## 1. Connection Concepts with Highest Prediction Power

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### I. Introduction and Main Empirical Result
- Research question: Do financial connection data between two economies help predict the degree of bilateral stock return comovement?
- Connection concepts explored: direct investment positions, portfolio investment positions, bank’s balance sheet positions (other investment), and trade flows.
- Conceptual note: analysis focuses on prediction capacity and does not address causality; both stock return comovement and international financial connection are endogenous.
- Main empirical result (summary):
  - International financial connection has prediction power on stock return comovement for large portfolio asset economies.
  - Using the United States as benchmark: the larger the U.S. portfolio investment asset position on a destination economy, the more likely that the economy’s stock return correlates with the U.S. stock return.
  - Cross-sectional pattern is stable over time and robust to specifications.
- Heterogeneity:
  - For large portfolio investment asset economies (e.g., United States, Germany), portfolio investment asset position vis-à-vis other economies is often the best predictor of bilateral stock return correlation.
  - For smaller economies, other connection concepts often exhibit higher prediction power.
- Theoretical mechanism (overview):
  - An N-country general equilibrium portfolio model rationalizes findings via shocks to risk attitudes (risk-on/risk-off). Investors increase all risky positions proportionally when more risk-tolerant; price impact larger for assets where an investor already has a large position, linking portfolio positions to comovement.

### II. Data: composition, coverage, and measurement details
- Equity indices:
  - Source: Thomson Reuters Global Equity Indices compiled by Refinitiv Datastream.
  - Coverage: 52 stock markets since April 1999.
  - Index construction: aggregates 99.5 percent of the market capitalization of the liquid securities in a market.
  - Returns used: total return index that includes issuance of dividends; price index excluding dividends used as robustness check.
- Financial connection databases (all quoted in US dollar):
  - Direct investment: Coordinated Direct Investment Survey (CDIS) compiled by the IMF.
    - Definition: equity and debt investment with significant influence (holding more than 10 percent share). Exception: parent bank loans to branches classified as other investment.
    - Provides annual inward and outward direct investment with geographical breakdown.
  - Portfolio investment: Coordinated Portfolio Investment Survey (CPIS) compiled by the IMF.
    - Definition: investment with less than 10 percent share (no significant influence) that includes securities traded in financial markets; excludes bank loans and deposits not traded in markets.
    - Provides biannual asset and liability of portfolio investment with geographical breakdown.
    - Portfolio investment is the benchmark connection concept; equity, total debt, long-term debt, and short-term debt components are analyzed separately.
  - Other investment (proxy for LBS): Locational Banking Statistics (LBS) compiled by the BIS.
    - Captures currency and deposits, loans, and other financial positions (residual of other functional categories).
    - Provides quarterly claims and liabilities of banks’ balance sheets with geographical breakdown.
  - Trade flow: Direction of Trade Statistics (DOTS) compiled by the IMF.
    - Provides quarterly value of merchandise exports and imports with geographical breakdown.
    - Export data use “free on board” and import data use “cost, insurance and freight” to maximize samples.
- Complementary macro data:
  - Exchange rate and GDP from International Financial Statistics (IMF) used only for robustness checks.
- Data characteristics and caveats:
  - Annex IX.A presents total external positions of top 20 economies by connection concept: United States largest in direct and portfolio investment assets; United Kingdom largest banking sector; China largest exports.
  - For the United States, correlation matrix of connection variables shows all connection data positively correlated with correlation at least 0.6.
  - Potential bias from financial centers (e.g., Cayman Islands, Luxembourg) is discussed: bias depends on whether the geographical distribution of indirect flows differs substantially from direct flows; paper does not trace ultimate beneficial owners.

### III. Empirical analysis: methods and comovement construction
- A. Definition of connection variables
  - Uses assets and liabilities from international investment positions and exports/imports for trade.
  - All variables quoted in US dollar.
  - Portfolio investment benchmark includes equities traded in stock markets but equity component may also include investment fund shares (which can hold debts, real estate, commodities).
  - Direct investment conceptually close to stock returns (equity positions > 10 percent), though some holdings may be unlisted.
  - Other investment and trade are indirect channels affecting comovement.
- B. Construction of comovement variables (frequency, similarity statistics, and time adjustment)
  - Frequency and sample window:
    - Comovement variables constructed quarterly.
    - Built using trading dates of the following 2 months from the end of each quarter (example: 2017Q4 comovement based on 2018 January and February trading-day data).
    - Two-month choice balances proximity to connection data recording dates and sample size.
    - Robustness check: two months around the end of the quarter (e.g., 2017 December and 2018 January) yields qualitatively similar results.
  - Three similarity statistics used:
    - Correlation: sample correlation coefficient between return series (chosen as benchmark).
    - Mean deviation: 1/T sum of absolute differences of returns.
    - Beta: regression coefficient from r_A = alpha + beta * r_B + epsilon; interpreted as how much A’s return increases if B’s return increases by 1 percent.
  - Rationale for benchmark choice:
    - Correlation normalized by volatility and less sensitive to outliers when projected on connection variables; consistent with common language describing comovement.
    - Beta is asymmetric and aligns better with theoretical spillover interpretation; used in theoretical analysis implications.
  - Time lag/time adjustment to account for non-overlapping trading hours:
    - For market pairs with substantial overlap in trading hours, same-day returns proxy the object.
    - For non-overlapping markets, baseline takes a 1-day lag when the counterpart market’s closing time is more than 7 hours ahead on the same day (e.g., when U.S. benchmark vs. Japan, take 1-day lag of U.S. data for U.S.–Japan comovement).
    - No lag taken when the domestic market closes first (e.g., when Japan is benchmark vs. U.S., no lag for Japan).
    - This rule yields consistent comovement variables across countries.
  - Additional time-adjustment robustness methods:
    - Raw end-of-day data without adjustment (conceptual asymmetry risk).
    - Max-of-lag-and-current method: compute correlations using combinations (current vs. lag) and take max for correlation and beta, min for mean deviation; this searches time convention that maximizes comovement but risks upward bias.
  - Conservatism: if time conventions fail to capture comovement (e.g., source economy changes daily), comovement measures may be downward biased, making empirical results conservative.

### IV. Empirical results — United States case and cross-sectional evidence
- Descriptive pooled evidence:
  - Figure 1 plots each counterpart economy–date pair as a dot: y-axis = stock return correlation with the United States; x-axis = log of U.S. portfolio investment asset.
  - Pooled scatter shows that more international financial connection is associated with more stock return comovement.
  - Two descriptive observations from pooled plot:
    - Comovement is mostly positive — typical comovement reflects wealth or risk-on/off effects pushing prices in same directions.
    - Stock return comovement with the United States is higher when the U.S. portfolio investment asset position on the destination economy is larger — novel observation and main contribution.
  - Stability over time:
    - Figure 2 (date-sliced chart) shows relationship stable over time despite fluctuations in comovement and connection.
- Interpretation:
  - The relationship is best interpreted as a cross-sectional relationship rather than a time-series relationship because a global time fixed effect (for example, risk-on/risk-off regimes) can dominate within-economy time slices.
  - When U.S. portfolio asset fluctuation is smaller than the comovement, charts sliced by economy can be dominated by global fixed effects and exhibit a weak relationship; Figure 1 should therefore be read as cross-sectional evidence.
- Robustness and alternative comovement statistics:
  - The result remains when the comovement concept is replaced by:
    - the mean deviation (median deviation between counterpart economy stock return and U.S. stock return), and
    - the regression coefficient of the counterpart economy’s stock return on the United States.
  - Outliers exist (for example, Greece crisis periods in 2014 and 2016), but the overall association persists.
  - Annex IX.E reports 5 additional robustness checks showing the relationship holds:
    1. after considering daily FX return,
    2. after normalizing the position by the GDP of the counterpart economy,
    3. if the connection variable is replaced by portfolio equity position or portfolio debt position,
    4. if the stock index is replaced by the price index that excludes dividends,
    5. if the benchmark time adjustment is replaced by the other two methods discussed in section IV.B.
  - Main takeaway: under various specifications, daily stock returns tend to comove more with the United States for economies with stronger measured international financial connection to the United States.
- Alternative connection measures:
  - The predictability is not always evident if the connection variable is not the portfolio investment asset position.
  - Example: replacing portfolio investment asset by U.S. bank asset divided by counterpart economy’s GDP yields a weaker predictive relationship.
  - This raises the question: “which connection concept predicts stock return comovement best for each economy?”

### V. Empirical exercise: top 20 portfolio investment asset economies — prediction power metrics and exact table entries
- Prediction power measured by:
  - R-square (푅푅2): percentage of variation in stock return comovement explained by a linear function of the connection variable (with time fixed effects).
  - Leave-one-out pseudo R-square (푅푅푝푝2): magnitude of the correlation between fitted value and actual value using leave-one-out fitted values.
- 푅푅2 and 푅푅푝푝2 tend to point to the same connection concept and give similar values; coincidence interpreted as robustness.
- Regression objective is prediction, not parameter estimation or causality; statistical significance and controls are not used.
- Table 1: Connection concepts with highest prediction power (exact entries)
  - DE — Highest 푅푅2 (in log): PI asset 0.58; Highest 푅푅푝푝2 (in log): PI asset 0.57
  - AT — Highest 푅푅2 (in log): PI asset 0.57; Highest 푅푅푝푝2 (in log): PI asset 0.55
  - BE — Highest 푅푅2 (in log): PI asset 0.57; Highest 푅푅푝푝2 (in log): PI asset 0.55
  - CH — Highest 푅푅2 (in log): DI inward 0.58; Highest 푅푅푝푝2 (in log): DI inward 0.54
  - CN — Highest 푅푅2 (in log): Bank's liability 0.58; Highest 푅푅푝푝2 (in log): Bank's liability 0.54
  - IT — Highest 푅푅2 (in log): PI asset 0.56; Highest 푅푅푝푝2 (in log): PI asset 0.54
  - NL — Highest 푅푅2 (in log): Export 0.55; Highest 푅푅푝푝2 (in log): Export 0.53
  - FR — Highest 푅푅2 (in log): PI asset (LTD) 0.55; Highest 푅푅푝푝2 (in log): PI asset (LTD) 0.53
  - ES — Highest 푅푅2 (in log): PI asset (LTD) 0.56; Highest 푅푅푝푝2 (in log): PI asset (LTD) 0.52
  - FI — Highest 푅푅2 (in log): PI asset (STD) 0.55; Highest 푅푅푝푝2 (in log): PI asset (LTD) 0.51
  - DK — Highest 푅푅2 (in log): Bank's asset 0.56; Highest 푅푅푝푝2 (in log): PI asset (STD) 0.51
  - SE — Highest 푅푅2 (in log): Import 0.50; Highest 푅푅푝푝2 (in log): Import 0.48
  - IE — Highest 푅푅2 (in log): PI liability (LTD) 0.49; Highest 푅푅푝푝2 (in log): PI liability (LTD) 0.46
  - CA — Highest 푅푅2 (in log): DI outward 0.47; Highest 푅푅푝푝2 (in log): PI asset (LTD) 0.45
  - GB — Highest 푅푅2 (in log): PI asset (LTD) 0.47; Highest 푅푅푝푝2 (in log): PI asset (LTD) 0.44
  - US — Highest 푅푅2 (in log): PI asset 0.45; Highest 푅푅푝푝2 (in log): PI asset 0.43
  - SG — Highest 푅푅2 (in log): Bank's liability 0.46; Highest 푅푅푝푝2 (in log): Bank's asset 0.40
  - HK — Highest 푅푅2 (in log): DI outward 0.48; Highest 푅푅푝푝2 (in log): Bank's asset 0.34
  - JP — Highest 푅푅2 (in log): DI outward 0.34; Highest 푅푅푝푝2 (in log): DI outward 0.30
  - KR — Highest 푅푅2 (in log): Bank's liability 0.37; Highest 푅푅푝푝2 (in log): Bank's liability 0.29
- Observations from Table 1:
  - 푅푅2 and 푅푅푝푝2 generally select the same connection concept and give similar magnitudes, supporting robustness.
  - Portfolio investment asset is not always the best predictor; different economies have different structures, so the most relevant connection concept differs across economies.

### VI. Theoretical analysis: model and closed-form relations preserved
- Objective: explain (1) why comovement tends to be positive and (2) why portfolio investment position contains informational content for predicting stock return comovement.
- Model: extension of Grossman and Stiglitz (1980) to N economies, with:
  - representative investor i in each economy,
  - random returns m = [m1, ..., mN]' distributed as N(μ̅i, Ω) under investor i's belief (heterogeneous beliefs allowed),
  - CARA preferences and exponential utility, risk-free rate Ri, risk tolerance τi, wealth ωi,
  - equilibrium defined by investor optimization and market clearing.
- Key closed-form relations (exact expressions):
  - First-order optimal portfolio: x_i(p) = Ω^{-1}(μ_i − p) w_i, μ_i ≔ μ̅_i / (1 + R_i), w_i ≔ τ_i(1 + R_i).
  - Equilibrium price: p* = (1/W) [ ∑_j w_j μ_j − Ω X ], W = ∑_j w_j.
  - Equilibrium position: x_i* = Ω^{-1}[ ∑_j (w_j/W)(μ_i − μ_j) + (1/W) Ω X ] w_i.
- Proposition (comovement as function of portfolio position): for a risk tolerance shock to economy i,
  - ∂p*_j / ∂τ_i = β_{ij} ∂p*_i / ∂τ_i, where
  - β_{ij} ≔ (∑_k Ω_{jk} x_{ik}^*) / (∑_k Ω_{ik} x_{ik}^*).
- Special case (Ω = σ^2 I): β reduces to ratio of i’s position on j to i’s position on i: ∂p*_j / ∂τ_i = (x_{ij}^* / x_{ii}^*) ∂p*_i / ∂τ_i.
- Intuition:
  - A change in investor i’s risk tolerance scales portfolio sizes across stocks proportionally; price impact is larger for economies where investor i already holds a large position.
  - Shocks to U.S. investor risk attitudes can therefore generate positive comovement and stronger comovement for stronger connections.
- Extension to multiple investors and shocks:
  - Allow i.i.d. non-degenerate shocks to all τ_i, X = 0, Ω = I; equilibrium price is weighted sum of investors’ beliefs p = ∑_j (w_j/W) μ_j.
  - Correlation between any pair of prices can take values between −1 and 1 depending on beliefs; higher beliefs on both home and destination economies by investor i can generate simultaneously higher correlation and larger position on j.
  - x_{ij} increases with μ_{i j}; when investors have strong home-and-destination valuations, prices for i and j move together driven by the same investors’ risk attitude shocks.

### VII. Mechanisms, extensions, and limitations
- Likely mechanisms:
  - Direct investment liability: parent firms with large subsidiaries abroad can cause home-firm returns to move with subsidiary-country returns as investors use foreign stock information to forecast parent performance; larger direct investment implies larger exposure and stronger comovement.
  - Bank liability: banks’ cross-border lending and exposures can make home investors sensitive to foreign equity information; larger bank liability exposure can increase comovement.
  - In general, any connection variable correlated with exposures can have predictive power; Table 2 in Annex IX.B shows connection variables are correlated.
- Unlikely mechanisms:
  - Diversification motive alone is unlikely: to diversify, investors would invest in economies with negative correlation, which runs counter to the observed positive relationship.
  - Pure sentiment or random statistical errors are unlikely drivers: linking stronger sentiment to larger positions is challenging; random measurement errors would unlikely be systematically proportional to daily stock return comovement.
- Extension to other asset classes: government bond yields
  - Short-term (3-month) government bond yield changes show almost no relationship with U.S. portfolio asset position.
  - Long-term (10-year) government bond yield changes show an increasing pattern with U.S. portfolio asset position.
  - Charts are similar if asset positions are replaced by liability positions.
- Government bond yields and limitations:
  - Government bonds are less informative than stock returns for the study of international portfolio comovement because:
    - Government bonds are often classified in confidential reserve assets and therefore do not show up in portfolio investment or direct investment data; this is particularly true for short term bonds.
    - Yields of government bonds are often direct policy instruments, so changes in yields may reflect different forces than the profit-maximizing motive that drives equity markets.
- Data granularity and extensions:
  - Equity indices are often available by industry; if connection data have an industry-level or institutional-sector-level breakdown, stock return analysis can be extended from country level to country-sector level.
  - From-whom-to-whom portfolio data are available in CPIS table 6 for 16 economies as of June 2018.

### VIII. Robustness, annex correlation matrix, and concluding policy notes
- Robustness checks (U.S. comovement vs connection) that preserve the main pattern:
  - (1) After considering daily FX return.
  - (2) After normalizing the position by the GDP of counterpart economy.
  - (3) If the connection variable is replaced by portfolio equity position or portfolio debt position.
  - (4) After excluding dividend if the stock index is replaced by the price index that excludes dividends.
  - (5) If the time-lag-adjusted U.S. stock return is replaced by the current or max as discussed in section IV.B.
- Annex IX.C — Table 2. Correlation Matrix of the U.S. International Financial Connections in Log (exact entries)
  - PI asset vs:
    - PI asset: 1
    - Bank asset: 0.87
    - Bank liability: 0.84
    - DI inward: 0.88
    - DI outward: 0.80
    - Export: 0.74
    - Import: 0.73
  - Bank asset vs:
    - PI asset: 0.87
    - Bank asset: 1
    - Bank liability: 0.88
    - DI inward: 0.81
    - DI outward: 0.73
    - Export: 0.69
    - Import: 0.62
  - Bank liability vs:
    - PI asset: 0.84
    - Bank asset: 0.88
    - Bank liability: 1
    - DI inward: 0.83
    - DI outward: 0.64
    - Export: 0.64
    - Import: 0.65
  - DI inward vs:
    - PI asset: 0.88
    - Bank asset: 0.81
    - Bank liability: 0.83
    - DI inward: 1
    - DI outward: 0.74
    - Export: 0.63
    - Import: 0.66
  - DI outward vs:
    - PI asset: 0.80
    - Bank asset: 0.73
    - Bank liability: 0.64
    - DI inward: 0.74
    - DI outward: 1
    - Export: 0.82
    - Import: 0.68
  - Export vs:
    - PI asset: 0.74
    - Bank asset: 0.69
    - Bank liability: 0.64
    - DI inward: 0.63
    - DI outward: 0.82
    - Export: 1
    - Import: 0.91
  - Import vs:
    - PI asset: 0.73
    - Bank asset: 0.62
    - Bank liability: 0.65
    - DI inward: 0.66
    - DI outward: 0.68
    - Export: 0.91
    - Import: 1
- Main empirical findings (Conclusion):
  - A stronger international financial connection is associated with stronger stock return comovement.
  - When using large portfolio investment asset economies such as the United States or Germany as the benchmark, bilateral portfolio positions have the highest prediction power.
  - For smaller economies, the best predictor of stock return comovement varies by country.
  - A general equilibrium portfolio theory is proposed that is consistent with the empirical patterns.
  - The empirical results support the intuition that a more connected world tends to have more comovement, while also highlighting that the meaning of "connection" might differ across countries.
- Policy applications and future work:
  - Stock return comovement is an important input for portfolio diversification and spillover analysis.
  - Stock return comovement can be used inversely to estimate international financial connection.
  - Exploring these policy applications is left for future research.

*Source: wpiea2019181-print-pdf — "1. Connection Concepts with Highest Prediction Power" and section "5. Comovement vs Connection, Government Bond Yield".*

### 1. Connection Concepts with Highest Prediction Power .........................................................15

### 1. Connection Concepts with Highest Prediction Power

### Contained Sections
- 1. Connection Concepts with Highest Prediction Power .........................................................15
- 2. Correlation Matrix of the U.S. International Financial Connections in Log .......................25

### Figures
- 1. Comovement vs Connection, Pooled ...................................................................................11
- 2. Comovement vs Connection, by Date .................................................................................12
- 3. Comovement vs Connection, Alternative Comovement Statistics ......................................13
- 4. Comovement vs Connection, Alternative Connection Variable ..........................................13

*Source: wpiea2019181-print-pdf - 1. Connection Concepts with Highest Prediction Power .........................................................15*

### 5. Comovement vs Connection, Government Bond Yield ......................................................20

### 5. Comovement vs Connection, Government Bond Yield

### I. Introduction
- Research question: Do financial connection data between two economies help predict the degree of bilateral stock return comovement?
- Connection concepts explored: direct investment positions, portfolio investment positions, bank’s balance sheet positions (other investment), and trade flows.
- Conceptual note: analysis focuses on prediction capacity and does not address causality; both stock return comovement and international financial connection are endogenous.
- Main empirical result (summary):
  - International financial connection has prediction power on stock return comovement for large portfolio asset economies.
  - Using the United States as benchmark: the larger the U.S. portfolio investment asset position on a destination economy, the more likely that the economy’s stock return correlates with the U.S. stock return.
  - Cross-sectional pattern is stable over time and robust to specifications.
- Heterogeneity:
  - For large portfolio investment asset economies (e.g., United States, Germany), portfolio investment asset position vis-à-vis other economies is often the best predictor of bilateral stock return correlation.
  - For smaller economies, other connection concepts often exhibit higher prediction power.
- Theoretical mechanism (overview):
  - An N-country general equilibrium portfolio model rationalizes findings via shocks to risk attitudes (risk-on/risk-off). Investors increase all risky positions proportionally when more risk-tolerant; price impact larger for assets where an investor already has a large position, linking portfolio positions to comovement.

### II. Literature (key contextual points)
- Prior empirical work:
  - Forbes and Chinn (2004): weak fit of connection variables despite rich controls.
  - IMF (2016): extended analysis pooling source and destination economies.
  - Chuluun (2017): centrality measures of portfolio investment network vs. world index.
- The present paper departs by conducting economy-by-economy analyses, allowing heterogeneous explanatory power across economies and focusing on bilateral positions rather than pooled or centrality measures.
- Related theoretical work:
  - Martin and Rey (2000): three-country model with transaction costs; coordinated shocks required to explain worldwide comovement.
  - Evans and Hnatkovska (2014): two-country model across financial integration stages.
- Other relevant strands:
  - Bekaert et al. (2016): equity returns correlated positively with globalization.
  - Diebold and Yilmaz (2009; 2014), Demirer et al. (2018): variance decomposition measures of connectedness from return data.
  - Literature on international financial connection (Lane and Milesi-Ferretti (2008); Schiavo et al. (2010); Kali and Reyes (2010); Benedictis and Tajoli (2011); Burger et al. (2018)) documents topology and drivers of positions and trade, abstracting from bilateral stock return comovement.

### III. Data (composition, coverage, and measurement details)
- Equity indices:
  - Source: Thomson Reuters Global Equity Indices compiled by Refinitiv Datastream.
  - Coverage: 52 stock markets since April 1999.
  - Index construction: aggregates 99.5 percent of the market capitalization of the liquid securities in a market.
  - Returns used: total return index that includes issuance of dividends; price index excluding dividends used as robustness check.
- Financial connection databases (all quoted in US dollar):
  - Direct investment: Coordinated Direct Investment Survey (CDIS) compiled by the IMF.
    - Definition: equity and debt investment with significant influence (holding more than 10 percent share). Exception: parent bank loans to branches classified as other investment.
    - Provides annual inward and outward direct investment with geographical breakdown.
  - Portfolio investment: Coordinated Portfolio Investment Survey (CPIS) compiled by the IMF.
    - Definition: investment with less than 10 percent share (no significant influence) that includes securities traded in financial markets; excludes bank loans and deposits not traded in markets.
    - Provides biannual asset and liability of portfolio investment with geographical breakdown.
    - Portfolio investment is the benchmark connection concept; equity, total debt, long-term debt, and short-term debt components are analyzed separately.
  - Other investment (proxy for LBS): Locational Banking Statistics (LBS) compiled by the BIS.
    - Captures currency and deposits, loans, and other financial positions (residual of other functional categories).
    - Provides quarterly claims and liabilities of banks’ balance sheets with geographical breakdown.
  - Trade flow: Direction of Trade Statistics (DOTS) compiled by the IMF.
    - Provides quarterly value of merchandise exports and imports with geographical breakdown.
    - Export data use “free on board” and import data use “cost, insurance and freight” to maximize samples.
- Complementary macro data:
  - Exchange rate and GDP from International Financial Statistics (IMF) used only for robustness checks.
- Data characteristics and caveats:
  - Annex IX.A (not summarized here) presents total external positions of top 20 economies by connection concept: United States largest in direct and portfolio investment assets; United Kingdom largest banking sector; China largest exports.
  - For the United States, correlation matrix of connection variables shows all connection data positively correlated with correlation at least 0.6.
  - Potential bias from financial centers (e.g., Cayman Islands, Luxembourg) is discussed: bias depends on whether the geographical distribution of indirect flows differs substantially from direct flows; paper does not trace ultimate beneficial owners.

### IV. Empirical analysis (methods, variables, and main empirical findings)
- A. Definition of connection variables
  - Uses assets and liabilities from international investment positions and exports/imports for trade.
  - All variables quoted in US dollar.
  - Portfolio investment benchmark includes equities traded in stock markets but equity component may also include investment fund shares (which can hold debts, real estate, commodities).
  - Direct investment conceptually close to stock returns (equity positions > 10 percent), though some holdings may be unlisted.
  - Other investment and trade are indirect channels affecting comovement.
- B. Construction of comovement variables (frequency, similarity statistics, and time adjustment)
  - Frequency and sample window:
    - Comovement variables constructed quarterly.
    - Built using trading dates of the following 2 months from the end of each quarter (example: 2017Q4 comovement based on 2018 January and February trading-day data).
    - Two-month choice balances proximity to connection data recording dates and sample size.
    - Robustness check: two months around the end of the quarter (e.g., 2017 December and 2018 January) yields qualitatively similar results.
  - Three similarity statistics used:
    - Correlation: sample correlation coefficient between return series (chosen as benchmark).
    - Mean deviation: 1/T sum of absolute differences of returns.
    - Beta: regression coefficient from r_A = alpha + beta * r_B + epsilon; interpreted as how much A’s return increases if B’s return increases by 1 percent.
  - Rationale for benchmark choice:
    - Correlation normalized by volatility and less sensitive to outliers when projected on connection variables; consistent with common language describing comovement.
    - Beta is asymmetric and aligns better with theoretical spillover interpretation; used in theoretical analysis implications.
  - Time lag/time adjustment to account for non-overlapping trading hours:
    - For market pairs with substantial overlap in trading hours, same-day returns proxy the object.
    - For non-overlapping markets, baseline takes a 1-day lag when the counterpart market’s closing time is more than 7 hours ahead on the same day (e.g., when U.S. benchmark vs. Japan, take 1-day lag of U.S. data for U.S.–Japan comovement).
    - No lag taken when the domestic market closes first (e.g., when Japan is benchmark vs. U.S., no lag for Japan).
    - This rule yields consistent comovement variables across countries.
  - Additional time-adjustment robustness methods:
    - Raw end-of-day data without adjustment (conceptual asymmetry risk).
    - Max-of-lag-and-current method: compute correlations using combinations (current vs. lag) and take max for correlation and beta, min for mean deviation; this searches time convention that maximizes comovement but risks upward bias.
  - Conservatism: if time conventions fail to capture comovement (e.g., source economy changes daily), comovement measures may be downward biased, making empirical results conservative.
- C. Empirical results: the case of the United States
  - Sample visualization (described):
    - Figure 1 plots each counterpart economy–date pair as a dot: y-axis = stock return correlation with the United States; x-axis = log of U.S. portfolio investment asset.
    - Pooled scatter shows that more international financial connection is associated with more stock return comovement.
  - Two descriptive observations from pooled plot:
    - Comovement is mostly positive — typical comovement reflects wealth or risk-on/off effects pushing prices in same directions; consistent with literature (e.g., Bekaert et al. (2016)).
    - Stock return comovement with the United States is higher when the U.S. portfolio investment asset position on the destination economy is larger — novel observation and main contribution.
  - Stability over time:
    - Figure 2 (date-sliced chart) shows relationship stable over time despite fluctuations in comovement and connection.
  - Robustness and extensions:
    - All portfolio investment asset data for these U.S. analyses are compiled by the United States, minimizing concerns about inconsistent methodologies across reporters.
    - Complementary analyses find that for large portfolio asset economies (United States, Germany), portfolio investment asset positions typically have the highest prediction power among connection concepts; for smaller economies, other connection concepts may dominate.

*Source: IMF Working Paper — section "5. Comovement vs Connection, Government Bond Yield" (content unit provided).*

### Annex IX.C. One can see that some economies with high correlations, such as Canada,

### Annex IX.C. One can see that some economies with high correlations, such as Canada,

### Empirical finding: connection predicts stock return comovement (cross-section)
- Stock return correlation with the United States is positively associated with the log of U.S. portfolio investment asset by CPIS date.  
- The relationship is best interpreted as a cross-sectional relationship rather than a time-series relationship because a global time fixed effect (for example, risk-on/risk-off regimes) can dominate within-economy time slices.
- When U.S. portfolio asset fluctuation is smaller than the comovement, charts sliced by economy can be dominated by global fixed effects and exhibit a weak relationship; Figure 1 should therefore be read as cross-sectional evidence.

### Robustness checks and alternative comovement statistics
- The result remains when the comovement concept is replaced by:
  - the mean deviation (median deviation between counterpart economy stock return and U.S. stock return), and
  - the regression coefficient of the counterpart economy’s stock return on the United States.
- Outliers exist (for example, Greece crisis periods in 2014 and 2016), but the overall association persists: more U.S. portfolio investment asset is associated with more stock return comovement.
- Annex IX.E reports 5 additional robustness checks showing the relationship holds:
  1. after considering daily FX return,
  2. after normalizing the position by the GDP of the counterpart economy,
  3. if the connection variable is replaced by portfolio equity position or portfolio debt position,
  4. if the stock index is replaced by the price index that excludes dividends,
  5. if the benchmark time adjustment is replaced by the other two methods discussed in section IV.B.
- Main takeaway: under various specifications, daily stock returns tend to comove more with the United States for economies with stronger measured international financial connection to the United States.

### Alternative connection measures
- The predictability is not always evident if the connection variable is not the portfolio investment asset position.
- Example: replacing portfolio investment asset by U.S. bank asset divided by counterpart economy’s GDP yields a weaker predictive relationship (Figure 4).
- This raises the question: “which connection concept predicts stock return comovement best for each economy?”

### Empirical exercise: top 20 portfolio investment asset economies — prediction power metrics
- Prediction power measured by:
  - R-square (푅푅2): percentage of variation in stock return comovement explained by a linear function of the connection variable (with time fixed effects).
  - Leave-one-out pseudo R-square (푅푅푝푝2): magnitude of the correlation between fitted value and actual value using leave-one-out fitted values.
- 푅푅2 and 푅푅푝푝2 tend to point to the same connection concept and give similar values; coincidence interpreted as robustness.
- The regression objective is prediction, not parameter estimation or causality; statistical significance and controls are not used.

### Table 1: Connection concepts with highest prediction power (exact entries)
- DE — Highest 푅푅2 (in log): PI asset 0.58; Highest 푅푅푝푝2 (in log): PI asset 0.57
- AT — Highest 푅푅2 (in log): PI asset 0.57; Highest 푅푅푝푝2 (in log): PI asset 0.55
- BE — Highest 푅푅2 (in log): PI asset 0.57; Highest 푅푅푝푝2 (in log): PI asset 0.55
- CH — Highest 푅푅2 (in log): DI inward 0.58; Highest 푅푅푝푝2 (in log): DI inward 0.54
- CN — Highest 푅푅2 (in log): Bank's liability 0.58; Highest 푅푅푝푝2 (in log): Bank's liability 0.54
- IT — Highest 푅푅2 (in log): PI asset 0.56; Highest 푅푅푝푝2 (in log): PI asset 0.54
- NL — Highest 푅푅2 (in log): Export 0.55; Highest 푅푅푝푝2 (in log): Export 0.53
- FR — Highest 푅푅2 (in log): PI asset (LTD) 0.55; Highest 푅푅푝푝2 (in log): PI asset (LTD) 0.53
- ES — Highest 푅푅2 (in log): PI asset (LTD) 0.56; Highest 푅푅푝푝2 (in log): PI asset (LTD) 0.52
- FI — Highest 푅푅2 (in log): PI asset (STD) 0.55; Highest 푅푅푝푝2 (in log): PI asset (LTD) 0.51
- DK — Highest 푅푅2 (in log): Bank's asset 0.56; Highest 푅푅푝푝2 (in log): PI asset (STD) 0.51
- SE — Highest 푅푅2 (in log): Import 0.50; Highest 푅푅푝푝2 (in log): Import 0.48
- IE — Highest 푅푅2 (in log): PI liability (LTD) 0.49; Highest 푅푅푝푝2 (in log): PI liability (LTD) 0.46
- CA — Highest 푅푅2 (in log): DI outward 0.47; Highest 푅푅푝푝2 (in log): PI asset (LTD) 0.45
- GB — Highest 푅푅2 (in log): PI asset (LTD) 0.47; Highest 푅푅푝푝2 (in log): PI asset (LTD) 0.44
- US — Highest 푅푅2 (in log): PI asset 0.45; Highest 푅푅푝푝2 (in log): PI asset 0.43
- SG — Highest 푅푅2 (in log): Bank's liability 0.46; Highest 푅푅푝푝2 (in log): Bank's asset 0.40
- HK — Highest 푅푅2 (in log): DI outward 0.48; Highest 푅푅푝푝2 (in log): Bank's asset 0.34
- JP — Highest 푅푅2 (in log): DI outward 0.34; Highest 푅푅푝푝2 (in log): DI outward 0.30
- KR — Highest 푅푅2 (in log): Bank's liability 0.37; Highest 푅푅푝푝2 (in log): Bank's liability 0.29

- Two observations from Table 1:
  - 푅푅2 and 푅푅푝푝2 generally select the same connection concept and give similar magnitudes, supporting robustness.
  - Portfolio investment asset is not always the best predictor; different economies have different structures, so the most relevant connection concept differs across economies.

### Theoretical analysis: model that rationalizes empirical patterns
- Objective: explain (1) why comovement tends to be positive and (2) why portfolio investment position contains informational content for predicting stock return comovement.
- Model: extension of Grossman and Stiglitz (1980) to N economies, with:
  - representative investor i in each economy,
  - random returns m = [m1, ..., mN]' distributed as N(μ̅i, Ω) under investor i's belief (heterogeneous beliefs allowed),
  - CARA preferences and exponential utility, risk-free rate Ri, risk tolerance τi, wealth ωi,
  - equilibrium defined by investor optimization and market clearing.
- Key closed-form relations (preserve exact expressions as presented):
  - First-order optimal portfolio: x_i(p) = Ω^{-1}(μ_i − p) w_i, μ_i ≔ μ̅_i / (1 + R_i), w_i ≔ τ_i(1 + R_i).
  - Equilibrium price: p* = (1/W) [ ∑_j w_j μ_j − Ω X ], W = ∑_j w_j.
  - Equilibrium position: x_i* = Ω^{-1}[ ∑_j (w_j/W)(μ_i − μ_j) + (1/W) Ω X ] w_i.
- Proposition (comovement as function of portfolio position): for a risk tolerance shock to economy i,
  - ∂p*_j / ∂τ_i = β_{ij} ∂p*_i / ∂τ_i, where
  - β_{ij} ≔ (∑_k Ω_{jk} x_{ik}^*) / (∑_k Ω_{ik} x_{ik}^*).
- Special case (Ω = σ^2 I): β reduces to ratio of i’s position on j to i’s position on i: ∂p*_j / ∂τ_i = (x_{ij}^* / x_{ii}^*) ∂p*_i / ∂τ_i.
- Intuition:
  - A change in investor i’s risk tolerance scales portfolio sizes across stocks proportionally; price impact is larger for economies where investor i already holds a large position.
  - Shocks to U.S. investor risk attitudes can therefore generate positive comovement and stronger comovement for stronger connections.
- Extension to multiple investors and shocks:
  - Allow i.i.d. non-degenerate shocks to all τ_i, X = 0, Ω = I; equilibrium price is weighted sum of investors’ beliefs p = ∑_j (w_j/W) μ_j.
  - Correlation between any pair of prices can take values between −1 and 1 depending on beliefs; higher beliefs on both home and destination economies by investor i can generate simultaneously higher correlation and larger position on j.
  - x_{ij} increases with μ_{i j}; when investors have strong home-and-destination valuations, prices for i and j move together driven by the same investors’ risk attitude shocks.

### Discussion of alternative mechanisms (likely and unlikely)
- Likely mechanisms:
  - Direct investment liability: parent firms with large subsidiaries abroad can cause home-firm returns to move with subsidiary-country returns as investors use foreign stock information to forecast parent performance; larger direct investment implies larger exposure and stronger comovement.
  - Bank liability: banks’ cross-border lending and exposures can make home investors sensitive to foreign equity information; larger bank liability exposure can increase comovement.
  - In general, any connection variable correlated with exposures can have predictive power; Table 2 in Annex IX.B shows connection variables are correlated.
- Unlikely mechanisms:
  - Diversification motive alone is unlikely: to diversify, investors would invest in economies with negative correlation, which runs counter to the observed positive relationship.
  - Pure sentiment or random statistical errors are unlikely drivers: linking stronger sentiment to larger positions is challenging; random measurement errors would unlikely be systematically proportional to daily stock return comovement.

### Extension to other asset classes: government bond yields
- The analysis extends to bond yields using changes (since yields are in percent):
  - Short-term (3-month) government bond yield changes show almost no relationship with U.S. portfolio asset position.
  - Long-term (10-year) government bond yield changes show an increasing pattern with U.S. portfolio asset position.
  - Charts are similar if asset positions are replaced by liability positions.

*Source: wpiea2019181-print-pdf (Annex IX.C, Annex IX.D, Annex IX.E, Annex IX.F, Table 1, Figures 2–5, and sections V–VI of the provided content).*

### 2017. The left chart is 3-month and the right chart is 10-year bond. It shows that the U.S.

### wpiea2019181-print-pdf - 2017

### Government bond yields and limitations
- Government bond yields are less informative than stock returns for the study of international portfolio comovement because:
  - Government bonds are often classified in confidential reserve assets and therefore do not show up in portfolio investment or direct investment data; this is particularly true for short term bonds.
  - Yields of government bonds are often direct policy instruments, so changes in yields may reflect different forces than the profit-maximizing motive that drives equity markets.
- These caveats should be noted when interpreting bond comovement.

### Data granularity and extensions
- Further granularity could improve analysis:
  - Equity indices are often available by industry; if connection data have an industry-level or institutional-sector-level breakdown, stock return analysis can be extended from country level to country-sector level.
  - From-whom-to-whom portfolio data are available in CPIS table 6 for 16 economies as of June 2018.
- Reference for collection of from-whom-to-whom portfolio data: Harutyunyan and Sánchez-Muñoz (2019).

### Main empirical findings (Conclusion)
- A stronger international financial connection is associated with stronger stock return comovement.
- When using large portfolio investment asset economies such as the United States or Germany as the benchmark, bilateral portfolio positions have the highest prediction power.
- For smaller economies, the best predictor of stock return comovement varies by country.
- A general equilibrium portfolio theory is proposed that is consistent with the empirical patterns.
- The empirical results support the intuition that a more connected world tends to have more comovement, while also highlighting that the meaning of "connection" might differ across countries.

### Policy applications and future work
- Stock return comovement is an important input for portfolio diversification and spillover analysis.
- Stock return comovement can be used inversely to estimate international financial connection.
- Exploring these policy applications is left for future research.

### Annex highlights: U.S. correlation matrix of international financial connections (log)
- Table 2. Correlation Matrix of the U.S. International Financial Connections in Log:
  - PI asset vs:
    - PI asset: 1
    - Bank asset: 0.87
    - Bank liability: 0.84
    - DI inward: 0.88
    - DI outward: 0.80
    - Export: 0.74
    - Import: 0.73
  - Bank asset vs:
    - PI asset: 0.87
    - Bank asset: 1
    - Bank liability: 0.88
    - DI inward: 0.81
    - DI outward: 0.73
    - Export: 0.69
    - Import: 0.62
  - Bank liability vs:
    - PI asset: 0.84
    - Bank asset: 0.88
    - Bank liability: 1
    - DI inward: 0.83
    - DI outward: 0.64
    - Export: 0.64
    - Import: 0.65
  - DI inward vs:
    - PI asset: 0.88
    - Bank asset: 0.81
    - Bank liability: 0.83
    - DI inward: 1
    - DI outward: 0.74
    - Export: 0.63
    - Import: 0.66
  - DI outward vs:
    - PI asset: 0.80
    - Bank asset: 0.73
    - Bank liability: 0.64
    - DI inward: 0.74
    - DI outward: 1
    - Export: 0.82
    - Import: 0.68
  - Export vs:
    - PI asset: 0.74
    - Bank asset: 0.69
    - Bank liability: 0.64
    - DI inward: 0.63
    - DI outward: 0.82
    - Export: 1
    - Import: 0.91
  - Import vs:
    - PI asset: 0.73
    - Bank asset: 0.62
    - Bank liability: 0.65
    - DI inward: 0.66
    - DI outward: 0.68
    - Export: 0.91
    - Import: 1

### Robustness checks (U.S. comovement vs connection)
- The main pattern survives multiple robustness checks:
  - (1) After considering daily FX return.
  - (2) After normalizing the position by the GDP of counterpart economy.
  - (4) If the connection variable is replaced by portfolio equity position or portfolio debt position.
  - (4) After excluding dividend if the stock index is replaced by the price index that excludes dividends.
  - (5) If the time-lag-adjusted U.S. stock return is replaced by the current or max as discussed in section IV.B.

### Additional notes from annexes
- Subplots of Figure 1 include ISO2 labels for each date; S1 means June and S2 means December.
- U.S. comovement vs connection relationship is weaker when Figure 1 is sliced by economy.
- Comovement vs Connection charts for top 6 R2 economies use December 2017 data; R2 in those charts is calculated with time fixed effect and therefore does not equal Table 1.

*Source: wpiea2019181-print-pdf - 2017*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019181-print-pdf.pdf_