## ch3onlineannex

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---

### Online Annex 3.1 — Data Sources and Sample Description
- Fund-level variables (Morningstar):
  - Fund net flow: Fund flow as percentage of fund total net assets of the previous quarter.
  - Fund return: Fund assets' performance as percentage of fund total net assets of the previous quarter.
  - Fund cash holdings: Deposit in portfolio base currency that can be withdrawn at any time. Negative fund cash holdings set equal to zero; fund cash holdings larger than 20 percent of the fund’s total net assets set equal to 20 percent of the fund’s net assets.
  - Fund cash equivalent holdings: Includes cash, certificates of deposit, currency, money market holdings and other high quality fixed income securities with maturity of less than 92 days. Negative values set equal to zero; values larger than 20 percent set equal to 20 percent.
  - Swing pricing (dummy): Equals one when fund is domiciled in a country where use of swing pricing is permitted and common across funds; baseline domiciles: Luxembourg and the UK.
  - Expense ratio: Percentage of fund assets used to pay operating expenses and management fees; total expense ratio (in percent) winsorized at the 1st and 99th percentiles.
  - Portfolio illiquidity: Holding-weighted average bid-ask spread excluding cash (IMF staff calculation).
  - ETF premium/discount: (ETF NAV − closing ETF price) / ETF NAV; observations winsorized at the 1st and 99th percentiles.
  - Total net assets: Fund assets under management in USD at end of each quarter.
- Security-level variables (Refinitiv, Factset, IMF staff calculations):
  - Bid-ask spread (equities: based on daily closing prices; other asset classes: multiple inputs).
  - Market capitalization; Return (total return index, winsorized at 1.5 percent level); Fraction MF (ETF) ownership; Security ratings (S&P long-term local currency ratings); Turnover; Age; Skewness of returns; Price-to-Book ratio; Volatility (standard deviation of daily or weekly returns over a quarter); Security-level swing exposure; Issuer; Coupon rate; Bond maturity.
- Macro-financial variables:
  - Change in global liquidity: BIS global liquidity indicator (GLIs), quarter-over-quarter change.
  - Commodity price shock: Pure oil price expectation shock as defined in Bauermeister (2021).
  - Domestic monetary policy shocks: Residuals from regressing policy rate on controls (contemporaneous and lagged inflation, log U.S. GDP, log foreign GDP, lagged policy rate, quadratic time trend).
  - Financial condition index (FCI): Principal component analysis of 11 price-based variables; positive values indicate tighter-than-average financial conditions.
  - Foreign GDP growth: Average real GDP growth of foreign economies relative to a given domestic economy.
  - GDP growth: Quarterly real GDP growth (IMF, World Economic Outlook; IMF staff calculations).
  - MPU: Monetary Policy Uncertainty index for the United States (Husted and others (2020)).
  - VIX: CBOE Volatility Index.
- Investment fund sample:
  - Data of 17,000 open-end funds sourced from Morningstar with portfolio holdings data from Factset.
  - About 14,000 were in existence at the beginning of 2021.
  - Sample period: 2013:Q4 to 2022:Q2.
  - Funds domiciled in 43 countries and grouped into allocation, alternative, equity, and fixed income categories.
  - Typical fund holds about 150 on average.
  - Comprehensive portfolio holdings data available starting 2013:Q4.

### Online Annex 3.2 — Construction of Asset-Level Vulnerability Measure
- Two-step construction (following Jiang and others (2022)):
  - Step 1: Fund-level illiquidity measure — weighted average of bid-ask spreads of assets held by the fund, weights are market values of asset holdings.
  - Step 2: Asset-level vulnerability measure — weighted average of investing funds’ illiquidity, weights represent funds’ relative holdings of the asset.
- Notation and precise formulations presented in equations (1) and (2) in the source.
- Note on potential endogeneity: typical fund holds about 150 assets on average, so excluding a specific asset from the fund-level illiquidity measure is unlikely to materially affect measures.

### Effect of Asset-Level Vulnerability on Asset Price Fragility
- Empirical approach:
  - Regressions estimated separately for each asset class (δ).
  - Dependent variable: σδc,i,t+1 = standard deviation of annualized weekly returns over the next quarter for asset i in country c, as a percent of the sample median.
  - Key explanatory variable: standardized asset-level vulnerability measure (standardized version of equation (2)).
  - Controls: country-time fixed effects (γc,t), asset fixed effects (γi). Standard errors clustered at quarter and asset levels.
  - Asset-class specific controls:
    - Bonds: bid-ask spread, log market capitalization, weekly returns, mutual fund ownership, time to maturity, security ratings.
    - Equities: bid-ask spread, log market capitalization, weekly returns, mutual fund ownership, turnover, log age, skewness, mid-price, one-year return, price-to-book ratio.
  - Regressions estimated for: all bonds; corporate bonds; high-yield corporate bonds; investment-grade corporate bonds; sovereign bonds; high-yield sovereign bonds; investment-grade sovereign bonds; all equities; small cap equities.
- Robustness checks include:
  - Alternative definitions of asset vulnerability (global equity funds only, fixed-income funds only, mixed funds only).
  - Alternative fixed effects specifications (country, borrower, time, borrower-time, borrower-time and asset fixed effects).
  - Alternative dependent variable: annualized daily return volatility.
  - Alternative timing for portfolio-level bid-ask spread: average spread in the quarter before portfolio holdings observed.
  - Including cash holdings when calculating fund-level illiquidity.
  - Restricting to funds with at least 100 securities per quarter.
  - Including lagged volatility in equity regressions.
  - Restricted sample of securities with high mutual fund ownership.
- Conclusion: Original conclusions are robust to these changes.

### Effect of Asset-Level Vulnerability on Asset Price Fragility in Times of Stress
- Empirical specification (equation (4)):
  - Tests whether asset-level vulnerabilities amplify impact of market stress (financial uncertainty measured by VIX or US monetary policy uncertainty) on next-quarter asset return volatility (standardized).
  - Sample period: 2013:Q4 to 2021:Q4. Quarterly data. Standard errors clustered by asset and time.
- Stress variables and timing:
  - VIX: CBOE Volatility Index; spiked in March 2020 during COVID-19 market turbulence.
  - US monetary policy uncertainty: textual analysis of Washington Post, Wall Street Journal, New York Times using specified keyword triple (Husted and others (2020)). Monetary policy uncertainty was elevated in 2019 and rising since end-2021. Monetary policy uncertainty series available until the third quarter of 2021.
- Robustness checks:
  - Alternative fixed effects (country, industry, country-time, industry-time).
  - Alternative stress measures (e.g., VIX dummy equal to 1 when VIX in upper decile).
  - Alternative definitions of vulnerable assets (top half or top quartile of asset vulnerability distribution by asset class).
  - Balanced panel starting from 2013:Q4.
- Findings:
  - VIX spiked in March 2020; monetary policy uncertainty elevated in 2019 and rising since end-2021.
  - Results indicate interaction between stress and asset-level vulnerability increases next-quarter volatility.

### Bond Returns During the March 2020 Dash-for-Cash Episode
- Weekly regression model (equation (5)) for Q1–Q2 2020:
  - Dependent variable: weekly return of security i at time t.
  - Key variables: asset-level vulnerability; I_Stress dummy equal to 1 in the last three weeks of February and first week of March (following Jiang and others, 2022); interaction I_Stress × asset-level vulnerability; controls as in equation (3) plus lagged weekly returns. All controls lagged as of 2019:Q4.
  - Fixed effects: industry-level or country-level. Standard errors clustered at asset and week levels.
- Result:
  - β3 is negative and statistically significant across all bond asset classes, supporting that asset-level vulnerabilities induced by fund illiquidity lead to a decline in asset returns (increase in asset price fragility) in periods of market stress.

### Cross-Border Spillovers to Emerging Market Securities
- Analysis:
  - Restricted version of equation (3) estimated for assets issued by firms of EMs using asset-vulnerability measure calculated only from funds domiciled in advanced economies.
  - Robustness checks analogous to earlier specifications performed.
- Findings:
  - Results are robust, indicating possible cross-border implications of open-end fund vulnerabilities on EM securities.

### Herding as an Amplifier of Asset-Level Vulnerabilities
- Herding measure (following Cai and others (2019)):
  - Herding defined as the extent to which trading of a security deviates from market-wide trading patterns — tendency of funds to trade a given asset together in the same direction more often than expected under independence.
  - Formulae provided for HHRi,t (equation (6)), proportion of buyers p_i,t (equation (7)), market-wide buying intensity p̄_t (equation (8)), Buy herding measure (BHM) for p_i,t > E[p_i,t] (equation (9)), Sell herding measure (SHM) for p_i,t < E[p_i,t] (equation (10)). Adjustment ensures expected value of herding measure is zero under null of no herding.
- Panel regression (equation (11)):
  - Dependent variable: next-quarter asset return volatility (standardized).
  - Explanatory variables: one herding measure, asset-level vulnerability, interaction herding × vulnerability, controls (average bid-ask spread, log bond issue size, bond rating, share of mutual fund ownership, maturity for bonds), asset and country-time fixed effects. Standard errors clustered by security and time.
- Interpretation:
  - Tests whether herding by open-end funds amplifies vulnerability-induced volatility.

### Aggregate Effect of Vulnerability on Financial Conditions
- Aggregate (country-level) vulnerability:
  - Weighted average of asset-level vulnerabilities across domestic assets, weights equal relative market values. Also reported by asset class.
- Panel quantile regression (equation (12)):
  - Dependent variable: τ quantile of the financial conditions index in country c at time t+1.
  - Explanatory variables: aggregate vulnerability and macro-financial/external controls (domestic and US monetary policy shocks, domestic GDP growth, foreign GDP growth, change in global liquidity, commodity price shocks).
  - Includes country fixed effects; coefficients common across countries but estimated for different quantiles (τ) of the FCI.
- Robustness:
  - Including autoregressive terms for dependent and independent variables.
  - Time fixed effects instead of time-varying global common factors.
  - Alternative FCIs based on factor model with time-varying parameters (Koop and Korobilis 2014).

*Source: IMF staff (Online Annex 3.1–3.4 of Chapter 3).*

### Chapter 3

### Chapter 3

### Online Annex 3.1 — Data Sources and Sample Description
- Fund-level variables sourced from Morningstar include:
  - Fund net flow: Fund flow as percentage of fund total net assets of the previous quarter.
  - Fund return: Fund assets' performance as percentage of fund total net assets of the previous quarter.
  - Fund cash holdings: Deposit in portfolio base currency that can be withdrawn at any time. Consistent with the literature (Jiang and others, 2022), negative fund cash holdings are set equal to zero and fund cash holdings larger than 20 percent of the fund’s total net assets are set equal to 20 percent of the fund’s net assets.
  - Fund cash equivalent holdings: Fund cash and equivalents include cash held in bank accounts as well as certificates of deposit, currency, money market holdings and other high quality fixed income securities with a maturity of less than 92 days. Consistent with the literature (Jiang and others, 2022), negative fund cash and equivalents holdings are set equal to zero and fund cash and equivalents holdings larger than 20 percent of the fund’s total net assets are set equal to 20 percent of the fund’s net assets.
  - Swing pricing (dummy variable): Dummy variable which is equal to one when the fund is domiciled in a country in which the use of swing pricing is permitted by regulators and common across funds, and equal to zero otherwise. In the baseline analysis, Luxembourg and the UK are classified as swing pricing domiciles.
  - Expense ratio: The percentage of fund assets used to pay for operating expenses and management fees, including 12b-1 fees, administrative fees, and all other asset-based costs incurred by the fund, except brokerage costs. The fund’s total expense ratio (in percent) is winsorized at the 1st and 99th percentiles.
  - Portfolio illiquidity: Holding-weighted average bid-ask spread excluding cash. (IMF staff calculation)
  - ETF premium/discount: Difference between ETF NAV and closing ETF price measured as a percentage of the ETF NAV. Observations are winsorized at the 1st and 99th percentiles.
  - Total net assets: The fund’s total assets under management in USD measured at the end of each quarter.
- Security-level variables sourced from Refinitiv, Factset, and IMF staff calculations include:
  - Bid-ask spread: For equities, based on daily closing prices; for other asset classes, based on multiple inputs using daily closing bid-ask prices from an exchange, composite bid-ask prices, and Refinitiv’s evaluated bid-ask prices.
  - Market capitalization, Return (total return index, winsorized at 1.5 percent level), Fraction MF (ETF) ownership, Security ratings (S&P long-term local currency ratings), Turnover, Age, Skewness of returns, Price-to-Book ratio, Volatility (standard deviation of daily or weekly returns over a quarter), Security-level swing exposure (ownership of a given asset by open-end mutual funds that use swing pricing as a percentage of its total mutual fund ownership), Issuer, Coupon rate, Bond maturity.
- Macro-financial variables:
  - Change in global liquidity: The BIS global liquidity indicator (GLIs). Quarter-over-quarter change used.
  - Commodity price shock: Pure oil price expectation shock as defined in Bauermeister (2021).
  - Domestic monetary policy shocks: Estimated by regressing the policy rate on controls; residuals used as identified shocks. Controls include contemporaneous and lagged values of inflation, log U.S. GDP, log foreign GDP, lagged policy rate and a quadratic time trend.
  - Financial condition index (FCI): Principal component analysis of 11 key price-based variables capturing the price of risk (refer to Online Annex 3.2 of the October 2017 GFSR). Positive values indicate tighter-than average financial conditions.
  - Foreign GDP growth: Average real GDP growth of foreign economies relative to a given domestic economy.
  - GDP growth: Quarterly real GDP growth (IMF, World Economic Outlook; IMF staff calculations).
  - MPU: Monetary Policy Uncertainty index for the United States obtained from text analysis of newspaper articles (Husted and others (2020)).
  - VIX: CBOE Volatility Index.

- Investment fund sample:
  - Data of 17,000 open-end funds sourced from Morningstar with portfolio holdings data from Factset.
  - About 14,000 were in existence at the beginning of 2021.
  - Sample period: 2013:Q4 to 2022:Q2.
  - Funds domiciled in 43 countries and grouped into allocation, alternative, equity, and fixed income categories.
  - Typical fund holds about 150 on average.
  - Comprehensive portfolio holdings data available starting 2013:Q4.

### Online Annex 3.2 — Construction of Asset-Level Vulnerability Measure
- Two-step construction (following Jiang and others (2022)):
  1. Fund-level illiquidity measure: weighted average of bid-ask spreads of assets held by the fund, where weights are market values of asset holdings.
  2. Asset-level vulnerability measure: weighted average of investing funds’ illiquidity, where weights represent funds’ relative holdings of the asset.
- Notation and precise formulations are presented in equations (1) and (2) in the source.
- Note on potential endogeneity: typical fund holds about 150 assets on average, so excluding a specific asset from the fund-level illiquidity measure is unlikely to materially affect measures.

### Effect of Asset-Level Vulnerability on Asset Price Fragility
- Empirical approach:
  - Regressions estimated for each asset class (δ) separately using:
    - Dependent variable: σδc,i,t+1 = standard deviation of annualized weekly returns over the next quarter for asset i in country c, as a percent of the sample median.
    - Key explanatory variable: standardized asset-level vulnerability measure (standardized version of equation (2)).
    - Controls: country-time fixed effects (γc,t), asset fixed effects (γi). Standard errors clustered at quarter and asset levels.
  - Controls specific to asset class:
    - Bonds: bid-ask spread, log of market capitalization, weekly returns, mutual fund ownership, time to maturity, security ratings.
    - Equities: bid-ask spread, log market capitalization, weekly returns, mutual fund ownership, turnover, log age, skewness, mid-price, one-year return, price-to-book ratio.
  - Regressions estimated separately for: all bonds, corporate bonds, high-yield corporate bonds, investment-grade corporate bonds, sovereign bonds, high-yield sovereign bonds, investment-grade sovereign bonds, all equities, small cap equities.
- Robustness checks performed include (but are not limited to):
  - Alternative definitions of asset vulnerability: from global equity funds only, fixed-income funds only, mixed funds only.
  - Alternative fixed effects specifications: country, borrower, time, borrower-time fixed effects, borrower-time and asset fixed effects.
  - Alternative dependent variable: annualized daily return volatility.
  - Alternative timing for portfolio-level bid-ask spread: average spread in the quarter before portfolio holdings observed.
  - Including cash holdings when calculating fund-level illiquidity.
  - Restricting to funds with at least 100 securities per quarter.
  - Including lagged volatility in equity regressions.
  - Restricted sample of securities with high mutual fund ownership.
- Conclusion: Original conclusions are robust to these changes.

### Effect of Asset-Level Vulnerability on Asset Price Fragility in Times of Stress
- Empirical specification (equation (4)):
  - Tests whether asset-level vulnerabilities amplify the impact of market stress (financial uncertainty measured by VIX or US monetary policy uncertainty) on next-quarter asset return volatility (standardized).
  - Sample period: 2013:Q4 to 2021:Q4. Quarterly data. Standard errors clustered by asset and time.
  - Stress variables:
    - VIX: CBOE Volatility Index; spiked in March 2020 during COVID-19 market turbulence.
    - US monetary policy uncertainty: obtained from textual analysis of Washington Post, Wall Street Journal, New York Times using specified keyword triple (Husted and others (2020)). Monetary policy uncertainty was elevated in 2019 and rising since end-2021. Monetary policy uncertainty series available until the third quarter of 2021.
- Robustness checks include:
  - Alternative fixed effects: country, industry, country-time, industry-time fixed effects.
  - Alternative stress measures: e.g., VIX dummy equal to 1 when VIX in upper decile.
  - Alternative definitions of vulnerable assets: top half or top quartile of asset vulnerability distribution by asset class.
  - Balanced panel starting from 2013:Q4.
- Findings summarized:
  - The VIX spiked in March 2020; monetary policy uncertainty elevated in 2019 and rising since end-2021.
  - Results (see source) indicate interaction between stress and asset-level vulnerability increases next-quarter volatility.

### Bond Returns During the March 2020 Dash-for-Cash Episode
- Weekly regression model (equation (5)) estimated for Q1–Q2 2020:
  - Dependent variable: weekly return of security i at time t.
  - Key variables: asset-level vulnerability, I_Stress dummy equal to 1 in the last three weeks of February and first week of March (following Jiang and others, 2022), interaction of I_Stress with asset-level vulnerability, control variables as in equation (3) plus lagged weekly returns. All controls lagged as of 2019:Q4.
  - Fixed effects: industry-level or country-level. Standard errors clustered at asset and week levels.
- Result:
  - β3 is negative and statistically significant across all bond asset classes, supporting that asset-level vulnerabilities induced by fund illiquidity lead to a decline in asset returns (increase in asset price fragility) in periods of market stress.

### Cross-Border Spillovers to Emerging Market Securities
- Analysis:
  - Restricted version of equation (3) estimated for assets issued by firms of EMs using asset-vulnerability measure calculated only from funds domiciled in advanced economies.
  - Robustness checks analogous to earlier specifications performed.
- Findings:
  - Results are robust (specific coefficients and statistical details in the source), indicating possible cross-border implications of open-end fund vulnerabilities on EM securities.

### Herding as an Amplifier of Asset-Level Vulnerabilities
- Herding measure (following Cai and others (2019)):
  - Herding defined as how much the trading pattern of a security varies from the market-wide trading pattern in the same period—the tendency of funds to trade a given asset together in the same direction more often than expected if they traded independently.
  - Formulae provided for:
    - Herding measure HHRi,t (equation (6))
    - Proportion of buyers p_i,t (equation (7))
    - Market-wide buying intensity p̄_t (equation (8))
    - Buy herding measure (BHM) for p_i,t > E[p_i,t] (equation (9))
    - Sell herding measure (SHM) for p_i,t < E[p_i,t] (equation (10))
  - Adjustment ensures expected value of herding measure is zero under null of no herding.
- Panel regression (equation (11)) tests whether herding amplifies impact of asset-level vulnerability on asset return volatility:
  - Dependent variable: next-quarter asset return volatility (standardized).
  - Explanatory variables: one of the herding measures, asset-level vulnerability, interaction between herding and vulnerability, controls (average bid-ask spread, log of bond issue size, bond rating, share of mutual fund ownership, maturity for bonds), asset and country-time fixed effects. Standard errors clustered by security and time.
- Interpretation:
  - Herding by open-end funds is tested as an amplifier of vulnerability-induced volatility; methodology and controls specified in detail in the source.

### Aggregate Effect of Vulnerability on Financial Conditions
- Aggregate (country-level) vulnerability:
  - Calculated as weighted average of asset-level vulnerabilities across all assets issued domestically, weights equal relative market values of assets.
  - Also reported for aggregate measures by asset class.
- Panel quantile regression (equation (12)) estimates effect on financial conditions index:
  - Dependent variable: τ quantile of the financial conditions index in country c at time t+1.
  - Explanatory variables include aggregate vulnerability and macro-financial/external controls: domestic and US monetary policy shocks, domestic GDP growth, foreign GDP growth (averaged), change in global liquidity conditions, commodity price shocks.
  - Model includes country fixed effects; coefficients common across countries but estimated for different quantiles (τ) of the financial conditions index.
- Robustness checks:
  - Including autoregressive terms for dependent and independent variables.
  - Time fixed effects instead of time-varying global common factors (US monetary policy rate, change in global liquidity).
  - Alternative financial conditions indices based on a factor model with time-varying parameters including broader macro-financial variables (as in Koop and Korobilis 2014).

*Source: IMF staff (Online Annex 3.1–3.2 of Chapter 3).*

### Annex 1.1 of  the  October  2018 GFSR) and a larg er  value  of  the  index  indicates  tig hter  financial   conditions

### Online Annex 3.3 Mechanisms Through Which Investment Fund Vulnerabilities Affect Asset Price Fragility

### Identification of shocks and asset-level vulnerability measures
- Domestic monetary policy shocks are estimated by regressing the policy rate on a set of controls and using the residuals as the identified shocks. The set of controls includes contemporaneous and lagged values of inflation, log U.S. GDP, log foreign GDP, as well as lagged values of the policy rate and a quadratic time trend.
- Commodity price shocks correspond to pure oil price expectation shocks, as defined in Bauermeister (2021). To filter out the “pure” expectation component, market-based surprises are regressed on fundamental oil supply and demand shocks.
- Alternative asset-level vulnerability measures considered include: (i) alternative aggregation of the portfolio-level bid-ask spread; (ii) more granular breakdown of asset classes; (iii) simple instead of weighted averaging across securities. The results are broadly robust to these alternative specifications.

### Cross-border spillovers from advanced-economy fund vulnerabilities to emerging markets
- Empirical specification: a modified version of equation (11) is estimated where the dependent variable FCI (financial conditions index) for emerging market economy c in period t+1 is regressed on:
  - the average asset-level vulnerability from funds located in advanced economies that hold assets in the emerging market economy c in period t;
  - domestic controls and fixed effects.
- Online Annex Figure 3.2.2 shows the magnitude of the spillover effects in emerging markets compared to that estimated for all the economies.
- Note: Solid dots and full bars indicate statistical significance at 10 percent or lower.

### Mechanism 1 — Vulnerable (illiquid) funds and extreme outflows
- Hypothesis: funds holding relatively illiquid assets tend to experience more extreme outflows in periods of stress due to strategic complementariness among investors.
- Fund-level panel regression estimated (equation (1)):
  - Dependent variable Y_{j,t}: outflows from fund j in period t — the negative fund flows (with sign inverted) expressed as a percentage of the fund’s size.
  - Key regressor: fund-level illiquidity measure defined in equation (1) of Online Annex 3.2.
  - Controls include fund size, fund age, past fund returns; fund fixed effects (γ_j); country-time fixed effects (μ_{c,t}).
  - Stress indicator S_{t} is an indicator variable that takes the value 1 when the VIX Index is above a given percentile of its sample distribution; results are presented for the percentiles 50, 55, ..., 95 to examine amplification effects.
  - Coefficients of interest: β_1 and β_2. If illiquid funds face larger outflows in time of stress, the sum of β_1 and β_2 is expected to be positive and increasing in the level of stress.

### Mechanism 2 — Asset-level vulnerabilities and selling pressure
- Selling pressure measure (equation (2)):
  - Selling pressure at issuer-asset level SA_{i,t} = sum across funds j of (par amount of security i sold by fund j in quarter t minus par amount purchased by fund j in quarter t) weighted by indicators for extreme fund flows; uses quarterly percentage flow of fund j adjusted for returns (Flow_{j,t}) and outstanding amount of security i.
  - Intuition: selling pressure captures the difference between sales and purchases of bonds by investment funds that experience extreme outflows or inflows. A large value indicates strong selling pressure.
- Quarterly regression (equation (3)):
  - Dependent variable: selling pressure for asset i in quarter t.
  - Key regressor: asset-level vulnerability measure (AAA_i_LA... VFI_F... as defined in the annex).
  - Controls include fund size (log), investment fund ownership percentage, issuer rating, average bid-ask spread, past volatility; country-time fixed effects and asset fixed effects.
  - Coefficient of interest: β_1. If assets exposed to vulnerable funds face stronger selling pressures the coefficient β_1 should be positive.

### Mechanism 3 — Pecking order of liquidation and sensitivity to fund outflows
- Hypothesis: funds follow a pecking order of liquidation; more liquid assets are sold earlier relative to less liquid assets within the same fund.
- Empirical model (equation (4)):
  - Dependent variable Y_{i,j,t}: percentage change of shares of security i sold by fund j at time t.
  - Regression includes fund outflows and an interaction of fund outflows with the pecking order (liquidation rank) of security i in fund j.
  - Pecking order (liquidation rank) L_{k,H,j} is computed as the share of other assets held by the same fund that are less liquid relative to asset k; assets are grouped into liquidity groups based on bid-ask spreads in the sample distribution each quarter.
  - If a pecking order is followed, coefficients λ_0 and λ_1 should be positive.
- Analysis focuses on the COVID-19 crisis event to identify liquidation behavior when large sell-offs were more likely to impact asset prices beyond fundamentals.

### Mechanism 4 — Selling pressure impact on asset prices (liquidity-adjusted selling pressure and price effects)
- Liquidity-adjusted selling pressure (equation (6)):
  - LQ_SellPressure_{H,t} constructed using estimated λ̂_0 and λ̂_1 from equation (4) and fund flows, thereby accounting for funds’ liquidation policies and reducing reverse causality concerns.
- Price impact regression (equation (7)):
  - Dependent variable: AVVR_{i,t+1} — the difference between the quarterly return and the size-weighted average return of a pool of comparable securities.
  - Key regressor: liquidity-adjusted selling pressure for asset i in quarter t.
  - Controls include turnover, credit rating, amount outstanding, maturity, issuer volatility, and country fixed effects (μ_H and θ_c).
  - Model estimated separately for each asset class; analysis focuses on COVID-19 episode for identification.
- Robustness: analyses repeated using ratings as an alternative measure of asset liquidity to define liquidity groups and on the full data sample (2010:Q1-2021:Q4) while controlling for time variation in sensitivity depending on VIX. Results broadly align with baseline specifications.

### Online Annex 3.4 — Analysis of liquidity management tools
- Swing Pricing
  - Regression specification (equation (1)) to analyze effect of swing pricing on fund-induced asset price fragility:
    - Dependent variable: σ_{i,t+1} (asset fragility/volatility measure for asset i).
    - Regressors include asset-level vulnerability, ownership of asset i by open-end mutual funds that use swing pricing as a percentage of total mutual fund ownership (SSF_i_Ax..._{i,t}), an interaction between swing ownership and asset vulnerability, VIX-minus-ask (VIX-ask), and asset controls.
    - Asset fixed effects (γ_i) and country-time fixed effects (μ_{H,t}) included.
  - Baseline definition of SSF at the security level (equation (2)): fraction of mutual fund ownership that is domiciled in countries where use of swing pricing by open-ended mutual funds is common; baseline set SSF_countries = {Luxembourg, UK} in the specification.
  - Robustness checks:
    - Using alternative definitions of the set of swing countries;
    - Including time-varying global stress indicators (such as the VIX index) instead of time fixed effects;
    - Using different sets of control variables.
  - Results are broadly robust to these alternative specifications.

- Role of Cash Buffers
  - Fund-level regression (equation (4)) based on Jiang and others (2020):
    - Dependent variable ΔCashHoldings_{j,t} = (Cash_{j,t} − Cash_{j,t−1}) / Cash_{j,t−1}, the percentage change in fund j’s holdings of cash and equivalents in quarter t.
    - Regressors include measures of net flows (NA_i inflow/outflow proxies), interactions with stress indicator S_{t}, fund characteristics and portfolio illiquidity.
    - Controls: log fund size, quarterly returns, expense ratio and portfolio illiquidity (average bid-ask spreads excluding cash equivalents) in lags.
    - Fund fixed effects (γ_j) included.
    - Results robust to focusing on specific fund types (e.g., bond or equity funds).

### Exchange-Traded Funds (ETFs) and relative fragility
- Hypothesis: in periods of stress, assets with higher ETF ownership may be less fragile than those mostly owned by open-end mutual funds.
- Regression specification (equation (5)):
  - Dependent variable: σ_{i,t+1} (asset fragility/volatility measure for asset i).
  - Regressors include percentage ownership of asset i by open-end mutual funds (OF_OWN_{i,t}) and by ETFs (ETF_OWN_{i,t}), interactions of both ownership measures with the stress indicator S_{t}, VIX-minus-ask, controls for fund ownership and other asset characteristics, and asset fixed effects (γ_H).
  - Ownership measures defined at security level by summing holdings of relevant fund types and normalizing by amount outstanding (equations (6) and (7)).
- Identification and endogeneity:
  - Key concern: ETFs and open-end mutual funds could endogenously self-select into assets with different and unobservable fragility.
  - Addressed by exploiting variation in ownership bases across nearly identical bonds (matching different corporate bonds held by ETFs and open-ended mutual funds while holding issuer, maturity, and coupon rate constant).
  - Regressions control for security-specific illiquidity proxies, including bid-ask spreads.
- Note: ETFs are redeemable in kind via authorized participants (APs) in primary markets; while ETFs avoid first-mover run risks, AP arbitrage activity can itself increase volatility (Ben-David and others, 2018). The differential impact of open-ended mutual funds and ETFs on security price volatility is an empirical question addressed by the chapter.

*International Monetary Fund | Online Annex 3.3 and 3.4 excerpts, October 2022*

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_Source: https://www.imf.org/-/media/files/publications/gfsr/2022/october/english/ch3onlineannex.pdf_