from MSCI indexes. Our dataset contains all the stock purchases and sales from the secondary market where these stocks are traded. Additionally, we observe the individual/institution involved in each transaction. To our knowledge, this is the first attempt to provide a complete picture on index rebalancing episodes by analyzing not only price changes, but also the actual trading behavior of the universe of investors in response to these episodes. Furthermore, our dataset allows us to measure also the demand elasticity for stocks using actual traded quantities, without having to make assumptions on funds’ behavior.

We find that inclusion into an international equity index leads to a median cumulative abnormal return, from the announcement to the implementation date, of 5.5%, which is line with recent studies of equity additions and deletions (Chang et al., 2014). We show that the price effect results from a large increase in the demand by foreign investors.<sup>4</sup> This group buys (sells) about 2.7% of the outstanding shares of stocks included into (removed from) the indexes, with most trades taking place on the effective day of the index recomposition rather than on the announcement day. Such portfolio rebalancings do not revert, at least in the month following the index redefinition. In addition to passive mutual funds and ETFs, most foreign investors – including active mutual funds, pension funds, investment firms, government agencies and sovereign wealth funds – also rebalance their portfolios in the direction of the index. The demand shock from such nonpassive investors is 1.7 times larger than the demand from purely passive funds. Foreign hedge funds, instead, tend to trade in the opposite direction of the index recomposition, possibly to speculate on the events. Yet, their trades are very small compared to those of the rest of foreign investors. Finally, we combine our results on prices and traded quantities and estimate a median elasticity of demand for stocks of -0.34. Thus, for the median stock in our sample, a 1% increase in the quantity demanded of shares (relative to the number of shares outstanding) leads instance, Chang et al. (2014), in their RDD study on the impact of stock inclusions into the Russell 1000 index, and contemporaneous exclusion from the Russell 2000, provide an estimated elasticity between -1.5 and -0.4, which implies that a 1% increase in the quantity demanded of a given stock leads to an increase in its price ranging from 0.67% to 2.5%. The latter is estimated assuming that only passive funds tracking both indexes rebalance their portfolios accordingly. The former is instead obtained under the assumption that all investors (passive and active) benchmarked against these indexes do so.

> 4In emerging markets, MSCI indexes are mostly tracked by foreign investors rather than domestic ones, as they have international focus and often include stocks from different countries. In fact, we show in Section 3 that domestic investors sell stocks when these are included in international indexes and buy them when they get removed.

3
to an increase in its price of 2.94%. This estimate is closer to the more inelastic estimates produced in prior studies.

Three main takeaways emerge from our analysis, all of which are consistent with theories of limits to arbitrage such as those developed by Koijen and Yogo (2019) and Gabaix and Koijen (2020). First, there is a broad range of investors (beyond passive funds and ETFs) that have ‘implicit’ mandates to closely track the composition of the indexes they follow so as to deviate very little from benchmark returns.<sup>5</sup> Second, hedge funds and other investors, that are supposed to act as arbitrageurs in financial markets, are too small to soften the price impact of demand shocks generated by investors with such ‘implicit’ mandates. Third, consistent with the other two results, the demand elasticity for stocks is highly inelastic, contrary to what is typically predicted in canonical asset pricing models.

# **2 Data and Institutional Framework**

To study rebalancing events, we exploit episodes of additions to and deletions of Colombian stocks from MSCI international equity indexes, together with transactionlevel data from the Colombian stock exchange, _i.e._ , the _Bolsa de Valores de Colombia_ (BVC, henceforth). In this section, we describe these episodes and discuss the main features of the BVC and the proprietary transaction data.

## **2.1 MSCI Additions and Deletions**

MSCI indexes are the most widely tracked international benchmarks for institutional investors in equity markets. Importantly, many of their flagship indexes contain stocks from different countries, and are thus followed mostly by large international investors. In our analysis, we exploit additions to and deletions of stocks from MSCI Standard Indexes, which are the largest in terms of the AUM benchmarked against these indexes.<sup>6</sup> Starting from the MSCI quarterly reports for the Standard Indexes, we identify 18 episodes of additions and deletions of Colombian stocks in the 2006-2017 period.<sup>7</sup> We retrieve from the reports the an-

> 5This behavior is consistent with benchmark indexes being the preferred habitat for many different investors. See for instance Pavlova and Sikorskaya (2020) and Kashyap et al. (2021).

> 6MSCI also provides other indexes, such as Small Caps, Value, and Growth indexes, that might differ in their composition from the Standard Indexes.

> 7Colombia is part of the MSCI All Country World Index, the MSCI Emerging Markets Index, and the MSCI EM Latin America, among other indexes. When a Colombian stock is announced to be included into or excluded from the Standard Indexes, this recomposition affects all of these indexes. Our sample includes 10 additions and 8 deletions. Stock ticker

4
nouncement date, which usually happens around mid-month, and the date when the rebalancing is made effective, which is the last trading day of the month, and thus occurs 11 to 17 days after the announcement. Also, the MSCI quarterly reports provide information on the benchmark weight (the relative weight) of each stock in each index.

To compute elasticity estimates with the conventional methods used in the literature, we collect from the MSCI website information about the AUM tracking the MSCI Emerging Markets Index (MSCI EM) and the MSCI All Country World Index (MSCI ACWI). Since these data are provided only for June 2015 and November 2016, we complement them with data from the EPFR Global Fund Flows database. This database covers a subsample of the population of mutual funds and ETFs and provides information on the benchmark indexes they track. For both indexes, we compute the ratio of the AUM reported by MSCI relative to those resulting from EPFR in each of the two periods for which we have data from both sources. Then, we compute the median coverage ratio for each index and multiply it by the AUM in EPFR to infer the total AUM benchmarked against the indexes.<sup>8</sup> Finally, to measure the AUM of passive funds and ETFs benchmarked against the indexes, we rely on EPFR data only, which has an extremely good coverage of the population of such funds. At the end of 2016, the Investment Company Institute (ICI) reported total assets for ETFs worldwide of 3.5 trillion dollars, which is also the total assets under management for ETFs in EPFR database.

# **2.2 The Colombian Stock Exchange**

The BVC runs like a standard electronic central limit order book. Trades are submitted via authorized broker-dealers registered at the exchange and buy and sell orders meet via an automated trading system. In contrast to fragmented markets in the United States and Europe, the BVC is the sole authorized trading venue for Colombian stocks, which means that we can observe the universe of transaction of Colombian stocks and avoid biases from incomplete reporting (e.g., from multiple trading venues such as multilateral trading facilities, dark pools, or from rival exchanges). Also, at the time of each addition/deletion, none of the stocks in our sample had dual listings, nor were they traded through global depositary receipts. Thus, all the transactions around rebalancing events, and hence, any change in ownership for stocks in our sample are reported in the BVC trading records.

symbols and announcement dates for each episode are given in Appendix Table OA1.

8We apply the ratio for the MSCI Emerging Markets Index also to the MSCI EM Latin America Index and the MSCI EM Colombia Index.

5
The BVC proprietary data consist of all the transactions in Colombian stocks during the 2006-2017 period. The data contain detailed execution information, including a time stamp (to the second), price, direction, quantity, and the broker routing the trade.<sup>9</sup> Each transaction record has a unique investor identification number. In addition, the BVC classifies investors into three broad groups – domestic individuals, domestic institutions, and foreign investors.<sup>10</sup> The stock exchange further classifies domestic institutions into mutual funds, pension funds, non-financial corporations, brokers trading on their own accounts, and other institutions.

To obtain a more detailed classification of foreign investors we proceed as follows. For the exclusive purpose of this project, the BVC discloses the name of foreign institutions involved in the transactions. We search manually on the web and cross-reference the names with Factset Ownership – a database with extensive global coverage on institutional investors – and classify each foreign investor into one of the following groups: Active mutual funds, passive mutual funds, pension funds, exchange-traded funds (ETFs), hedge funds, government institutions (e.g., sovereign wealth funds and central banks), and investment firms. Other investors include foreign individuals, trust funds, and private endowments.

The BVC database has about 17 million records during our 12-year period. Domestic institutions represent over half of the traded value in domestic stocks. Consistent with international trends in cross-border portfolio investments (IMF, 2017), the presence of foreign investors in Colombia increases over time. The number of foreign investors rose from 324 in 2006 to almost 4000 at the end of 2017 and the share of total traded value by this group increased from 4.5% to 31.8%. In addition to the generalized growth of foreign flows to emerging markets after the 2008 global financial crisis, there are two key related events in Colombia in the period that contribute to explain the surge of foreign investors: (i) Colombian sovereign debt recovered its investment grade in June 2011, and (ii) in 2013, taxes on foreign investors’ earnings from domestic securities were reduced from 33% to 14%. Between 2012 and 2017, foreign mutual funds accounted for 7.8% of the total traded value, with investment banks, ETFs, and government funds representing each 5.2%, 3.5%, and 2.8% respectively (Table OA2, Panel A).

According to the annual statistics of the World Federation of Exchanges (WFE, 2019), at the end of 2017, Colombia had the fourth largest stock market in Latin

> 9Since February 2012, the market hours are synchronized with the New York Stock Exchange trading session, with a closing batch auction during the last five minutes of each trading day.

10In Colombia, there are no individual or aggregate ownership limits on foreign investors. Foreign individuals and institutions are allowed to either reinvest or transfer earnings such as dividends or capital gains with little restrictions.

6
America by market capitalization, and the fourteenth largest among developing countries. Relative to developed countries, the Colombian stock market is small – its size relative to the total value of U.S. listed companies at the end of our sample is 0.4%. However, MSCI indices typically include the largest companies and the most actively traded stocks in each country. The average market capitalization of our sample stocks is six times larger than the average size of other listed companies in Colombia. Similarly, the yearly traded value of our sample stocks is seven times larger than that of the other listed companies (Table OA2, Panel B). Moreover, in terms of market capitalization, the stocks in our analysis are similar the largest ten stocks in the Russell 2000 index – a group that has been extensively used to analyze many key question in finance, including the price impact of index recompositions, the role of institutional ownership on price informativeness, and the effect of passive investors on corporate decisions, among many others (e.g., Chang et al., 2014; Boone and White, 2015; Appel et al., 2016).

# **3 Empirical Analysis and Results**

We analyze three main issues related to equity index rebalancings. First, we measure the price impact of these episodes. Second, we analyze the behavior of investors in response to these episodes. Finally, we combine the information on prices and traded quantities to estimate the demand elasticity for stocks.

## **3.1 The price effect of index additions and deletions**

We measure the price impact of index additions and deletions by looking at the price dynamics of Colombian stocks included into or removed from MSCI international equity indexes. We calculate abnormal returns as the difference between the stock returns and the implied returns from a single factor model, _Rst − β_<sup>ˆ</sup> _sRt_<sup>_D/s_</sup> . The stock’s beta, _β_<sup>ˆ</sup> _s_ , is estimated using daily stock returns in the year prior to the addition/deletion event and the return of the COLCAP, a value-weighted index of the Colombian stock market. To avoid spurious correlation, we exclude the return of stock _s_ itself from the index, _Rt_<sup>_D/s_</sup> . Returns are measured in Colombian pesos in excess of the domestic deposit rate.<sup>11</sup> Figure 1, Panel A, depicts the average cumulative abnormal return (CAR) of stocks in our sample from 3 trading days before the announcement date onwards. Deletions are normalized to be additions by multiplying the CAR of removed

> 11We use the 90-day DTF rate, an interest rate composite, calculated as the weighted average of the interest rates on 90-day Certificates of Deposits offered by Colombian banks and institutions.

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stocks by -1.<sup>12</sup> CARs immediately increase after the announcement date, and they drift slightly upwards until the implementation date (since the implementation date varies across events, this is represented as a shaded area in the figure). We report detailed statistics about the price effect of the rebalancings in the first column of Table 1. In this case, CARs are computed from the day prior to the announcement date to the day of the actual index recomposition.<sup>13</sup> CARs range between 0.87% and 22.32%. The median CAR is 5.45%, while the average is 6.65% and is statistically different than 0 at the 1% significance level.<sup>14</sup> The average price impact of our 18 events is broadly in line with those found in previous studies. For example, Chang et al. (2014) find that inclusions into and deletions from the Russell 2000 have an average price effect of about 5%. This is particularly interesting as the market capitalization of stocks in our sample is close in magnitude to those in the sample by Chang et al. (2014). In a sample of almost 200 stock additions to the S&P 500, Wurgler and Zhuravskaya (2002) instead find the average CAR to be around 3%, which goes up to 5% when focusing on abovemedian demand shocks, that is, additions which are predicted to be associated with larger inflows because of the size of index funds tracking the index.

# **3.2 Investor behavior and traded quantities**

We now analyze the behavior of investors in response to the rebalancings in the MSCI Standard Indexes. As in the previous section, we pool together additions and deletions by considering sales as purchases, and vice versa, in case of deletions. Since MSCI indexes are mostly tracked by international investors, we start

> 12As shown in Chang et al. (2014), index additions and deletions have comparable price effects. Throughout the rest of the analysis we follow this approach and describe our results as if all events were additions.

> 13Since the number of days between the announcement and the implementation dates differ across episodes, the average CAR in Table 1 is slightly different than the one in Figure 1 (where we report the average CAR for each day after the announcement date).

> 14It is possible that the right asset pricing model differs across stocks in our analysis. As an alternative, we estimate abnormal returns using an international factor model with two factors following Bekaert et al. (2014) – a global factor and a domestic factor [ _Rt_<sup>_G, R_</sup> _t_<sup>_D/s_</sup> ]. The two factors are value-weighted market indexes, so that the model potentially embeds a global CAPM, a domestic CAPM, and the mixed case when both global and domestic markets affect the pricing of a particular stock. In this case, returns are measured in U.S. dollars in excess of the three-month U.S. T-Bill rate. The median and mean CAR of stocks in our sample computed using the mixed model are 5.21% and 6.28% respectively. Thus they are very close to the estimates we get with our baseline domestic, one-factor model. In Appendix Table OA3, we report all of our results obtained using the mixed two-factor model.

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our analysis by looking at the behavior of foreigners in response to the rebalancings. Figure 1, Panel B, provides a first graphical representation of these results. Specifically, it reports the cumulated fraction of outstanding shares bought by foreigners starting from 3 trading days before the announcement onwards, averaged across episodes. After the announcement date, there is a slight increase in foreign holdings, but most flows into affected stocks occur on the day when the rebalancing is made The granularity of our dataset allows us to dig even deeper into the behavior of investors, by looking separately at the behavior of different classes of both foreign and domestic investors around the rebalancing period. Figure 2, Panel A, depicts the total fraction of outstanding shares bought by different classes of foreign investors. All classes of foreign investors, except for hedge funds, purchase shares of stocks added to MSCI indexes. The main difference across investor types is the timing of their portfolio adjustments. Not surprisingly, passive mutual funds and ETFs are those who buy more shares on the actual implementation date and trade very little between the announcement and the implementation. Active mutual funds tend to start adjusting their portfolios already when the rebalancing of the index is announced, possibly to minimize the price impact of their orders. Perhaps more surprisingly, there are different types of investors besides passive funds and ETFs that trade significantly on the implementation date, suggesting ‘implicit’ mandates to follow their benchmark indexes. Panel B, instead depicts the behavior of domestic investors in response to the rebalancings. What is remarkable in this case is that all domestic investor types take the opposite position of foreigners after the rebalancing, thus essentially absorbing their demand (supply) of newly included (deleted) stocks. Interestingly, domestic brokers that could also act as arbitrageur, do not take particularly large positions on the opposite direction of foreign investors.

We next look specifically at the trades that are driven by the willingness of foreigners to mimic the indexes, _i.e._ , the rebalancing-driven demand shocks, which we will use also to compute elasticities in the following section. In fact, not all foreign investor trades may necessarily be due to the index rebalancing _per se_ . Some of them could be due to speculative reasons: for instance, while overall all investor classes rebalance in the direction of the indexes, some investors within each class might also trade in the opposite direction. Thus, in order to measure the specific trades of foreign investors replicating the index, we first look only at the subsample of those who increase their holdings of newly included stocks in the period that goes from the announcement to the implementation – Figure 2, Panel C – and then on those who only do so in the implementation date – Figure 2, Panel E. The latter, in particular, are the investors who most likely trade for 9
purely passive motives.<sup>15</sup> The figure that emerges in both cases is very similar to that in Panel A, except for two groups: investment firms and investors classified as Others (i.e., foreign individuals, trust funds, and private endowments). It seems that while some investors in these groups passively mimic the indexes, others take the opposite position, possibly to speculate on the events.

Quantitative details about investors’ demand shocks are presented in Table 1, Panel B, columns 2 through 4. Specifically, we report the total shares purchased by investors tracking the index relative to the total number of outstanding shares, _i.e._ , ∆ _Q/Q_ , computed in different ways. Column 2 presents descriptive statistics for the total purchases of shares between the announcement and implementation date by all foreign investors trading in the direction of the index. On average, foreign investors that trade in the direction of the index buy 3.21% of the outstanding shares of the stock, with a median of about 2.7%. Column 3 reports the foreign purchases on the implementation date only. These are precisely the trades that are most likely due to investors’ willingness to replicate the index composition. Foreign investors trading in the direction of the index during the implementation date purchase on average 2.37% of the shares outstanding, the median being 2.0%. That is, 74% of foreigners’ net flows take place precisely on the implementation day of the index rebalancing. In Column 4, we also include domestic investors that trade in the direction of the index on the implementation date. Estimates are very similar to those obtained considering only foreign investors. This piece of evidence is particularly important as it corroborates the view that MSCI indexes are mostly followed by international investors.

We also want to quantitatively compare the actual rebalancing of foreign investors to those one would obtain following the conventional methodologies used in the index rebalancing literature – those that exploit the AUM of funds benchmarked against the indexes. For this, we compute: where _j_ indicates the index the stock is being included into (removed from), _MCAPi_ is the market capitalization of the stock _i_ , _wj_<sup>_i_isthebenchmarkweight</sup> (the relative importance of stock _i_ in index _j_ ) after being included into the index, and _AUMj_ indicates the AUM benchmarked against index _j_ . Consistent with previous studies, we make two assumptions to compute these estimated inflows. We assume that either all funds tracking the indexes rebalance their portfolios

> 15In Figure 2, Panels D and F, we complement this evidence by focusing on domestic investors who sell (buy) newly added (deleted) stocks from the announcement to the implementation date, and on the implementation date, respectively.

10
accordingly ( _k_ = _Total_ ), or that only passive funds do so ( _k_ = _Passive_ ), and present summary statistics for these inflows in columns 5 and 6 of Table 1, Panel A, respectively. The assumption that all funds rebalance leads to a median estimated inflow (relative to market capitalization) of 16.9%, while using only passive funds implies an inflow of 0.94%. Overall, using all AUM benchmarked against the indexes largely overestimate inflows. Using passive AUM on the other hand, generates closer estimates to the actual flows in our sample. Yet, these estimates are still less than 50% than the actual observed flows.

There are several reasons that might explain why using all AUM benchmarked against the indexes systematically overestimate the inflows. An important one is that while many active investors rebalance their portfolio following index redefinitions, not all of them do so. More importantly, active AUM are typically much larger than passive AUM. In our sample, among foreigners trading in the direction of the index on the implementation day, passive funds and ETFs purchase 0.87% of the outstanding shares of newly included stocks, while other investors purchase 1.50% of them. Thus, the inflows from non-passive investors are 1.73 times those from other investor classes, while those estimated using the AUM would imply ‘active’ inflows to be 17 times larger than the ‘passive’ ones.

# **3.3 The price elasticity of demand for stocks**

Because of their features, index rebalancing episodes offer an ideal framework to estimate the slope of stock demand curves, as we do in this section. We start with the theoretical framework developed by Gabaix and Koijen (2020) to flesh out how we estimate this elasticity. Even though their analysis focuses on macro-elasticities – on the effects of flows from bond to equity markets and vice versa – the main insights from their model can be applied to our setting. The key assumptions that generate large price impacts of inflows in Gabaix and Koijen (2020) are: i) bond/stock funds have strict mandates which prevent them from freely adjusting their portfolios into other asset classes; ii) hedge funds are too small to arbitrage demand shocks. We can apply this framework to our setup by considering instead of bond/equity funds, a framework with equity funds that track different benchmark indexes.<sup>16</sup> Under this small change, both assumptions seem to find support in our data. First, different investors seem to mimic index composition by rebalancing their portfolio accordingly. Moreover, they mostly do so on the

> 16While it is true that stocks are more likely to have closer substitutes, and therefore micro-elasticities should in principle be smaller than macro-elasticities, we argue that, consistent with the evidence we provide in the previous section, several equity funds face ‘implicit’ mandates on their portfolio composition similar to those of bond and equity funds.

11
implementation date rather than when inclusions or deletions are announced. Second, hedge funds (and domestic brokers) appear to take the opposite position with respect to other international investors, but their positions are small especially if compared to those taken by the rest of investors.

The model by Gabaix and Koijen (2020) fits very well our empirical setting for another key reason: in their model, expected exogenous inflows generate immediate price impacts, even when actual inflows are expected to materialize later in time, exactly as we observe in our data. In their model, the price effect of expected future inflows is given by the following expression: where _ρ_ is the effective discount rate, _fT_ is the inflow (relative to the size of the market) that is expected to happen at time _T_ and _ξ_ is the demand elasticity for the stock.<sup>17</sup> Under this framework, a permanent and anticipated inflow – such as those implied by index additions (or deletions) on the implementation date – generates an increase in the price on the date the inflow is expected – the announcement date, in our setting – and a drift from the announcement to the implementation date, consistent with our findings. Furthermore, Gabaix and Koijen (2020) predict the price change to be permanent, which is also something that appears to be true in our context. The overall price impact of the expected inflow, from the announcement until the implementation, is therefore given by _pT ≡_<sup><u>∆</u></sup> _P_<sup>_<u>P</u>_</sup> =<sup>_<u>f</u>_</sup> _ξ_<sup>_<u>T</u>_.Thus,bringingthissettingtoourdata,onecouldmeasurethe</sup> elasticity of demand for the included/excluded stocks, _ξ_ , from the price impact and the expected inflows.

Of course, we do not observe ‘expected inflows’ but rather the realized ones. Yet, we can reasonably proxy for expected rebalancing-driven inflows by taking the quantity of shares purchased (sold) by foreigners on the effective inclusion (exclusion) date. These are indeed the trades that are most likely entirely due to funds being replicating the index composition – different than those occurring in the days between the announcement and the implementation, which may be due to speculative reasons as well – and can be anticipated by market participants. More specifically, we compute _fT_ as ∆ _Q/Q_ from Table 1, Panel B, column 3.

Then, we calculate the change in stock prices between the day preceding the announcement and the closing price of the implementation day. The elasticity is calculated dividing _fT_ by<sup><u>∆</u></sup> _P_<sup>_<u>P</u>_.ResultsfromtheseestimatesaregiveninFigure3</sup> for each event and summarized in Table 1, Panel B, Column 3. The elasticity of

> 17 _pt_ refers to the price impact at time _t_ relative to a baseline price before any shock is announced. In our empirical setup, we consider this baseline to be the stock price before the announcement date.

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demand for stocks in our sample ranges between -3.27 and -0.01, with a median of -0.34. The average elasticity is -0.67 – larger in absolute value than the median because of few stocks whose demand is much more elastic than the rest of the sample (as displayed in Figure 3). When considering the purchases occurring between the announcement and the implementation date (Column 2 in Panel B), the estimated elasticity becomes larger (in absolute value) but still close to the baseline value in Column 3. That is because most inflows materialize on the implementation date. Similarly, estimates do not change much when including also purchases by domestic investors, as very few domestic investors rebalance their portfolios in the direction of the indexes (Column 4 in Panel B).

Our results show that the demand for stocks is particularly inelastic, contrary to the prediction of traditional asset pricing models, such as the CAPM. To illustrate how our estimates relate to previous studies, we calculate the elasticity of each event using inferred flows (as opposed to actual flows) based on conventional methods from the index rebalancing literature. To be precise, we calculate the change in quantities, Equation 1, using both the total AUM benchmarked against the indexes, and the AUM of passive funds only, _i.e._ , _k_ = _{Passive, Total}_ . We combine these changes in quantities with the change in prices to obtain a range of inferred elasticities. The findings are reported in Figure 3 and Table 1, Panel B, columns 5 and 6. The key result is that our baseline elasticity – computed using actual transaction data – is much closer to the elasticity obtained under the assumption that only passive funds rebalance their portfolios in response to index recompositions. Using all AUM benchmarked against a given index tends to overestimate (in absolute value) the elasticity of stock demand curves, much more than using only passively managed assets seems to underestimate this elasticity.<sup>18</sup> Finally, we compare our estimates with the ones from recent literature for the United States using Russell Indexes. Chang et al. (2014) report an average elasticity of -1.5 using the assumption that all investors rebalance, and an elasticity of -0.46 when only passive funds rebalance. Our elasticity estimate, slightly be-

> 18Of course our estimate of the demand elasticity also relies on some assumptions. That is, we focus on foreign flows on the effective date and price changes from announcement to implementation. We replicate the estimation using the change in shares bought by all investors from the announcement to the implementation – considering both foreigners trading in the index direction and domestic investors doing so and obtain a median elasticity of -0.56. We also re-estimate our baseline elasticity but using the change in price only at the announcement date and obtain a median elasticity also of -0.56. This number increases (in absolute value) to -0.59, when we consider the change in shares by all investors and the change in price at the announcement date only. All in all, all of these estimates are close to our baseline one, and much smaller (in absolute value) than the estimated elasticity one would get using the total AUM of funds benchmarked against the indexes.

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low this number, is for a different market and thus is not directly comparable to United States estimates. However, one can use a back-of-the-envelope calculation to provide a more precise elasticity estimate between the two bounds reported by Chang et al. (2014). From Table 1, we find that the median elasticity measured using traded quantities for foreign investors is -0.34, which is 1.62 times larger (in absolute value) than the one we obtain under the assumption that only passive funds rebalance. We can apply this factor to the lower bound elasticity estimate in Chang et al. (2014), to obtain an estimated elasticity of -0.74. Interestingly, in a recent paper, Pavlova and Sikorskaya (2020) estimate, using quarterly portfolio data, for the United States, how many active funds might be behaving as passive when rebalancing as a consequence of changes in Russell indexes. With that strategy, they find an estimated stock demand elasticity for the United States of -0.7, remarkably close to our back-of-the-envelope calculation. Overall, our estimations can be used to back out more precise measures of stock demand elasticities for different markets when data on traded quantities is unavailable.

# **4 Conclusion**

In this paper, we exploit transaction-level data from the Colombian stock market together with episodes of stock additions and deletions from major international equity indexes to shed novel light on the price impact of equity index rebalancings, the behavior of investors around these events, and the elasticity of demand for stocks.

A key takeaway from our analysis is that most large international investors do rebalance their portfolios in the direction of the rebalancing of the indexes they follow. This is consistent with the view that many investors, even when formally active, have ‘implicit mandates’ not to deviate from their benchmark indexes. Instead, arbitrageurs, such as hedge funds, trade very little around these events. As a result, stock demand curves are very inelastic.

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