metadata: authors: 0: author: Afanador,Juan Pablo
1: author: Davis,Richard Mark
2: author: Pedraza Morales,Alvaro Enrique
count: World
docna: 0: docna: Estimating the Gains from International
            Diversification : The Case of Pension Funds
docty: Policy Research Working Paper
subtopic: Social Funds and Pensions,Capital Markets and Capital Flows,Capital Flows,Non Bank Financial Institutions,International Trade and Trade Rules,Financial Sector Policy,Adolescent Health
teratopic: Social Protections and Labor,Finance and Financial Sector Development,International Economics and Trade,Health, Nutrition and Population
abstracts: cdata!: For pension funds, international assets
            represent an opportunity to improve their returns while
            possibly reducing risks. Nonetheless, pension funds in many
            developing countries face regulations that limit the choice
            of international investments. This paper proposes a new
            methodology to estimate the gains from international
            diversification in which the optimal asset allocation of
            pension funds is constrained by financial frictions. The
            empirical strategy is applied to the aggregate holdings of
            pension funds in a large group of countries to calculate the
            gains from increasing the current level of exposure to
            international securities. The methodology should give policy
            makers the opportunity to identify jurisdictions where
            pension funds could benefit the most from expanding their
            foreign holdings.
repnme: repnme: Estimating the Gains from International
            Diversification : The Case of Pension Funds
display_title: Estimating the Gains from
            International Diversification : The Case of Pension Funds
listing_relative_url: /research/2021/04/33012511/estimating-gains-international-diversification-case-pension-funds
topicv3: Pension Funds m1326066 611,Trade m1326924 698,Financial Sector Development m1327681 1920,Aging m1504792 3491,Coronavirus (COVID-19) m1939478 4828
publishtoextweb_dt: 2021-04-20T00:00:00Z
dois: 10.1596/1813-9450-9635
historic_topic: Social Protections and Labor,Finance and Financial Sector Development,International Economics and Trade,Health, Nutrition and Population
origu: Development Research Group (DECRG)
no_of_pages: 57
author_keys: 0: author_key: 1621214
1: author_key: 1321207
model_extractions: Policy Research Working Paper 9635 Estimating the Gains from International Diversification The Case of Pension Funds _Juan Pablo Afanador Richard Davis Alvaro Pedraza_ Finance, Competitiveness and Innovation Global Practice & Development Economics Development Research Group April 2021
Policy Research Working Paper 9635

# **Abstract**

For pension funds, international assets represent an opportunity to improve their returns while possibly reducing risks. Nonetheless, pension funds in many developing countries face regulations that limit the choice of international investments. This paper proposes a new methodology to estimate the gains from international diversification in which the optimal asset allocation of pension funds is constrained by financial frictions. The empirical strategy is applied to the aggregate holdings of pension funds in a large group of countries to calculate the gains from increasing the current level of exposure to international securities. The methodology should give policy makers the opportunity to identify jurisdictions where pension funds could benefit the most from expanding their foreign holdings.

This paper is a product of the Finance, Competitiveness and Innovation Global Practice and 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 rdavis4@worldbank.org and apedrazamorales@worldbank.org.

_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
# **Estimating the Gains from International Diversification: The Case of**

# **Pension Funds**

Juan Pablo Afanador<sup>1</sup> Richard Davis<sup>2</sup> Alvaro Pedraza<sup>3</sup>

## **JEL Classification:** G11, G15, G23

**Keywords:** Pension funds, international diversification.

> 1 <u>juanafmo@unisabana.edu.co, Universidad de la Sabana.</u>

2 <u>Rdavis4@worldbank.org. Senior Financial Sector Specialist, World Bank</u> 3 <u>apedrazamorales@worldbank.org. Research Economist, World Bank</u> We have benefited from the comments of Bryan Gurhy, Davide Salvatore Mare, Gabriel Petre, Andrius Skarnulis and Fiona Stewart. We acknowledge financial support from _FIRST INITIATIVE_ – Project: International Diversification of Pension Funds _._
# **1. Introduction**

What is the appropriate asset allocation between domestic and foreign securities for pension funds? Increased access to financial markets across the globe has provided expanding opportunities for individuals and institutional investors to diversify their portfolios. While it has been widely recognized that cross-border diversification offers significant advantages,<sup>4</sup> there is ample evidence that most investors do not exploit such opportunities, as they allocate a relatively large fraction of their wealth to domestic securities; the so-called “home bias.”<sup>5</sup> According to the Capital Asset Pricing Model (CAPM), the workhorse of modern portfolio theory, holding of foreign assets should be inversely proportional to the size of the domestic market in the world portfolio. Since developing countries represent only a small fraction of the world’s market capitalization, the optimal allocation of domestic investors in these countries should be largely skewed towards foreign assets; up to 100% of portfolio investments exclusively in foreign assets. For pension funds, such extreme allocations are likely unfeasible or impractical,<sup>6</sup> whether the country’s pension system is defined-benefit or defined-contribution, centrally or individually managed, publicly or privately managed, mandatory or voluntary. To the extent that estimates of the benefits of international diversification are calculated relative to the theoretical prescription of the CAPM, such gains might be either misleading or largely exaggerated. To promote useful policy actions in these countries, one needs proper estimates of the benefits from increasing the exposure to international securities.

> 4 For example, see Grubel (1968), Levy and Sarnat (1970), Solnik (1974), Grauer and Hakansson (1987), Eldor, Pines, and Schwartz (1988), DeSantis and Gerard (1997), among many others.

> 5 Home bias in portfolio holdings has been documented for mutual funds (Chan et al., 2005), individual investors (Lewis, 1999), and in both high income and developing countries (Pedraza et al. 2019).

> 6 One reason for this impracticality may be the exclusion from this analysis of any non-financial returns associated with domestic investment, such as the promotion of domestic social goals.
In this paper, we propose a new methodology to estimate the gains from international diversification in which the optimal asset allocation of pension funds is constrained by financial frictions. We apply our empirical strategy to the aggregate holdings of pension funds in a group of 49 countries (19 developed and 30 developing) to calculate the gains from increasing the current (or last reported) level of exposure to international securities.

The intuition of our strategy can be explained as follows: Using the asset allocation of pension funds between 2002 and 2019 for a group of 77 countries, we estimate as a benchmark the “natural” level of foreign exposure, that is, the expected level of foreign holdings for pension funds operating in a country with a particular level of financial market development, integration to international markets, and where the pension system characteristics, such as its total size, size of contributions among other observables, are considered. Notably, the benchmark rate is not a first best (optimal) allocation – specifically, it is not normative. Instead, it might be interpreted as a peer benchmark, providing a pragmatic view of what is possible elsewhere. We then use portfolio optimization techniques to calculate the maximum gains that a pension fund operating in a given country can achieve if it increases its level of foreign exposure to the benchmark rate. We refer to this analysis as the constrained optimization problem and compare the findings to a setting where financial frictions play no role. The latter case denotes the scenario where pension funds can achieve the maximum allocation suggested by standalone portfolio optimization.

To be more precise, we use the latest reported portfolio holdings in domestic equity, domestic debt, foreign equity and foreign debt, by all the pension funds operating in a specific country. Following the well-known approach of Black and Litterman (1992), we estimate the expected returns and risk (i.e. standard deviation of returns) of an investor domiciled in the country with unhedged foreign positions. We then estimate the maximum expected returns if the investor increases her foreign assets to the benchmark rate, maintaining the current level of risk. The increase in returns are precisely the gains from augmenting the foreign exposure to the natural level that is given by macro and financial variables. Overall, the analysis presented in this paper
can be applied to any pension system, public or private, that is not purely pay-as-you-go.

We find that the potential gains from increasing the foreign holdings in pension systems under the benchmark rate are similar for both high-income and developing countries; 0.08% of additional returns per month or close to 1.00% per year. Although such gains appear to be modest at first glance, over a 40-year accumulation timeframe for a pension fund the compounded impact of such an increase is powerful. Further, there are significant variation across countries. For example, among developing countries, pension funds in Brazil, Indonesia, Kenya, Thailand, and Turkey could increase their expected returns by over 150 basis points per year if they were to reach their respective benchmark level of foreign holdings. This level of prospective improvement in average annual returns would provide very significant benefit for the pension funds in these countries. As in many parts of the world, some of these same countries are experiencing rapid aging across broad segments of the population and their funded pension systems are not producing the level of returns needed to provide an adequate level of retirement income in future years. The combination of rapid aging and scheme inadequacy is an emerging crisis for funded pension systems. This opportunity of increased returns could aid not only private funded pension systems but funded portions of public systems that will bear even more of the burden of rapid aging and system inadequacy.

We also use our methodology to examine the evolution of foreign holdings over time and the gains or losses from changes in international securities in the pension funds’ portfolios. For instance, in Mexico, up until 2013, the international allocation of pension funds was mostly in line with the estimated natural rate of foreign exposure (as the pension system based on definedcontributions and individual capitalization accounts matured, so did the portfolios’ exposure to international securities). After 2013, there were no further increases in the relative exposure to foreign assets. According to our estimates, the lack of further growth in the share of foreign assets represented a loss in the expected forward-looking returns of over 90 basis points per year in the next six years. While quantitative limits on foreign assets were not binding during these years (set at 20% by local authorities), lack of access to international mutual funds due to regulatory
restrictions appear to have discouraged management companies to further boost their participation in international markets, due to the added costs of direct foreign holdings.

Overall, our methodology provides a simple measure to compare across countries, evaluate current limits on foreign securities, and examine the dynamical allocation of pension funds to foreign assets.

The rest of the paper is organized as follows. In section 2, we review the literature that presents the common arguments in favor and against international diversification by pension funds. Section 3 describes the data used in the analysis. In Section 4, we examine how foreign holdings of pension funds have evolved over time and estimate the benchmark rate of foreign holdings. Section 5 presents our empirical methodology and main findings. Section 6 concludes.

# **2. Pension systems and the case for international diversification**

There are several explanations for the existence of home bias in portfolio investments. These include: (i) hedging motives in frictionless financial markets, that is, real exchange rate and nontradable income risk (Stockman and Dellas, 1989; Wheatley, 2001), (ii) higher asset trade costs in foreign markets (such as transaction costs, differences in tax treatments between national and foreign assets or differences in legal frameworks), (iii) informational frictions (Brenan and Cao, 1999; Portes and Rey, 2005; Leuz et al., 2010; Pedraza et al., 2020) and (iv) behavioral biases (Bailey et al., 2011; Riff and Yagil, 2016). While disentangling the contribution of each motive on the bias towards domestic assets is difficult, it is well-known that portfolio investments in foreign markets are influenced by market development in both the source and target countries, by investor familiarity with each market as suggested by common language, bilateral trade flows, and both geographic and cultural proximity (Chan et al, 2005). Such factors could be viewed as proxies for a behavioral bias toward familiar investments, but these might also operate as proxies for market access, information asymmetries, and market imperfections (Froot and Ramadorai, 2008; Aluquerque et al., 2009).
In addition to the above explanations for home bias in the investment literature, pension funds often face other restrictions that limit the amount of international assets in their portfolios (Raddatz et al., 2013; Pedraza, 2015). The public or mandatory nature of these funds often promotes a regulatory framework that constrains the exposure to foreign securities (Morales et al., 2017). Quantitative restrictions are used to limit the amount of international investments with the general idea that other assets perceived to be less risky will better protect the pensions of their participants, but there are also additional arguments that might call for stringent limits on international securities. First, policy makers might desire to keep domestic savings invested in the home country to support local development goals. If the social return of domestic investments is higher than the private returns of pension funds, the state would aim to target higher levels of home bias. Such argument, however, requires the presence of additional market frictions. For instance, when market integration is low, it might be more expensive to raise funds from international investors than from domestic ones, generating a wedge between domestic and foreign sources of financing (Menil 2005). While this goal might be well-intentioned, it usually involves a subordination of the welfare of pensioners in favor of a domestic development goal in the situation where the two goals are at odds. These same pensioners may be helped indirectly by such domestic development, but they would be disproportionately bearing the cost for it.

Second, if hedging currency risk is expensive, then the currency denomination of the liabilities becomes important. All else equal, having large domestic currency liabilities (as the pension funds do) would argue for positive home bias. Another reason behind reluctance to allow non-domestic investment is a desire to avoid currency exchange rate volatility within the investment portfolio (Thomas et al., 2014). The logic behind this reasoning is that the ultimate pension liability will be in domestic currency, so the investments ought to similarly be priced in domestic instruments. However, some investments (as an example, equity over the long term) may even benefit from the dynamics of foreign exchange volatility when considered holistically as part
of the broader volatility of these investments over many years. Further, many domestic equity markets are overly concentrated (i.e., few issuers in a small group of industries), and the inclusion of non-domestic holdings may allow much broader sectoral diversification that more than offsets the near-term currency mismatch (Cetorelli et al., 2007).

Finally, differences in risk perception between domestic and foreign assets, especially between domestic and foreign government bonds, can significantly affect the portfolio allocation. For instance, while fixed rate bonds issued by the sovereign are subject to interest rate risk and default risk, from the point of view of a domestic pension fund, the default risk might be negligible. The argument is that a default by the sovereign is often preceded or accompanied by a takeover of the pension system. In other words, from the perspective of the domestic fund, rather that realizing losses from a default by the local government, a default would entail an absorbing state in which the private pension industry is nationalized. For any other investor (e.g., a foreign investor), the default probability implies a potential loss. Such difference in risk perception creates a gap between the holdings of domestic vis-à-vis foreign pension funds, generating a rational overweighting of domestic government bonds for the former group. As part of this final point, it is worth mentioning that absolute levels of interest rates for domestic government bonds likely also play a role in willingness of the domestic market to diversify; with those markets enjoying relatively high rates usually less willing to enact such a change.

In contrast to the arguments against international diversification for pension fund assets, the portfolio selection theory has shown extensive evidence that portfolio risk can be reduced significantly by investing in international stocks (Solnik, 1995), and has documented that global portfolios provide a substantial risk-return improvement (Michaud et al. 1996; Laster 1998; Clarke and Tullis 1999; Grinblatt and Keloharju 2001). Importantly, in developing countries where the domestic financial sector might be too small, local markets might not provide the amount of financial assets required by rapidly growing pension funds (Chan-Lau, 2005). To the extent that
some pension funds are large relative to their domestic financial markets, an over-reliance on local assets could distort asset prices, as allowable domestic securities in the pension portfolio would experience abnormal demand (Pedraza & Pulga, 2019). Moreover, ownership concentration is often associated with low trading activity in secondary markets and to mispricing (Leaño & Pedraza, 2018; Pedraza, 2019).

Finally, the recent COVID-19 shock has brought to the forefront the importance of international diversification due to liquidity motives. There is anecdotal evidence that pension funds in Chile, Colombia, and Peru disproportionally sold foreign securities to meet (expected) sudden withdrawal demand from account holders or to meet collateral requirements in derivative holdings. Such access to liquidity would have been prohibitively expensive in their relatively small domestic markets.<sup>7</sup> An increasing concern also related to COVID-19, however, is that that domestic

> 7 Documented from interviews with local authorities in these countries and with fund managers.
pension funds may be targeted by authorities to finance increasing levels of public debt. Policy makers in countries with little fiscal space might promote home bias to support increased public assistance spending resulting from the COVID-19 lockdowns (Stewart, Davis & Knaack 2021 forthcoming).

In line with arguments in favor of international diversification, foreign exposure of pension funds has increased over the last two decades, from 16% of assets in 2002, to 36% by the end of 2019 (data and details in Section 3). However, such systematic increase in international exposure has been uneven, with pension funds in many countries displaying little or no change. Taken as a whole, whether through regulatory imperative or behavioral tendencies to avoid international investment, many pension funds around the world are delivering less than their full potential and exhibiting much higher volatility than necessary given their lack of international diversification. This is occurring despite what is generally a building crisis in adequate pension provision in many countries –mainly due to the rapid aging happening across the world, coupled with what have been some unsustainable parametric design features for existing schemes. Given the magnitude of this unfolding dilemma, it will be important for funds to consider better incorporating the benefits of international diversification and regulators to reconsider restrictions that have shortchanged many systems at the likely future cost to their members.

Most of the financial literature investigating home bias takes the perspective of a US investor. Research on home bias outside of the US is scarce and, if available, does not explain the dynamics of home bias in mature markets. Because the gains from international diversification vary considerably across markets, there is room to study home bias in other markets. In this sense, the pension industry offers an invaluable opportunity to further explore the determinants of home bias. The availability of multi-asset data in many pension jurisdictions with a sufficiently long horizon provides the opportunity to study the cross-sectional variation in domestic bias in the
portfolio choices of institutional investors over time and across asset classes.

# **3. Data**

We use data from two main sources. First, we use information from the Global Pension Statistics Project administered by the OECD which covers funded and private pensions components of pension systems across the world. Between 2002 to 2019, the data set provides country-year coverage of pension assets, including data on domestic and international holdings disaggregated by asset class (e.g., equity vs. fixed income assets). In recent years, the GPS data set has added new countries to its coverage. We use an unbalanced panel of 77 countries for a total of 853 country-year pairs. Second, we collect country data on financial and economic development from the World Development Indicators (WDI). We use information on financial integration, measured as foreign direct investment inflows, currency account, and the existence of a common currency (e.g., for euro zone countries). Other variables capture capital market development, such as the total market capitalization of the domestic stock market and trading volume, as well as economic development, including GDP per capita and GDP growth (Table A.1 includes a list of countries and summary statistics for each variable).<sup>8</sup> 8 We also collect, for a subsample of countries in Latin America –Chile, Colombia, and Peru – detailed portfolio information from local pension supervisory authorities. The data set includes comprehensive security-level information covering the entire portfolio composition of pension funds in these countries. The data set is useful as it provides a clear picture of the type of assets that pension fund managers are using to access international markets, and to compare how these relate to domestic security selection.
# **4. International allocation of pension funds**

Pension assets are a large component of global capital markets and have grown in size over the last two decades (Figure 1). Although total pension assets reached $48.1 trillion at the end of 2019, the growth has not been constant over time and it has been mostly uneven across countries. For example, while pension contributions peaked in 2005, these declined after the 2008 Global Financial Crisis (GFC) and have not reached pre-crisis levels since (Figure 2). Following the drop in contributions, and exacerbated by lower portfolio valuations during the GFC, pension assets experienced a decline in size relative to global GDP between 2008 and 2011. After 2012, global pension assets experienced modest growth, rising from 25% to 30% of GDP at the end of 2019.

According to the OECD Global Pension Statistics, during the last 20 years, pension funds across the world have significantly increased their share in foreign holdings. In 2002, pension funds had 16% of their portfolio allocated to international investments. Foreign exposure rose consistently in the next two decades, reaching 36% of total assets by 2019 (Figure 3). Although the level and pace at which pension funds have increased their foreign assets vary across regions, the data suggests that over time, pension funds systematically gain exposure to international assets (see Figure 4). For example, while pension funds in ECA and MENA countries had almost no foreign exposure in 2002, the share of foreign assets grew to 11% and 20% respectively by 2019. We find similar patterns in Latin America, Western Europe and East Asia and Pacific regions.

**Figure 1.** Pension assets

**Figure 2.** Pension funds’ contributions
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operation for a sample of 15 countries operating DC pension schemes.<sup>9</sup> Figure 5 provides two sets of related evidence. First, consistent with the overall sample, as pension funds are more established and their assets grow, they increase their international holdings over time. The pattern is interesting because it reveals a natural convergence towards foreign assets that depends on the development stage of each system. For instance, by 2019, the share of foreign assets of Colombian pensions was 33%. While this is significantly smaller than Chilean pension funds in that same year (42% of foreign holdings), the benchmark in the region, the Colombian number is actually above that of Chile if we count from the first year of operation of the system (24 years since the introduction). Importantly, such analysis is useful because it allows us to identify countries with pension assets are under the trend even after controlling for maturity. For instance, within Latin America, Mexico lags its peer countries in foreign exposure with 10% of assets in its 21st year of operation.

Figure 5 also provides a clear distinction between the levels of foreign holdings across countries. In the upper section of the figure (highlighted in a box) are countries under common currency regimes. In these countries, pension funds allocate a large fraction of their portfolio to non-domestic assets. For example, pension funds in the Slovak Republic, where the euro has been the official currency since 2009, hold more than 50% of their assets in foreign securities during most years in the sample. On the contrary, in countries without common currency regimes, such as Romania, Costa Rica, Mexico, Peru, Chile, and Colombia, foreign holdings are significantly

> 9 These countries are Bulgaria, Chile, Colombia, Costa Rica, Croatia, Estonia, Latvia, Lithuania, Mexico, Nigeria, North Macedonia, Peru, Poland, Romania, and Slovak Republic.
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represents countries in which the variable takes the lowest (highest) values. Consistent with previous findings, foreign holdings by pension funds are larger in countries where cumulative assets represent a greater share of GDP, where yearly contributions are a higher share of GDP, and in countries with common currency regimes. For example, while foreign holdings account for 21% of total assets in countries with the lowest level of yearly contributions (quartile 1), in countries where contributions are the highest, foreign holdings are on average 37% of the pension portfolio.

**Table 1.** Average of foreign holdings sorted by variables of interest

|||**Foreign Holdi**|**ngs (Average)**||
|---|---|---|---|---|
||**Q1 **|**Q2 **|**Q3 **|**Q4 **|
|Pension Funds’ Assets as % of GDP|17%|29%|26%|31%|
|Contribution as % of GDP|21%|25%|24%|37%|
|Common Currency|15%|||60%|
|Current Account as % of GDP|21%|22%|30%|28%|
|FDI as % of GDP|25%|21%|26%|29%|
|GDP Growth as % of GDP|25%|29%|26%|20%|
|Market Capitalization as % of GDP|18%|19%|24%|24%|
|Stocks Traded (Value) as % of GDP|19%|16%|20%|25%|
|Portfolio equity, net inflows (current US)|25%|27%|22%|27%|
|Bills and Bonds as % of Total Assets|34%|34%|26%|11%|
|Short Term Assets as % of Total Assets|23%|26%|27%|30%|
|Mutual Funds Assets as % of Total Assets|8%|17%|32%|44%|

Source: OECD and WDI. Authors’ calculations.

The results have several potential explanations. On the one hand, it is possible that when pension portfolios become large, as inflows from new contributions drive asset accumulation, they grow too large relative to domestic financial markets; in effect domestic opportunities are insufficient. Large institutional investors often also face disproportional transactions costs, particularly those that operate in illiquid markets. In such cases, in order to mitigate the negative price-impact from portfolio transactions in local securities, fund managers are ‘pushed’ to accommodate inflows towards foreign assets, potentially into more liquid markets. At the same time, it is possible that the positive correlation between the size of contributions and foreign holdings is spurious. For example, if countries with more developed financial systems have a higher savings rate, a larger exposure to foreign assets may arise because of the availability of
securities that provide foreign currency hedging, mitigating the exchange rate risk derived from international holdings. To evaluate the correlation between contributions, fund size, and other related variables with the share of foreign investments, we perform a parametric analysis as follows.

We estimate the share of foreign assets in country _c_ in year _t_ as follows: cc,tt yy + γ + λ (1) cc,tt cc tt cc,tt cc,tt cc,tt yy = αα + δδ + εε where the vector of controls includes measures of economic development (GDP growth and cc,tt GDP per capita), financial integration (foreign direct investment flows, current account balance, γγ and a common currency identifier), and stock market development (market capitalization and trading volume). Following our previous discussion, and to capture potential variation in levels given the different cohorts in which different pension reforms were introduced, we include country-fixed effects . Also, to account for systematic shocks in different years of the sample, cc such as the GFC, we add year-fixed effects. αα Our methodology examines the extent to which different characteristics of the pension industry are related to foreign holdings, once we control for other observables in the country. cc,tt In addition to including pension fund size relative to the domestic economy and the yearly level of λλ contributions in , we include the explicit regulatory limit (if applicable) of foreign holdings for cc,tt each country-year pair. The variable takes values between 0 and 1 capturing the maximum allowed λλ level of foreign exposure set by local by regulatory authorities.

The variables that capture financial integration explain most of the variation in the share of foreign holdings ( = 0.52). In particular, pension funds in countries with common currency have on average 37% more foreign holdings than other pension funds. The three variables that capture RR<sup>2</sup> pension fund characteristics explain 27% of the variation in foreign assets. As expected, countries where regulatory authorities set a higher limit in foreign exposure do in fact maintain a larger share
in foreign assets. The evidence also confirms previous findings whereas systems in which contributions represent a larger share of GDP tend to invest more actively in international markets. Interestingly, after controlling for economic development and financial integration, we find a negative correlation between the domestic market capitalization and foreign holdings. This finding confirms the idea that in smaller markets, when pension assets are large relative to the domestic equity market, they tend to allocate more funds internationally.

To summarize, to the extent that pension funds are growing in size, especially in countries where the population is still young and in the accumulation stage, there is consistent growth in the share of foreign assets. Currency risks seems to be a limiting factor driving the disproportional allocation towards domestic assets. Another common driver of home bias are information asymmetries, since investors are expected to be more familiar with local conditions, and thus tend to overinvest locally. As funds grow, however, and driven by push and pull factors documented above, economies of scale imply that the average cost of information acquisition about foreign markets declines over time.
**Table 2.** Determinants of foreign holdings

||**Predicted**<br>|**Economic De**<br>**Variab**<br>|**velopment**<br>**les**<br>|**Financial In**<br>|**tegration**<br>|**Stock M**<br>**Develo**<br>|**arket**<br>**pment**<br>|**Pension**<br>**Characte**<br>|**Funds**<br>**ristics**<br>|**All**<br>|<br>|
|---|---|---|---|---|---|---|---|---|---|---|---|
|**Variable Name**|**Sign**|Coeff.|t-stat|Coeff.|t-stat|Coeff.|t-stat|Coeff.|t-stat|Coeff.|t-stat|
|_CONSTANT_||0.530***|**(2.647)**|0.164***|**(17.07)**|0.193***|**(13.15)**|0.0132|**(0.642)**|0.545*|**(1.736)**|
|_GDPGROWTH_||-1.449***|**(-3.288)**|||||||-0.453|**(-0.803)**|
|_LOGGDPCONSTANT_||-0.00929|**(-1.221)**|||||||-0.0164|**(-1.456)**|
|_FDINETINFLOWS_||||-0.0868|**(-0.592)**|||||-0.243**|**(-2.261)**|
|_CURRENTACCOUNTB_||||0.125|**(1.052)**|||||-0.238|**(-1.474)**|
|_CURRENCYDUMMY_||||0.372***|**(17.21)**|||||0.248***|**(7.685)**|
|_MARKETCAP_||||||-0.0172|**(-0.995)**|||-0.0671***|**(-3.294)**|
|_STOCKSTRADED_||||||0.0736**|**(2.195)**|||-0.0427|**(-1.186)**|
|_LIMIT_||||||||0.292***|**(9.666)**|0.0568*|**(1.950)**|
|_PASPGDP_||||||||0.00818|**(0.139)**|0.367***|**(5.904)**|
|_CONTRIBUTION_||||||||2.536***|**(2.857)**|0.281|**(0.308)**|
|_._<br>Adjusted R^2||**0.097**||**0.522**||**0.113**||**0.269**||**0.648**||
|Observations||474||474||315||310||184||

# **Robust t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1**

This table reports results from panel regressions of the share of foreign pension holdings on contemporaneous variables. These variables include GDP growth rate, GDP per capita, net flows of foreign direct investments, current account balance, domestic market capitalization, trading volume (% of market cap) and a dummy that takes the value of one when the country is in a common currency regime and zero otherwise. Pension fund variables include the allowable limit of foreign holdings set by local regulatory authorities, the size of the pension portfolio (total assets/GDP) and the yearly contributions normalized by GDP. We correct for heteroskedasticity and autocorrelation in errors by using Newey and West (1987) standard errors computed with the optimal number of lags according to Newey and West (1994). Foreign holdings span the period 2002 to 2019.
# **5. Measuring the gains of foreign exposure**

This section introduces a quantitative model of international asset allocation with financial frictions. The objective is to present a quantitative estimation of the gains from international diversification. The methodology is applied to the countries for which data have been compiled by OECD.

# **5.1. Model**

We measure the value of global diversification as the degree to which allowing foreign assets into a portfolio raises the optimal portfolio frontier. That is, to what extent can a portfolio manager increase her expected returns for a given level of risk when more international securities are included in the portfolio.

An efficient frontier is constructed from _expected_ returns and an estimate of the covariance matrix of returns. There are, however, some limitations to using this measure. First, expected returns are often proxied by realized average returns from a sample period. While such proxy is commonly used due to its simplicity and availability, it is widely known to lead to highly concentrated portfolios and input sensitivity, leading to overestimation in the gains from diversification.<sup>10</sup> Second, the methodology assumes that there are no extra costs to international investments; thus relaxing the constraint against foreign holdings cannot make the investor worse off.

> 10 The ex post frontier derived from realized returns describes the portfolio of precisely the investor who correctly predicted the realized returns on each asset. In turn, when realized returns are used to proxy for expected returns the optimal portfolio will tilt toward those assets that generated the best opportunities in the past, largely overestimating the returns per unit of risk from holding those assets.
To deal with these concerns, we use an equilibrium concept from the international capital asset pricing model (ICAPM) to input expected returns in the construction of the efficient frontier. Furthermore, we account for potential frictions –those that might limit domestic pension fund managers from reaching the unconstrained level of international diversification– by estimating a benchmark level of foreign holdings according to each country’s financial integration.

We start with the unconstrained portfolio optimization. Consider a model of portfolio choice with N assets of a pension fund located in country _c_ . A number F of these are foreign assets and N-F are local. For example, the foreign assets might include fixed-income and equity securities in international markets. For each asset _i_ , we estimate its beta from a regression of realized excess returns on the world portfolio returns measured in domestic currency of country _c_ (i.e., from the point of view of an investor domiciled in country _c_ ), − r (R − r (2) ii,tt,cc tt,cc ii,cc ii,cc tt,cc tt,cc ii,tt,cc rr = αα + ββ RR ) + εε where r is the risk-free rate. We obtain the expected excess return on each asset by tt,cc multiplying the estimated beta of the asset by the world portfolio expected excess return; or in vector notation = β ]. Using the expected returns and the variance-covariance cc cc cc cc ππ EE[R RR − r matrix of the N assets Σ, the portfolio optimization problem is simply the selection of the vector of weights that maximizes the expected returns for a given level of risk. To be precise, assuming cc that the current asset allocation of a pension fund manager in country ww _c_ is 0, we want to find the portfolio that maximizes the expected returns, maintaining the variance of the current portfolio ww ( Σw0). More formally, 0 0 σσ<sup>2</sup> = ww<sup>′</sup>
In this mean-variance setting, the gains from international diversification can be measured in absolute terms as the difference between the expected returns of the optimal portfolio and those that form the current allocation, π. Alternatively, we can measure the additional ww<sup>∗</sup> TT expected returns in units of risk wwπ −<sup>∗′</sup> π − ww <mark>wT π)/(w</mark><sup>′</sup> <mark>T ΣwT</mark> )<sup>1/2</sup> ; which represents the associated (ww<sup>∗′′′</sup> increase in the portfolio’s Sharpe Ratio.

# **5.2. Including financial frictions**

According to our discussion in the previous section, frictions which typically affect the allocation of domestic managers include information frictions, capital shortages, and portfolio adjustment costs. For instance, to the extent that national savings are small in a country that is not fully integrated with international markets, there might be a social cost from replacing the exported capital when pension funds invest abroad. Similarly, even in the case when a pension fund manager recognizes the benefits from international diversification, portfolio adjustment costs would slow the reallocation toward foreign assets. In such cases, a manager would avoid rebalancing their portfolio by selling domestic securities and thus generating a downward pressure in domestic asset prices, and instead buy new securities abroad with new contributions or from dividend payments from its investments. Portfolio ‘inertia’ is likely stronger in less competitive markets even if restrictions on foreign assets are lifted.

To account for the role of these financial frictions, we estimate the expected level of foreign exposure in country c in year _t_ , , , using the country’s economic development, financial cc tt integration and pension system characteristics according to equation (1) in Section 3. That is, yyβ , , , . We refer to , as the “natural” share of foreign exposure, which is the cc tt cc tt cc tt cc tt yyβbenchmark rate that we use to compare to the current level of foreign holdings. For instance, a = γγβγγ + λλλλ yyβ
country with observable characteristics described by and , where the total share of foreign cc,tt cc,tt assets in the pension’s portfolio is below , , is said to be underexposed to foreign aγγ λλ ssets –with cc tt foreign holdings under the natural level. yyβ Our objective is to include a restriction based on idiosyncratic factors measured at the country level which effectively constrains the sum of foreign holdings F to that level, ∑ λλ ii=1<sup>ωωii ≤ yyβcc,tt. Using this additional restriction in the portfolio selection problem (equation 3),</sup> we calculate the maximum expected returns and measure the gains relative to the current portfolio. In sum, our strategy estimates the efficient frontier when the maximum level of foreign assets is obtained from macro and financial factors in each country (e.g., size of pension industry and yearly contributions, portfolio FDI, GDP growth, common currency regime, etc.). Effectively, we are limiting the potential gains for international diversification to the benchmark level of foreign assets at any given point in time. For any point in time _T_ , the step-by-step methodology is summarized as follows:

- i. For each country _c_ and asset _i_ pair, calculate monthly returns in local currency from the first period with information 0 up to _T-1_ . That is, for _t_ ={ 0, 1, ..., _T_ -1}

- ii. For each country _c_ and asset tt _i_ pair, estimate equation (2) using the returns of the world tt tt portfolio in local currency (R ). That is, estimate betas for each asset _s_ and country _c_ . tt,cc

- iii. Calculate the variance-covariance matrix RR Σ using local currency returns in each country cc

- iv. Estimate expected returns using = β ] cc cc cc

- ππ EE[R RR − r cc

- v. Use pension fund holdings in country _c_ at time _T_ to calculated current returns π and TT

- portfolio variance ww<sup>′</sup> TT TT

- vi. Use portfolio maximization (equation 3) to obtain the unconstrained optimal portfolio ww<sup>′</sup> Σww TT

- ww<sup>∗</sup>
vii. Calculate the benchmark share of foreign holdings for country c at time _T_ : , , + cc TT cc TT yyβ = γγβγγ , cc TT viii. λλUse portfolio maximization to obtain constrained optimal portfolio with benchmark λλ holdings <mark>∑</mark><sup>λλ</sup> <mark>i=1</mark> , : ii cc TT ωω ≤ yyβ wwβ<sup>∗</sup> TT ix. Compare gains of excess returns from current holding to constrained and unconstrained holdings.

# **5.3. Assets**

We based our analysis on four asset classes: domestic stocks, domestic fixed income assets, world stocks, and world bonds. This will be sufficient to consider the potential role of international assets in the investment portfolio, though in reality the pension fund may have a chance to invest more broadly in assets such as real estate, infrastructure projects, corporate bonds, private equity, inflation-protected bonds, hedge funds, options, derivatives, and more narrowly defined international investments involving particular sectors or regions.<sup>11</sup> Data is available through the beginning of 2020 for 49 countries, though the starting dates differ for countries, ranging from 2000 to 2010. For each country, we use the longest time period in which all the necessary data could be collected. The local bond and stock returns are calculated as the monthly percent change in local currency above the inflation rate for the major bond and equity indices respectively. Monthly excess returns are calculated relative to the domestic short-

> 11 For example, a potential benefit of international diversification is drawdown mitigation for the pension fund in periods when the domestic equity market is having a meltdown (which typically coincides with a real GDP crisis for the country, lower ability of the sponsors to meet pension contributions, currency depreciation, etc.). In those periods developed market assets and in particular USD denominated assets tend to outperform when translated in domestic currency terms. In such cases, there might be disproportionate benefits from having a specific type of international exposure as opposed to a generalized approach focused on global market indices. Whether such extreme scenarios would deliver more concentrated foreign holdings is left for future study.
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Finally, to calculate the market risk premium , − r ], we assume a constant cc cc parameter of risk aversion for all countries in our sample, EE[R RR, and use the variance of the world portfolio returns =0.14% in USD such that − rλλ = 3 = 0.41%. While it has been cc cc well-established that risk aversion coefficients vary across countries (Gandelman & Hernández- σσ<sup>2</sup> EE[R RR ] = λλσσ<sup>2</sup> Murillo; 2015), from the perspective of a domestic investor, the curvature of the efficient frontier will not be affected by the estimate of the world portfolio excess return. A higher estimate will simply shift the curve upward. Since our gains from diversification are estimated in relative terms, such levels will not affect our quantitative results.

# **5.4 Results**

Table 3 presents our main findings. For each country, the table reports the share of foreign holdings as of December 2019, the expected monthly returns and portfolio standard deviation. The table also presents the optimal unconstrained asset allocation, and the optimal allocation when the benchmark level of foreign holdings is introduced. For ease of exposition, high income and developing countries are presented separately and sorted by the potential gains from reaching the benchmark rate of international diversification.

As previously noted, by the end of the sample period, pension funds in developing countries have on average lower exposure to foreign assets – 26% of their total assets relative to 38% among high-income countries. However, according to the optimal portfolio model, pension funds in developing countries are precisely the ones that would benefit the most from increasing their international exposure. Using the estimates from the unconstrained model, a mix of 73% of assets invested in foreign equity and 11% of foreign debt securities would represent an average gain in monthly excess returns of 0.3% (5.9% per year in excess of the risk-free asset). Such gains are up to three time larger than the potential gains of pension funds in high-income countries if
these were to reach their unconstrained level of foreign exposure: 59% in equity and 18% in debt securities. As expected, the unconstrained model generates extreme outcomes, where pension funds are better off (in risk-return terms) under exclusive foreign exposure. The outcome is most common among developing countries. For example, in Brazil, Indonesia, Thailand, Turkey, and several others, the optimal portfolio is composed by 100% investments in international stocks.

The benchmark share of foreign holdings introduces a natural upper bound to the exposure in foreign assets, anchoring the gains from international diversification. Importantly, since this benchmark is associated with variables that capture the level of financial development and financial integration, it is precisely lower for developing countries (24% on average) relative to high-income countries (39%). In practical terms, by using this natural rate we avoid generating portfolios with extreme outcomes, and the potential gains from international diversification are, in addition to being determined by the covariance structure of the assets under considerations and their expected returns, benchmarked relative to the current level of domestic market development.

According to the table, at the end of 2019, the potential gains relative to the natural rate of foreign holdings are similar for both high-income and developing countries –0.08% of excess returns per month or close to 1.00% per year. We ranked countries relative to these potential gains as of December 2019. By using the model with the benchmark holdings, we avoid holdings that might be unrealistic given the current size of the pension industry in each country. Considering the example of Costa Rica, we can read the full table as follows: By December 2019, given the actual aggregate holdings of pension funds in the country (87% in local assets and 13% of foreign holdings), the expected excess monthly returns of the portfolio are 0.08%, with an expected standard deviation of 2.1% per month. An optimal unconstrained portfolio of foreign assets would be constituted by 58.8% of international equity and no foreign debt holdings. Such portfolio is
expected to yield 0.4% returns in excess of the risk-free asset per month. In addition, the estimated benchmark level of foreign holding is 21.8%. For that ratio of foreign holdings, an optimal portfolio would yield 0.18% of returns, a net gain of 0.10% relative to the current level of holdings (1.16% per year).

Some interesting trends should be highlighted. For pension funds in Latin America, those in Brazil, Mexico, and Costa Rica would benefit the most from increasing their current levels of foreign holdings. For pension funds in Chile, Colombia, and Peru their current levels of foreign holdings appear to be in line with the optimal allocation.<sup>12</sup> According to our findings, several developing countries in our sample from Eastern Europe and Central Asia are under-exposed to international securities and could significantly improve their risk-return profile by increasing their foreign assets. These include Turkey, Hungary, Poland, the Russian Federation, Serbia, and Ukraine.

> 12 Of note, the negative values for a few countries at the bottom of each portion of Table 3 do not indicate “too much” international diversification for those countries but rather international diversification somewhat ahead of trend. Recall the benchmark is not normative but rather based upon existing trends.
# **Table 3.** Gains from international diversification

||**Cu**|**rrent holdin**|**gs**||**Optim**|**al portfolio**||||**Benchmark**||
|---|---|---|---|---|---|---|---|---|---|---|---|
||Forein|||||<sup>Forein</sup>|||Foreign|||
|Country|g<br>Holdings<br>%|Expected<br>returns|Std.<br>Deviation|International<br>Stocks|International<br>Bonds|<sup>g</sup><br>Holdings<br>%|Expected<br>returns|Gains<br>(returns)|<br>Holdings<br>%|Expected<br>returns|Gains<br>(returns)|
|Iceland|29.0%|0.15%|2.3%|49.9%|19.2%|69.1%|0.4%|0.2%|56.3%|0.35%|0.20%|
|Malta|0.0%|0.10%|2.3%|68.0%|9.9%|77.9%|0.5%|0.4%|32.3%|0.30%|0.20%|
|United Kingdom|30.0%|0.33%|2.9%|92.1%|3.8%|95.9%|0.63%|0.3%|34.2%|0.50%|0.16%|
|Luxembourg|30.0%|0.37%|2.5%|73.5%|4.7%|78.1%|0.5%|0.1%|60.5%|0.48%|0.12%|
|Israel|20.0%|0.27%|2.7%|98.7%|0.4%|99.1%|0.6%|0.4%|27.7%|0.36%|0.09%|
|Germany|46.0%|0.37%|2.2%|57.5%|16.6%|74.1%|0.4%|0.1%|46.6%|0.40%|0.03%|
|Canada|37.0%|0.29%|1.6%|39.1%|13.7%|52.8%|0.3%|0.0%|32.2%|0.31%|0.02%|
|Netherlands|88.0%|0.39%|2.2%|47.4%|24.6%|72.0%|0.4%|0.0%|87.8%|0.39%|0.00%|
|Switzerland|41.0%|0.28%|2.0%|36.4%|37.3%|73.7%|0.32%|0.0%|40.1%|0.28%|0.00%|
|Norway|30.0%|0.34%|2.2%|56.3%|13.5%|69.8%|0.5%|0.1%|20.8%|0.34%|-0.01%|
|Finland|69.0%|0.37%|2.1%|44.4%|31.6%|76.0%|0.4%|0.0%|57.3%|0.36%|-0.01%|
|Denmark|43.0%|0.32%|2.1%|50.5%|18.5%|69.0%|0.4%|0.1%|23.7%|0.31%|-0.01%|
|Italy|62.0%|0.37%|2.2%|44.5%|36.9%|81.4%|0.4%|0.0%|56.5%|0.35%|-0.02%|
|Mauritius|33.0%|0.15%|1.7%|43.6%|27.9%|71.5%|0.3%|0.2%|20.7%|0.11%|-0.04%|
|New Zealand|50.0%|0.29%|1.7%|42.4%|7.3%|49.7%|0.3%|0.0%|23.0%|0.23%|-0.06%|
|Portugal|69.0%|0.34%|2.0%|41.2%|38.4%|79.6%|0.36%|0.0%|58.3%|0.28%|-0.06%|
|**Average **|**42.3%**|**0.3%**|**2.2%**|**55.3%**|**19.0%**|**74.4%**|**0.4%**|**0.1%**|**42.4%**|**0.3%**|**0.039%**|
||**Cu**|**rrent holdin**|**gs**||**Optim**|**al portfolio**||||**Benchmark**||
||Foreign<br>|Expected|Std.|International|International|<sup>Foreign</sup><br>|Expected|Gains|Foreign<br>|Expected|Gains|
|Country|Holdings<br>%|returns|Deviation|Stocks|Bonds|Holdings<br>%|returns|(returns)|Holdings<br>%|returns|(returns)|
|Brazil|4.0%|-0.12%|5.8%|100.0%|0.0%|100.0%|0.6%|0.7%|17.8%|0.10%|0.22%|
|Jamaica|9.0%|0.01%|3.1%|97.9%|2.1%|100.0%|0.6%|0.6%|24.4%|0.16%|0.15%|
|Thailand|1.0%|0.18%|3.7%|100.0%|0.0%|100.0%|0.63%|0.4%|18.9%|0.34%|0.15%|
|---|---|---|---|---|---|---|---|---|---|---|---|
|Indonesia|0.0%|0.07%|4.6%|100.0%|0.0%|100.0%|0.6%|0.6%|16.8%|0.21%|0.14%|
|Turkey|1.0%|-0.09%|6.1%|100.0%|0.0%|100.0%|0.63%|0.7%|12.8%|0.05%|0.13%|
|Hungary|1.0%|0.11%|4.0%|100.0%|0.0%|100.0%|0.6%|0.5%|14.6%|0.24%|0.13%|
|Kenya|3.0%|0.19%|3.9%|100.0%|0.0%|100.0%|0.6%|0.5%|14.6%|0.32%|0.13%|
|Poland|1.0%|0.11%|3.2%|100.0%|0.0%|100.0%|0.63%|0.5%|17.0%|0.24%|0.12%|
|Pakistan|0.0%|0.11%|3.9%|100.0%|0.0%|100.0%|0.65%|0.5%|16.5%|0.22%|0.11%|
|Serbia|0.0%|0.21%|4.0%|100.0%|0.0%|100.0%|0.65%|0.4%|18.4%|0.31%|0.11%|
|Ukraine|0.0%|0.13%|6.2%|100.0%|0.0%|100.0%|0.64%|0.5%|12.3%|0.23%|0.10%|
|Costa Rica|13.0%|0.08%|2.1%|58.8%|0.0%|58.8%|0.4%|0.3%|21.8%|0.18%|0.10%|
|Croatia|13.0%|0.22%|2.7%|83.8%|4.8%|88.6%|0.6%|0.4%|23.4%|0.31%|0.09%|
|Zambia|7.0%|0.03%|3.6%|37.0%|8.7%|45.8%|0.28%|0.2%|17.7%|0.11%|0.08%|
|Mexico|13.0%|0.23%|2.8%|79.4%|1.2%|80.6%|0.6%|0.4%|19.1%|0.30%|0.07%|
|Czech Republic|16.0%|0.24%|3.0%|89.4%|2.2%|91.6%|0.6%|0.4%|19.2%|0.29%|0.05%|
|South Africa|22.0%|0.21%|2.4%|40.5%|19.4%|59.9%|0.35%|0.1%|27.8%|0.25%|0.03%|
|North Macedonia|28.0%|0.23%|3.3%|100.0%|0.0%|100.0%|0.6%|0.4%|21.6%|0.26%|0.03%|
|Nigeria|12.0%|0.09%|4.3%|56.6%|20.7%|77.3%|0.5%|0.4%|12.9%|0.12%|0.03%|
|Romania|23.0%|0.24%|3.5%|100.0%|0.0%|100.0%|0.64%|0.4%|18.4%|0.27%|0.03%|
|Estonia|86.0%|0.37%|2.1%|53.4%|18.1%|71.5%|0.4%|0.0%|61.7%|0.39%|0.02%|
|Slovak Republic|75.0%|0.31%|1.9%|43.0%|23.0%|66.0%|0.32%|0.0%|58.8%|0.32%|0.01%|
|Slovenia|61.0%|0.32%|2.0%|39.0%|34.5%|73.5%|0.35%|0.0%|58.6%|0.32%|0.00%|
|Peru|44.0%|0.26%|2.2%|72.3%|19.6%|91.9%|0.47%|0.2%|21.8%|0.26%|-0.01%|
|Latvia|81.0%|0.34%|1.9%|41.9%|33.7%|75.6%|0.4%|0.0%|58.9%|0.30%|-0.04%|
|Chile|45.0%|0.24%|1.6%|27.0%|23.2%|50.2%|0.3%|0.0%|31.1%|0.19%|-0.05%|
|Lithuania|79.0%|0.36%|2.0%|41.4%|35.3%|76.6%|0.4%|0.0%|59.1%|0.30%|-0.05%|
|Colombia|34.0%|0.18%|1.6%|32.7%|17.0%|49.8%|0.3%|0.1%|21.5%|0.12%|-0.05%|
|Bulgaria|58.0%|0.31%|2.0%|57.0%|18.8%|75.8%|0.4%|0.1%|20.9%|0.19%|-0.12%|
|**Average **|**25.2%**|**0.2%**|**3.2%**|**74.2%**|**9.7%**|**83.9%**|**0.5%**|**0.3%**|**26.1%**|**0.2%**|**0.088%**|
# **5.5 Measuring portfolio gains over time**

The analysis in the previous section is useful to identify in the cross-section, countries where pension funds would benefit the most from increasing their current exposure to foreign assets. We also use the methodology to study the evolution of foreign holdings over time and the gains or losses from changes in international securities in the pension funds’ portfolios. In other words, in addition to examining the most recent snapshot based of pension holdings, we also evaluate how different pension funds have improved or worsened their investment profile over time. The methodology follows the one described in subsection 5.2, but instead of using information from the most recent portfolio of pension funds, we calculate past returns up to the measurement period, covariances, and systematic risk relative to the world market.<sup>13</sup> To be precise, for a country _c_ , we calculate the optimal unconstrained portfolio using the variance-covariance matrix and CAPM model (equation 2) from asset returns from the first data point to the 0,cc observation month (requiring at least 60 months with continuous data). The benchmark tt share of foreign assets , is estimated based on the country observables for each corresponding month, and cc TT it is then used to calculate the constrained optimal portfolio. yyβ To illustrate how we use of our model in the time series, we present complete yearly findings for three selected countries: Mexico, Romania, and Slovenia. In Figure 7-Panel A, we compare the actual level of foreign holdings relative to the “natural” level from 2007 to 2018. In Panel B, we estimate the gains in excess returns for the unconstrained and constrained portfolio relative to the actual portfolio in each year.

> 13 We perform our analysis for country-time pairs with at least 60 months of prior return data.
In Mexico, starting in 2010, pension fund management companies (AFORES for their Spanish acronym) were authorized to invest up to 20% of their assets under management in foreign securities. Interestingly, while these institutional investors quickly raised their foreign exposure following the relaxation of the foreign limit –international holdings grew from 7% to 13% between 2010 and 2013 – further increases in foreign exposure stopped after 2013. Overall, AFORES do not seem to have taken fully advantage of the benefits from additional exposure to foreign assets. In fact, the constraint model suggests that had AFORES continued to increase their share in foreign assets following 2013, to a level of up to 19% (the benchmark level), pension portfolios would have received an additional 1.00% of yearly forward-looking excess returns. Note that such returns are not realized returns, but instead, these are expected returns calculated at the end of each year.

One potential explanation for the slowdown in the rate that funds added foreign assets, might be related to regulatory constraints. Before 2018, AFORES were not allowed to invest in international mutual funds. Notably, as we documented in section 4, this is the preferred investment instrument to access foreign securities among pension fund management companies in the region. Lack of access to international mutual funds might limit an AFORES’ ability to enhance, due to the added costs of direct holdings in international markets. A key remaining question is whether the most recent investment regulation, which among other conditions, authorized multiple international holdings in mutual funds starting in 2019 would yield better outcomes in the following years. We should continue our country surveillance to assess the gains from new asset classes, and to examine whether such exposure is at a pace that is closing the gap from the current level of underexposure.

In addition to Mexico, we use our model to estimate the time profile of foreign holdings and gains/losses from diversification in Romania. As the mandatory funded pillar has grown in
size since its introduction in 2008, pension portfolios have largely concentrated in domestic assets, and in particular, in government bonds. One possible reason may be the relative return guarantee requirements in the system based on fund averages that encourage conservative and broadly similar investment behavior. This level of concentration has come at the opportunity cost from investing in well-diversified international portfolios, rendering lower than expected risk-adjusted returns during 10 consecutive years. The case in Romania is also interesting for another reason; domestic debt, measured from the point of view a local investor, is the riskiest among the countries in our sample (Figure 7-Panel B). More precisely, Romanian fixed-income securities, which are mostly government bonds, have the highest beta relative to the world portfolio in our sample. In turn, domestic pension funds have high systemic risk, to the extent that the unconstrained optimal portfolio is a fully international portfolio, with no domestic securities. While such portfolio allocation is likely unfeasible, both from practical and political reasons, it underscores the nature of the losses in terms of risk and return from maintaining single digit share of assets under management in foreign securities. The low returns come at the backdrop of an already small level of contributions, which was reduced from 5.1% to 3.75% starting in 2018.

Finally, we present the case of Slovenia. Similar to other common currency countries, the benchmark level of foreign holdings is high throughout the sample period, between 45 and 59 percent. Nonetheless, after 2013, pension funds have significantly increased the share in foreign assets. Such gains narrowed the difference between the optimal and the actual level of portfolio returns. According to the Central Bank, most foreign holdings are equity ETFs and mutual funds focused in developed markets, particularly in the euro area.
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# **5.6 Limitations**

Our approach examines only the asset side, whereas pension funds need to model assets in relation to their future liabilities and the risk characteristics of those liabilities (Blake, 2000). Compared to our approach of using only assets, the asset-liability approach considers asset allocation with respect to the time horizons and risks of the liabilities which will be funded. We do not use this approach, because it requires a full actuarial model for future pension obligations, and because the pension systems in many developing countries are still young with mostly longterm liabilities. In this case, the differences between the two approaches should be minimal. Indeed, it is for pension systems with short-run funding needs where the two approaches may produce material differences.<sup>14</sup> Second, the benchmark rate that we introduce is not a normative level of foreign holdings. This measure is an estimate to prove a reference based on peers’ experience. In other words, it might still be optimal to further increase the exposure to foreign assets beyond the benchmark rate with potential gains to pension portfolios. For our setting, the estimated level of foreign exposure is useful as it provides and feasible level or anchor to which current policy could be compared.

# **6. Conclusions**

For a policy maker, Table 3 provides a straightforward illustration of the magnitude of opportunity for their country from liberalizing international pension investment rules in relationship to others.

> 14 As a related point, lifecycle funds, which represent current best approach for incorporating liability aspects into investment design for defined contribution plans, benefit significantly from being able to incorporate international investments. Typically using only domestic equity assets is difficult.
We recognize that there are many other considerations that policy makers must evaluate when deciding on possible liberalization of such rules, such as a desire to maximize funding of domestic growth. While we discuss other likely causes of resistance to international diversification, given the magnitude of the rapid demographic aging dynamics that are causing unprecedented strain on scheme finances, it becomes increasingly difficult to ignore the levels of opportunity illustrated by our analysis.

In terms of practical advice for policy makers looking to take action on international diversification, we would suggest the following broad principles. First, any change envisioned should be implemented gradually, ideally in a way that is triggered automatically perhaps based upon size of pension assets relative to size of the economy or based upon a combination of more than one of the major variables discussed above. Secondly, progress should be tracked, perhaps against the opportunity as portrayed in Table 3, with a goal of closing any opportunity gaps vs. the wider benchmarks. Finally, implementation should be encouraged in a manner suitable to the capabilities of the funds investing overseas. Specifically, as is apparent from the LAC examples in Appendix B and the Slovenia case, countries that have higher levels of international pension fund investing are often achieving this via international mutual funds, and in many cases indexed funds. This type of lower cost instrument is likely most suitable to pension funds new to international investing and should be encouraged.

# **6. Bibliography**

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Maginn, D. L. Tuttle, D. W. McLeavey, & J. E. Pinto, Managing Investment Portfolios: A Dynamic Process (págs. 230-327). Hoboken, New Jersey, USA: John Wiley & Sons.

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**APPENDIX A.**

# **Table A.1 Summary statistics by country**

|**Country**|**_Year on_**<br>**_Sample_**|**_Previous mayor_**<br>**_pension reform_**|**_For_**|**_eign Holdi_**|**_ngs_**|**_GDP_**<br>**_GROWTH_**|**_LOGGDP_**<br>**_CONSTANT_**|**_FDINET_**<br>**_INFLOWS_**|**_CURRENT_**<br>**_ACCOUNTB_**|**_CURRENCY_**<br>**_DUMMY_**|**_MARKET_**<br>**_CAP_**|**_STOCKS_**<br>**_TRADED_**|**_LIMIT_**|**_PASPGDP_**|**_CONTRI-_**<br>**_BUTION_**|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
||First<br>Last|Year|Min|Max|Mean|Mean|Mean|Mean|Mean|Value|Mean|Mean|Mean|Mean|Mean|
|_Albania_|2011 2018||0,0%|0,0%|0,0%|2,3%|23,3|8,5%|-9,6%|0|||30,0%|0,1%|0,0%|
|_Armenia_|2014 2018|2018|11,4%|30,4%|24,8%|3,6%|23,2|2,6%|-3,9%|0|||40,0%|1,3%|0,5%|
|_Brazil_|2011 2018||0,1%|0,4%|0,2%|0,3%|28,5|3,6%|-2,5%|0|39,8%|28,9%|8,8%|12,1%|0,4%|
|_Bulgaria_|2001 2018|2002|0,0%|58,2%|28,8%|3,6%|24,6|9,2%|-5,7%|0|16,6%|2,6%|100,0%|5,8%|1,0%|
|_Canada_|2000 2018||20,5%|37,1%|29,2%|2,0%|28,1|3,0%|-1,0%|0|116,2%|79,2%|95,0%|64,1%|2,5%|
|_Chile_|2002 2018|1981|15,9%|45,1%|35,8%|3,9%|26,1|7,1%|-0,4%|0|105,7%|15,4%|67,9%|61,2%|3,6%|
|_Colombia_|2001 2018|1994|4,5%|34,5%|16,5%|4,0%|26,3|3,8%|-2,7%|0|47,4%|5,4%|36,7%|15,3%|1,7%|
|_Costa Rica_|2007 2018|2000|1,5%|12,7%|5,6%|3,9%|24,4|6,1%|-4,4%|0|5,3%|0,1%|50,0%|11,8%|1,3%|
|_Croatia_|2014 2018|2002|9,2%|13,3%|11,7%|2,2%|24,8|3,6%|3,5%|0|38,1%|0,8%|100,0%|24,8%|1,7%|
|_Czech_||||||||||||||||
|_Republic_|2001 2018||4,4%|16,1%|12,5%|2,0%|26,0|4,5%|-2,0%|0|16,0%|9,3%|100,0%|6,0%|0,8%|
|_Denmark_|2001 2013||25,5%|42,7%|33,4%|0,9%|26,5|0,9%|4,2%|0|52,7%|26,4%|91,1%|36,1%|0,6%|
|_Estonia_|2001 2018|2002|28,2%|85,9%|74,4%|2,5%|23,7|6,8%|-2,5%|1||5,2%|100,0%|7,7%|1,2%|
|_Finland_|2002 2008||1,9%|69,3%|43,2%|2,7%|26,2|5,6%|4,9%|1|97,5%|94,1%|100,0%|58,5%|9,6%|
|_Germany_|2000 2008||5,7%|46,1%|25,2%|1,4%|28,8|1,8%|3,8%|1|45,1%|63,4%|44,0%|4,0%|0,2%|
|_Guyana_|2015 2018||21,1%|30,6%|24,2%|||||0||||6,8%|0,3%|
|_Hong Kong,_<br>_China_|2001 2018|2000|0,0%|80,2%|53,1%|||||0||||30,4%|3,1%|
|_Hungary_|2002 2009|1998|0,0%|0,7%|0,4%|-0,4%|25,6|16,9%|-4,7%|0|18,0%|16,0%|100,0%|8,9%|1,4%|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|_Iceland_|2008 2018||23,2%|29,1%|25,1%|1,8%|23,4|0,3%|-2,3%|0|||100,0%|134,8%|6,8%|
|_Indonesia_|2017 2018||0,0%|0,0%|0,0%|5,1%|27,7|2,0%|-1,6%|0|51,3%|9,1%|100,0%|1,8%|0,2%|
|_Israel_|2001 2018||0,0%|19,9%|9,0%|3,3%|26,1|3,6%|2,4%|0|72,6%|26,5%|95,0%|40,8%|2,0%|
|_Italy_|2014 2018||46,9%|62,1%|52,7%|1,0%|28,4|0,8%|2,1%|1|||100,0%|7,2%|0,6%|
|_Jamaica_|2012 2018||5,2%|9,5%|7,7%|0,6%|23,3|5,0%|-5,5%|0||2,1%|20,0%|24,8%||
|_Kenya_|2008 2009||2,3%|3,5%|2,9%|1,8%|24,3|0,3%|-5,0%|0|29,9%|1,3%||10,8%|1,1%|
|_Korea_|2002 2009||0,0%|0,8%|0,2%|||||0|||100,0%|2,2%|0,4%|
|_Kosovo_|2012 2016|2002|71,2%|98,0%|88,6%|3,1%|22,6|4,3%|-6,5%|1|||100,0%|18,9%|4,4%|
|_Latvia_|2009 2018|2001|53,6%|81,0%|66,1%|0,7%|24,0|2,8%|-0,1%|1|||100,0%|1,2%|0,2%|
|_Lesotho_|2011 2011||80,0%|80,0%|80,0%|||||0||||10,7%||
|_Lithuania_|2010 2018|2004|68,5%|78,8%|73,1%|3,4%|24,5|2,1%|-0,7%|1|||100,0%|5,4%|0,6%|
|_Luxembourg_|2005 2010||10,0%|30,3%|19,7%|2,7%|24,7|28,2%|8,7%|1|194,1%|1,0%|100,0%|1,4%|0,4%|
|_Malawi_|2016 2018||0,0%|0,0%|0,0%|3,2%|22,9|5,2%|-16,5%|0|||100,0%|11,8%|1,5%|
|_Maldives_|2011 2013||0,0%|0,0%|0,0%|6,1%|21,8|11,4%|-8,0%|0||||3,6%|1,5%|
|_Malta_|2011 2011||0,0%|0,0%|0,0%|1,3%|22,9|82,1%|-0,1%|1|36,1%|0,5%|100,0%|0,5%|0,5%|
|_Mauritius_|2015 2018||16,0%|32,5%|25,9%|3,7%|23,2|2,8%|-4,1%|0|65,8%|3,3%|70,0%|3,7%|0,5%|
|_Mexico_|2001 2018|1997|0,0%|13,3%|8,7%|1,7%|27,7|2,8%|-1,7%|0|33,1%|9,1%|18,3%|12,1%|0,9%|
|_Namibia_|2010 2016||25,0%|61,4%|37,9%|4,9%|23,3|5,0%|-8,2%|0|13,3%|0,3%|65,0%|77,2%|3,2%|
|_Netherlands_|2000 2018||0,0%|88,0%|57,4%|1,3%|27,5|29,3%|7,5%|1|87,4%|85,5%|100,0%|133,6%|4,3%|
|_New Zealand_|2001 2018||0,0%|50,1%|21,9%|3,7%|25,7|1,0%|-3,1%|0|39,6%|6,3%|100,0%|18,2%|1,5%|
|_Nigeria_|2008 2011|2005|1,8%|11,7%|4,6%|7,0%|26,6|2,3%|4,9%|0|12,2%|2,2%|0,0%|3,4%|0,9%|
|_North_<br>_Macedonia_|2007 2018|2006|1,5%|28,2%|17,3%|2,8%|23,0|4,1%|-3,8%|0|||50,0%|5,1%|0,8%|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|_Norway_|2001 2018||0,0%|29,7%|18,1%|1,5%|26,8|2,0%|11,8%|0|52,6%|36,1%|100,0%|7,6%|0,5%|
|_Pakistan_|2008 2014||0,0%|0,0%|0,0%|2,7%|25,9|1,4%|-3,0%|0|19,9%|9,3%||0,0%|0,0%|
|_Papua New_||||||||||||||||
|_Guinea_|2013 2013||12,8%|12,8%|12,8%|3,8%|23,5|0,1%|-16,2%|0||||18,0%|1,9%|
|_Peru_|2001 2018|1993|4,8%|43,8%|23,4%|5,1%|25,6|4,1%|-1,8%|0|40,9%|2,5%|40,9%|16,7%|1,3%|
|_Poland_|2000 2013|1999|0,0%|1,4%|0,4%|3,5%|26,7|3,3%|-3,4%|0|26,5%|8,7%|29,0%|8,0%|1,2%|
|_Portugal_|2000 2018||40,3%|68,6%|52,9%|0,5%|26,2|4,0%|-6,0%|1|34,7%|22,5%|94,3%|10,6%|1,0%|
|_Romania_|2007 2018|2008|0,0%|22,9%|8,9%|3,1%|25,9|2,9%|-4,8%|0|9,7%|1,0%|100,0%|2,3%|0,5%|
|_Russia_|2005 2005|2003|0,0%|0,0%|0,0%|||||0||||1,5%|0,2%|
|_Serbia_|2007 2018||0,0%|0,5%|0,1%|1,4%|24,5|6,1%|-7,4%|0|21,9%|1,8%|10,0%|0,5%|0,1%|
|_Slovak_<br>_Republic_|2001 2018|2005|7,8%|74,9%|48,4%|3,5%|25,2|3,9%|-2,7%|1|4,6%|0,9%|95,0%|6,9%|1,6%|
|_Slovenia_|2004 2018||7,6%|60,6%|37,0%|1,7%|24,6|1,9%|0,6%|1|20,8%|1,7%|100,0%|4,5%|0,5%|
|_South Africa_|2003 2016||0,0%|21,7%|10,7%|2,8%|26,6|1,4%|-3,7%|0|233,8%|66,4%|21,8%|50,3%|3,5%|
|_Sweden_|2005 2006|1999|0,0%|0,0%|0,0%|||||0||||8,6%||
|_Switzerland_|2000 2018||4,2%|41,0%|25,1%|1,8%|27,1|5,6%|10,1%|0|212,2%|127,7%|55,0%|107,8%|7,5%|
|_Thailand_|2009 2018||0,1%|0,8%|0,5%|3,2%|26,6|2,2%|5,2%|0|90,8%|67,6%|100,0%|6,1%|0,8%|
|_Trinidad &_||||||||||||||||
|_Tobago_|2006 2012||8,5%|23,1%|12,8%|2,6%|23,8|-0,4%|19,0%|0|||20,0%|19,1%|0,4%|
|_Turkey_|2004 2012||0,0%|0,6%|0,3%|5,7%|27,3|1,7%|-4,4%|0|32,7%|43,1%|100,0%|1,6%|0,3%|
|_Ukraine_|2010 2011||0,0%|0,0%|0,0%|4,6%|25,7|4,6%|-4,2%|0|22,2%|1,4%|20,0%|0,1%|0,0%|
|_United_||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|_Kingdom_|2001 2016|2012|24,4%|29,6%|27,0%|1,8%|28,5|4,3%|-3,4%|0|115,4%|87,1%|100,0%|78,4%|2,4%|
|_Uruguay_|2016 2016|1996|10,0%|10,0%|10,0%|1,7%|24,6|-0,9%|0,6%|0||||23,1%|1,9%|
|_Zambia_|2014 2014||6,9%|6,9%|6,9%|4,7%|24,0|5,6%|-1,4%|0|||30,0%|3,4%|0,4%|
**Table A.2.** Summary statistics for realized excess returns in sample countries

|Country|Index|First date|Excess Re<br>Average|turns (%)<br>Std. Dev.|Monthly<br>devaluation (%)|beta<br>|
|---|---|---|---|---|---|---|
|Brazil|BOVESPA Index|Jan-00|0.03|6.93|0.47|-0.01|
|Bulgaria|SOFIX Index|Oct-00|0.92|8.16|-0.07|1.25|
|Canada|TSX - Toronto|Jan-00|0.19|3.86|-0.01|0.75|
|Chile|S&P IPSA|Jan-00|0.39|4.50|0.22|0.63|
|Colombia|COLCAP Index|Jan-08|0.08|4.58|0.45|0.19|
|Costa Rica|IACR Index|Jan-00|0.23|5.70|0.12|0.28|
|Croatia|CROBEX Index|Jan-00|0.45|6.31|-0.03|1.24|
|Czech Republic|PX Prague SE Index|Jan-00|0.39|5.97|-0.14|1.40|
|Denmark|OMX Cop 20 Index|Jan-00|0.63|5.17|-0.01|0.95|
|Estonia|OMX Tallinn Index|Jan-00|1.03|6.88|-0.02|1.46|
|Finland|OMX Helsinki 25 Index|Jan-00|0.14|5.69|-0.02|1.11|
|Germany|DAX 30 Index|Jan-00|0.32|5.88|-0.02|1.21|
|Hong Kong SAR,|Hang Seng Index|Jan-00|0.38|5.93|0.00|1.07|
|China|||||||
|Hungary|Budapest SE Index|Jan-00|0.44|6.32|0.13|0.96|
|Iceland|OMX Iceland All Share Index|Jan-00|0.38|7.28|0.29|0.28|
|Indonesia|Jakarta SE Composite Index|Jan-00|0.47|6.05|0.31|0.47|
|Israel|Tel Aviv 35 Index|Jan-00|0.41|5.23|-0.04|0.73|
|Italy|FTSE Italia All Sahre Index|Dec-02|0.09|5.44|0.01|1.07|
|Jamaica|JSE Market Index|Feb-10|1.24|5.01|0.34|-0.03|
|Kenya|Nairobi Stock Exchange All Share index|Jan-08|-0.14|5.68|0.27|1.09|
|Korea, Rep.|Korea SE Kospi Index|Jan-00|0.29|6.17|0.06|0.82|
|Latvia|OMX Riga Index|Jan-00|0.99|6.37|-0.02|0.84|
|Lithuania|OMX Vilnius Index|Jan-00|0.89|6.52|-0.02|1.20|
|Luxembourg|Luxembourg SE LuxX Index|Jan-00|0.03|6.27|-0.02|1.14|
|Malta|MSE Share Index|Jan-00|0.00|4.03|-0.02|0.24|
|Mauritius|Semdex Index|Jan-00|0.48|3.97|0.17|0.49|
|Mexico|S&P/Bmc IPC Index|Jan-00|0.67|5.19|0.33|1.36|
|Netherlands|Amsterdam Exchange Index|Jan-00|0.00|5.31|-0.02|1.11|
|New Zealand|S&P/NZX 50 Index|Dec-00|0.55|3.36|-0.10|0.89|
|Nigeria|Nigerian Stock Ex All Share Index|Jan-00|0.34|6.92|0.53|0.42|
|North Macedonia|Macedonian SE 10 Index|Dec-04|0.94|9.49|0.13|1.08|
|Norway|Oslo SE Equity Index|Jan-00|0.64|5.87|0.08|0.95|
|Pakistan|KSE 100 Index|Jan-00|1.23|7.43|0.47|0.64|
|Peru|S&P Lima General Index|Jan-00|1.10|7.82|-0.01|1.65|
|Poland|Waraw SE WIG Pol Index|Jan-00|0.61|5.85|0.03|0.98|
|Portugal|Euronext Lisbon PSI 20 Index|Jan-00|-0.35|5.30|-0.02|0.75|
|Romania|Bucharest SE BET Index|Jan-00|1.48|8.08|0.40|0.96|
|Russian Federation|MOEX Russia Index|Jan-00|1.20|7.90|0.39|1.36|
|Serbia|Belex 15 Belgrade Index|Oct-05|-0.68|8.13|0.30|1.14|
|Slovak Republic|SAX Index|Jan-00|0.63|5.21|-0.02|0.36|
|Slovenia|Ljubljana SE SBI TOP Index|Apr-06|-0.04|5.19|0.12|1.17|
|South Africa|FTSE/JSE SA ALL Share Index|Jan-00|0.26|4.69|0.46|1.07|
|Sweden|OMX Stockholm 30 Index|Jan-00|0.20|5.42|0.08|1.09|
|Switzerland|Swiss Market Index|Jan-00|0.16|3.81|-0.18|0.68|
|Thailand|SET Index|Jan-00|0.51|6.25|-0.07|1.30|
|Turkey|BIST 100 Index|Jan-00|-0.09|10.21|1.12|0.34|
|Ukraine|PFTS Index|Jan-00|0.79|10.91|0.74|0.85|
|United Kingdom|FTSE 100 Index|Jan-00|-0.06|3.83|0.12|0.82|
|Zambia|Lusaka All Share Index|Jan-00|0.57|5.31|0.83|0.02|
**Table A.3.** Restrictions on foreign investments (2019)

|**Countries**|**Asset classes**|**Limit**<sup>**1**</sup>|**Data**|
|---|---|---|---|
|India|All|0%|Central and State Government Pension, National Pension System- Government, National Pension System-<br>Swavalamban: 0% (World). Pension funds cannot invest abroad. It is prohibited by PFRDA Act 2013. National<br>Pension System- Private: 0% (World). Pension funds cannot invest abroad. It is prohibited by PFRDA Act 2013.|
|Nigeria|All|0%|Defined Contribution Pension Scheme: 0% (World) Defined Benefit Pension Scheme: 0% (World)|
||||Mandatory funded pillar, default option: 20% of total portfolio. Securities of international financial organisations.<br>Mandatory funded pillar, conservative option (introduced in 2009): 0% (World) Mandatory funded pillar, life|
|Russia|All|0%-30% depending<br>on the pillar and plan|annuities portfolio: 20% of total portfolio. Securities of international financial organisations. Mandatory funded<br>pillar, term annuities portfolio: 20% of total portfolio. Securities of international financial organisations. Mandatory<br>funded pillar, Investment portfolios chosen by participants: 20% (World). Securities of international financial<br>organisations. Mandatory funded pillar, Non-state pension funds: 20% (World). Voluntary pension plan: 30%<br>(World).|
|Brazil|All|10%-40% depending<br>on the Fund Class|Closed pension funds: Up to 10% (World). Open Pension Fund (Defined Contribution Plans) to Qualified<br>Participants: 40% (World). Limits do not apply to the emission ́s Place of Issue but to the existence of currency risk.<br>Open Pension Fund (Defined Contribution Plans) to all other Participants: 20% (World). Limits do not apply to the<br>emission ́s Place of Issue but to the existence of currency risk. Traditional Plans: 10% (World). Limits do not apply to<br>the emission ́s Place of Issue but to the existence of currency risk.|
|Kenya|All|15%-90% depending<br>on the asset|15%. This limit refers to bank deposits, government securities, quoted equities and rated Corporate Bonds or<br>collective investment schemes reflecting these assets.|
|Jamaica|All|20%|20% (Canada, the United States of America, the United Kingdom or any other country declared as a recognised<br>jurisdiction by the Financial Services Commission) or the limit prescribed under the Bank of Jamaica Act whichever is<br>lower.|
|Mexico|All|20%|All Afores, (Siefore) All Funds: 20% (Eligible countries) Other / Comments: Commodities are not considered foreign<br>assets nor do FX positions.|
|Trinidad and Tobago|All|20%|20% (World). 90% of investments held in member countries of CARICOM is considered as foreign assets, while the<br>remaining 10% of investments in CARICOM countries is considered as local assets.|
|Ukraine|All|20%|20% (World)|
|South Africa|All|25%|25% (Listed instruments - listed on an exchange that is a full member of the World Federation of Exchanges)<br>Other/Comments:Maximum of 25% of the total fair value of the assets of a fund. An additional allocation of 5% of<br>the total fair value of assets can be invested in African countries|
|Zambia|All|30%|30% (World). Not more than 30% of its fund size outside the Republic as may be authorised by the Minister under<br>the Act.|
|---|---|---|---|
|Poland|All|30%-100%<br>depending on the<br>Plan|Open pension funds (OFE): 30% Employee pension funds (PPE): 30% (EU, EEA, OECD Countries) Employee Capital<br>Plans (PPK): No specific limit. Investments restricted to the assets denominated in currencies of EU and OECD<br>countries. 30% in the non-Polish currencies|
|Colombia|All|40%-70% depending<br>on the Fund Class|Conservative Fund: 40% (World). There is no specific limit for each type of investment issued overseas.<br>Nevertheless, these investments must be rated investment grade. Moderate Fund: 60% (World). There is no specific<br>limit for each type of investment issued overseas. Nevertheless, these investments must be rated investment grade.<br>High Risk Fund: 70% (World). There is no specific limit for each type of investment issued overseas. Nevertheless,<br>these investments must be rated investment grade. Programmed Retirement Fund: 40% (World). There is no<br>specific limit for each type of investment issued overseas. Nevertheless, these investments must be rated<br>investment grade.|
|Costa Rica|All|50%|Mandatory complementary pension funds (ROP), Voluntary Private Pensions System, Special Occupational<br>complementary pensions funds (DB: Lotery, FRE, ICE and DC: BCAC Ind, BCAC Col, ICT, BCR and Hybrid: BNCR): 50%<br>(World)|
|||50%-100% depending|Transformed pension schemes (3rd pillar): At least 50% of the assets have to be invested in the currency of the|
|Czech Republic|All|on the Fund Class|fund ́s liabilities. Participation funds: conservative schemes (3rd pillar): No specific limit. Currency risk has to be<br>hedged. Participation funds: other schemes (3rd pillar): No specific limit|
||||Mandatory open pension fund: No more than 50% of the value of the assets of the mandatory pension fund may be<br>invested in instruments issued by a foreign issuer outside the Republic of North Macedonia. Allowed countries|
|North Macedonia|All|50%|abroad are members of the EU or OECD. Voluntary open pension fund: No more than 50% of the value of the assets<br>of the voluntary pension fund may be invested in instruments issued by a foreign issuer outside the Republic of<br>North Macedonia. Allowed countries abroad are members of the EU or OECD.|
|Hong Kong (China)|All|70%|At least 30% of a fund must be held in Hong Kong dollar currency investments, e.g. currency forward contracts to<br>buy Hong Kong dollars.|
|Korea|All|70%-100%<br>depending on the<br>Plan|Personal pension insurance: No specific limit (World) Personal pension trust: No specific limit (World) Defined<br>benefit (DB) Retirement pension plans, Defined benefit (DB) Retirement insurance / Retirement trust: Up to 70%<br>(World) Defined contribution (DC) Retirement pension plans, Defined contribution (DC) Retirement insurance /<br>Retirement trust: Up to 70% (World)|
|Chile|All|80%|All AFPs, Fund A: 100% (World). All AFPs, Fund B: 90% (World). All AFPs, Fund C: 75% (World). All AFPs, Fund D:<br>45% (World). All AFPs, Fund E: 35% (World). Other/Comments: The joint limit for all funds is 80%.|
|Albania|All|100%|No specific limit (EU Member States or OECD countries)|
||||Mandatory pension fund - balanced funds: No specific limit (World) Mandatory pension fund - conservative funds:|
|---|---|---|---|
|Armenia|All|100%|No specific limit (World) Mandatory pension fund - fixed income funds: No specific limit (World) Voluntary pension<br>fund: No specific limit (World)|
|Australia|All|100%|No specific limit (World)|
|Austria|All|100%|No limit, but prudent person rule.|
|Belgium|All|100%|IORP: No specific limit (World) Insurance undertakings (all life products): No specific limit (World)|
|Bulgaria|All|100%|Supplementary mandatory universal pension funds (UPF), Supplementary mandatory professional pension funds<br>(PPF): - Generally no specific limit in EU countries, in non-EU countries specified in an ordinance of the national<br>competent authority. - Limit in the rest of the world = 0%, except bills and bonds issued by public administration. -<br>Generally the foreign investments are not treated differently than the domestic. Supplementary voluntary pension<br>funds with occupational schemes (VPFOS): - Generally no specific limit in EU countries, in non-EU countries<br>specified in an ordinance of the national competent authority. - Limit in the rest of the world = 0%, except bills and<br>bonds issued by public administration. - Generally the foreign investments are not treated differently than the<br>domestic. Supplementary voluntary pension funds (VPF): - Generally no specific limit in EU countries, in non-EU<br>countries specified in an ordinance of the national competent authority. - Limit in the rest of the world = 0%, except<br>bills and bonds issued by public administration. - Generally the foreign investments are not treated differently than<br>the domestic.|
|Canada|All|100%|No specific limit (World)|
|Denmark|All|100%|Pension savings in ATP, LD, pension funds, life insurance and banks: No specific limit|
|Estonia|All|100%|Mandatory funded pension: No specific limit (World) Voluntary funded pension: No specific limit (World)|
|Finland|All|100%|Voluntary plans: company pension funds and industry-wide pension funds: - No specific limit in OECD/EEA<br>countries; - Limit for countries outside the OECD/EEA = 10%. Earnings-related statutory pension provisions for<br>private sector workers, seamen and self-employed persons: No specific limit in OECD/EEA countries.|
|Germany|All|100%|Pensionskassen: No specific limit (World). There is no specific limit on foreign investments. However, where certain<br>legal risks can arise, foreign investments must be kept at a prudent level. Pensionsfonds: No specific limit (World).<br>There is no specific limit on foreign investments. However, where certain legal risks can arise, foreign investments<br>must be kept at a prudent level.|
|Gibraltar|All|100%|No specific limit (World)|
|Greece|All|100%|No specific limit (World). There is no specific limit on foreign investments.|
|Hungary|All|100%|Voluntary privately managed pension funds (magánnyugdíjpénztár): The ratio of securities issued by non-OECD and<br>non-EEA countries shall not exceed 20% of the foreign investments. Voluntary privatepension funds(önkéntes|
|nyugdíjpénztar): The ratio of securities issued by non-OECD and non-EEA countries shall not exceed 20% of the|
|---|
|foreign investments.|

|Iceland|All|100%|Investment only permitted in OECD, EU and Faroe Islands securities. But foreign currency exposure should not<br>exceed 50% of accrued liabilities. Limit for investments outside the OECD, EU and Faroe Islands = 0%.|
|---|---|---|---|
|Ireland|All|100%|Occupational pension plans, Trust retirement annuity contracts: No specific limit (World) Personal Retirement<br>Savings Accounts (PRSAs): Direct investment not allowed.|
|Israel|All|100%|- Limit on securities issued by a country rated at least BBB- = 100%; - Limit on securities issued by OECD residents =<br>100%; - Limit on securities issued countries which are rated below BBB- and which are not part of the OECD = 0%.|
|Italy|All|100%|No specific limit (World)|
|Japan|All|100%|Employees' Pension Fund (EPF), corporate DB pension funds, corporate DC pension funds, individual DC funds,<br>national pension funds: No specific limit (World). Mutual aid associations (MAAs): No specific limit (World).|
|Luxembourg|All|100%|Pension savings companies with variable capital (SEPCAVs), Pension savings associations (ASSEPs): No specific limit<br>(World) Defined benefit CAA supervised pension funds: No specific limit (World)|
|Malta|All|100%|Personal Retirement Schemes: No specific limit|
|Netherlands|All|100%|No specific limit (World)|
|New Zealand|All|100%|No specific limit (World)|
|Norway|All|100%|No specific limit|
|Portugal|All|100%|pension funds: No specific limit (OECD / EU regulated markets) - Limit for investments not traded in an EU and OECD<br>regulated market = 10%.<br>Closed pension funds, Open pension funds: No specific limit (OECD / EU regulated markets) - Limit for investments<br>not traded in an EU and OECD regulated market = 15%. Personal retirement saving schemes (PPR) financed through|
|Romania|All|100%|Private pension fund - second pillar: No specific limit (World). No specific limits on investments in foreign assets. The<br>limits are established for each asset class. Private pension fund - third pillar: No specific limit (World). No specific<br>limits on investments in foreign assets. The limits are established for each asset class.|
|Slovak Republic|All|100%|Privately managed mandatory pension system - Bonds Guaranteed Fund: No specific limit (OECD / EU regulated<br>markets/ European Economic Area) Privately managed mandatory pension system - Equity Non-Guaranteed Fund:<br>No specific limit (OECD / EU regulated markets/ European Economic Area) Privately managed mandatory pension<br>system - Other types of funds: No specific limit (OECD / EU regulated markets/ European Economic Area) Voluntary<br>personal pension plans - contributory pension funds: No specific limit (OECD / EU regulated markets/ European<br>Economic Area) Voluntary personal pension plans - pay-out pension funds: No specific limit (OECD / EU regulated<br>markets/ European Economic Area)|
|Slovenia|All|100%|No specific limit, unless specifically disclosed|
|---|---|---|---|
|Spain|All|100%|No specific limit (OECD). Limit for assets not admitted to be traded on a regulated market. Only investments in OECD<br>countries is permitted. In this case, offshore investing is forbidden by the Law.|
|Sweden|All|100%|Friendly societies: No specific limit (World) Life insurance undertakings: No specific limit (World) Providers of<br>occupational retirement pensions: No specific limit (World)|
|Switzerland|All|100%|No specific limit (World)|
|Thailand|All|100%|100% but subject to the following conditions: - Securities must be regulated by regulator that is an IOSCO member,<br>including Cambodia, Lao PDR and Myanmar; - Listed instruments must be listed on an exchange that is a full<br>member of the World Federation of Exchanges.|
|Turkey|All|100%|No specific limit (World)|
|United Kingdom|All|100%|No specific limit (World)|
|United States|All|100%|No specific limit; no additional limitations are applicable. (World)|
|Maldives|All|NA|No specific limit. Maldives Retirement Pension Scheme has not yet started investing in any foreign assets, hence no<br>limit has yet been set for foreign investments.|
||||Private pension funds under VPS - equity sub-fund: No specific limit (World) Private pension funds under the<br>Voluntary Pension System (VPS) - debt sub-fund: No specific limit (World) Private pension funds under the Voluntary|
|Pakistan|All|NA|Pension System (VPS) - commodity sub-fund: No specific limit (World) Other/Comments: Regulations are silent on<br>foreign investments (neither prohibit nor allow), however no pension fund manager has approached SECP for<br>investment in foreign assets. If a request is received, SECP will consider it on merit.<br>Pension System (VPS) - money market sub-fund: No specific limit (World) Private pension funds under the Voluntary|
|Tanzania|All|NA|According to the social security schemes investment guidelines 2015, Off-shore investment by the schemes shall be<br>in accordance with, and governed by the Foreign Exchange Act and Regulations, Directives and Rules issued by the<br>Bank from time to time, in this case offshore investments have only been allowed for east Africa region.|
|**1**|Limit refers to the p|ercentage of funds t|hat is allowed to invest overseas|
|_Source_|_Annual Survey of Inv_|_estment Regulation_|_s of Pension Funds and Other Pension Providers (OECD)_|
# **APPENDIX B.**

# **B.1 International securities**

In Section 4, we analyze the main drivers of foreign holdings. An outstanding question is the type of securities that managers use to access international markets. Table 1 provides some suggestive evidence. For instance, pensions funds with a higher share of fixed income investments tend to invest more domestically. It is possible that these funds have a higher concentration in domestic government securities and thus allocate only a small portion of their portfolios internationally. According to Table 1, funds with the lowest exposure to foreign assets (in quartile 1) invest up to 40% of their assets in treasury bills and in bonds. Conversely, it appears that funds that allocate a larger portion of their investments through investment companies, and in particular, via mutual funds, invest more internationally. The evidence however is only suggestive since OECD does not collect detailed portfolio information.

To examine the international investment strategies of pension funds, we use detailed security-level data collected from local supervisory authorities for a sample of Latin American countries – Chile, Colombia, Mexico, and Peru.<sup>15</sup> We differentiate between direct holdings of securities among these investors, and delegated assets into other investment funds. For example, pension fund investments into fund of funds, mutual funds, or in Exchange Traded Funds (ETFs). Finally, to examine the level of active management among these investors, we examine portfolio allocations to passive strategies –investment in equity and fixed-income funds that passively track a benchmark index.

> 15 Complete portfolio data is available for Colombian funds between 2008 and 2018. For Chile, the data covers the years 2013-2018 and for Peru, 2014 to 2018.
<!-- Start of picture text --> Asset Allocation - Equity<br>°: SS=a<br>7<br>"4<br>f=)<br>S008 e010 ane ata 2016 wa<br>Year<br>—?*— ona —*+— Cie<br>Ag: Peeraemagp of Total Fremege——AnnasPau<br><!-- End of picture text --> <!-- Start of picture text --> Overtime Delegated Foreign Holdings<br>=|a ees<br>a+<br>od<br>oq<br>2008 2ono maiz 2014 20g a8<br>‘Your<br>—#*— Colombia —t— Chie<br>‘Ad Pesmertageoi Tous Forme——AasetsPani<br><!-- End of picture text -->
<!-- Start of picture text --> son. Atoual Mean of Assats by Type of Holdings - Colombia<br>=<br>i,<br>ri<br>nm<br>=<br>er<br>ta<br>Led<br>om<br>oy ee eae<br>«Oeegmed Direct<br><!-- End of picture text --> <!-- Start of picture text --> See Cana oo amen Dy Toes PRON = ree<br>Lid<br>acs<br>TH<br>om<br>ya<br>_<br>an<br>7h.<br>im<br>Eau Fined bene ‘Ouhar<br>siieiciniie sae<br><!-- End of picture text --> <!-- Start of picture text --> an Annual Mean of Assets by Type of Hollings - Peru<br>nd<br>ms<br>ek]<br>éa<br>_<br>ms<br>ms<br>a<br>iL Equity Fised income Omer<br><!-- End of picture text -->
In this case, uninformed managers seeking to invest in global markets might self-select into explicit index funds perhaps attracted by their low fees.

The process of financial globalization fostered by capital account liberalizations, electronic trading, increasing exchanges of information across borders, and falling transaction costs has certainly led to a large increase in cross-border asset trade. For pension funds, lenient regulation with recent increases in the limits of foreign holdings allows more international exposure.<sup>16</sup> At least for pension funds in Chile, Colombia, and Peru, foreign exposure has provided an opportunity for global diversification. In Figure B.4, we report the international focus of the mutual funds and ETFs that pension funds are using to access foreign assets. The figure reports as a percent of delegated assets, the focus of each fund. For example, a pension fund that invests in an international mutual fund with exclusive focus to developed countries would be classified under this group.<sup>17</sup> Importantly, there is large variation in the focus of the funds that pension management companies are using. During the last five years, pension funds in Peru have increased their exposure to developing countries.

In summary, international holdings of pension funds in Chile, Colombia, and Peru, are more passive, are often performed via investment funds, and have been expanding their international focus to multiple markets in recent years.

> 16 It is of interest to note that such regulations are not always “binding,” meaning that in some cases the level of international assets held is well below the allowable limit, as mentioned in this paper regarding cases in Mexico and Colombia.

> 17 The classification is based on the objective of the fund. For example, a LATAM fund differs from an emerging markets fund in that the LATAM fund would exclusively focus on securities in Latin America.
<!-- Start of picture text --> i Delegated Holdings Composition - Colambia<br>ne<br>ue<br>ay<br>_<br>=<br>-_<br>oa<br>mm Z<br>mt 2 AO Mt PAE ee A eh oe<br>Aa Perverruaye 4) a! Total Foreign (Deekegaeed)=<Asati<br><!-- End of picture text --> <!-- Start of picture text --> Li Delegaled Holdings Composition - Chile<br>ip’<br>_<br>if<br>=.<br>mm<br>an<br>or<br>OR b= _— * — = aps +<br>Paar) ie Pa} Bote maT aa<br>(Ab Picunrrtage (ai ort Total Fosmge (Duteganed) Asents<br><!-- End of picture text --> <!-- Start of picture text --> a DelegatedHoldings Composition « Peru<br>Cd<br>Cou<br>bid<br>bo Cod<br>2|:at<br>~<br>:<br>“rh<br>Lad i<br>ata wa eal 2 aoa<br>Ag Porcpelnge (4) af Tahal Fospage (Deteqaies) Aeon |<br>PT<br><!-- End of picture text -->
ways, these investments have been an important stabilizing force for the pension fund portfolios; perhaps most notably in 2020 as a key source of liquidity during moments of market stress.

Administradoras de Fondos de Pensiones (AFPs) in Colombia began to significantly incorporate international investments after 2005 as domestic yields started a steady decline. Additionally, the relative size of the AFPs vis-à-vis the domestic market began to be more of a concern as well given increased trading costs and reduced liquidity for the investment lot sizes needed by the pension funds. Currently, regulation in Colombia allows AFPs to invest up to 40% of their portfolio overseas – this has not been a binding limit historically but the trend over time has continued to increase. The advent of the multifund system helped contribute to this increase and the recent rule change (decree 959) of 2018 to the multifund system that will result in younger participants defaulting to the high-risk fund (with relatively higher international investment) will further amplify this trend.

In moving toward more foreign investments, there has been a learning curve for the AFPs. They have had to navigate the process of negotiating fees and structure concerns with global investment management firms. They have made this process easier for themselves by focusing largely on overseas developed market equity, and by most typically using passive fund structures based upon highly liquid and well-known indices. These instruments provide strong diversification benefits while still being available at a competitive cost level. The financial supervisory regulator in Colombia (Superfinanciera de Colombia – SFC) has encouraged the move to largely developed market equities via regulatory requirements that allow foreign investments only in countries with strong credit ratings, good equity listing requirements and regulations that either meet or exceed those in Colombia.
Recent experience during the COVID-19 market gyrations of early 2020 have shown the importance of maintaining a significant portion of their portfolio in overseas investments. As markets seized up in March, in some cases the international holdings provided the only reasonable source of liquidity on short notice. Additionally, despite the dramatic volatility, non-Colombian equity investments performed relatively better in 2020 on a Colombian peso (COP) basis; although the MSCI All Country World Index (ACWI) declined about 1% in the first half of the year in USD terms, in Colombian peso terms it was up by about 10%. Meanwhile the MSCI Colombia index was down by roughly 30% in the same period in local currency terms. Given this reality, it is clear that AFP portfolios with relatively higher investments overseas performed relatively better than those with only domestic equity investments.