## ch2annex ## Source details **Canonical URL:** [ch2annex](https://www.imf.org/-/media/files/publications/gfsr/2025/april/english/ch2annex.pdf) ## Other formats - [Markdown version](/-/media/files/publications/gfsr/2025/april/english/ch2annex.pdf.md) - [Structured JSON version](/-/media/files/publications/gfsr/2025/april/english/ch2annex.pdf.json) --- ### Data, definitions, and methodology - War periods used: World War I (July 28, 1914 – November 11, 1918) and World War II (September 1, 1939 – September 2, 1945). Country-specific market closures/limits noted for Japan and Germany. - GPR indices: global and country-specific indices from Caldara and Iacoviello (2022); “major” events = country GPR index > country mean by more than 2 standard deviations; total identified major events: 452 country-month observations; share ≈ 2.5 percent; international military conflicts ≈ 15 percent of major events. - VAR sample and estimation: - Sample for VAR analysis: 43 AEs and EMDEs, 1986–2024 (unbalanced panel). - Baseline panel VAR with country and pandemic country-time fixed effects; Bayesian estimation (Gibbs sampler) with Minnesota priors; P = 2 lags (BIC). - Endogenous monthly variables Z_it: GPR, industrial production index, CPI, policy and long-term interest rates, real equity prices (CPI-deflated stock indices in USD), real price of oil (US CPI-deflated WTI), VIX. Logs used except for interest rates. - Identification: recursive (Cholesky) ordering with GPR first. - Firm-level event regressions: - Global panel: about 60 thousand firms from 20 AEs and 20 EMEs; alternative analyses up to 39 countries with about three thousand and twenty thousand firms depending on exposure measure. - Primary dependent variable: firm monthly excess returns (USD, in excess of monthly US Treasury yields). - Key regressors: domestic major GPR dummy; weighted trading-partner event dummy (weights = previous-year trade exposures); controls: firm size (log total assets), leverage (equity-to-total assets), return on assets; country-(4-digit)sector-month fixed effects absorb time-varying country- and sector-specific factors. - Option-implied volatility estimation: - IV estimated from one-month-ahead put options using deltas {15,20,25,30,35,40,45}; downside risk proxied by IV at deltas {40,45}; tail risk proxied by slope across deltas; daily data over a one-week window; normalization and winsorization procedures applied as specified. ### Macro VAR results — asset-price and macro responses to GPR shocks - Equity markets: - Average aggregate stock market response to average country-specific GPR shocks: ca. -0.3% at peak. - Stock market response to large country-specific GPR shocks: ca. -2% at peak. - Comparative literature: responses between ca. 0% to ca. -6% across studies. - Option-implied volatility and VIX: - Option-implied volatility: spike contemporaneously. - VIX: contemporaneous spike. - Oil prices: - While oil prices fluctuate in the first month, cumulative effect peaks at ca. -1 percent several months after the shock (larger for global or large country-specific GPR shocks). - Real activity and inflation: - Industrial production: contraction. - Inflation (CPI): modest upward pressure. - Yield curve and policy: - Yield curve: bear flattens (consistent with more proactive monetary policy). - Heterogeneity: - G7 stock markets: more negative and more persistent reactions relative to average. - Commodity-exporting economies: equities suffer larger declines (reflecting negative oil price response). ### Firm-level empirical results — average effects and transmission channels - Main estimated impacts (exact magnitudes preserved): - Home-country major geopolitical risk event: - Firm stock returns decline by 0.7 percentage points in local-currency terms. - Firm stock returns decline by 1 percentage point in excess US dollar terms. - Sample average monthly US dollar excess return: about 0.6 percent. - Trade-linkage transmission: - Trading-partner involvement (10 percent trade weight): - Decline in firms’ stock returns by about 0.4 percentage points in AEs. - Decline in firms’ stock returns by about 0.7 percentage points in EMEs. - Note: 10 percent trade share ≈ 2½ standard deviations above the mean. - Home-country military conflict by country type: - Home country involvement in an international military conflict has more adverse effect on stock returns for EMEs: by more than 4.5 percentage points on average. - Impact for firms in AEs: not statistically significant. - Firm-level exposure margins: - Revenue exposure: two-standard-deviation higher ex-ante revenue exposure → estimated average decline ≈ 0.2 percentage points (same country-sector). - Subsidiary presence in affected country → estimated average decline ≈ 0.5 percentage points (driven mainly by AE firms). - Parent company in affected country matters, particularly for EM firms after major non-war conflicts in parent’s country. - Anticipatory effects: - Firms’ stock returns in AEs appear to have declined by about 5 percentage points, on average, a month before the country’s involvement in an international military conflict (controlling for contemporaneous events). - Anticipation of a trading partner’s involvement also weighs on contemporaneous returns, especially for EMEs when partner is a major export destination or import source. - Persistence and exchange-rate contribution: - Impact persistence: effects persist for at least 6 months for EMEs. - Exchange rate contribution: - About a third of contemporaneous impact driven by exchange rate movements. - About one-fifth of the impact six months after driven by exchange rate movements. ### Regression outputs and statistical sample metrics (selected exact figures) - Firm-level regression columns report: - Weight for Foreign GPR (international military conflict): coefficients include -9.707**, -9.656**, -10.350*, -2.321*, -3.587*, -0.284, 1.166, 1.213, -1.225; standard errors in parentheses: (4.378), (4.539), (5.809), (1.240), (1.887), (0.665), (1.031), (1.047), (1.202). - W. Aveg. Foreign GPR (others): coefficients include -0.639, -0.328, -1.116, -0.188, -0.269, -0.055, -0.297**, -0.173, -0.612***; standard errors reported. - Sample counts (as reported across columns): - Number of Firms: 2,829; 1,636; 1,193; 25,142; 19,283; 5,859; 23,644; 17,218; 6,426. - Number of Countries: 37; 20; 17; 40; 20; 20; 40; 20; 20. - Total Obs. (Firm-Month): 312,897; 172,895; 140,002; 1,764,153; 1,357,934; 406,219; 684,736; 517,208; 167,528. - R2: 0.58; 0.56; 0.60; 0.35; 0.31; 0.49; 0.43; 0.39; 0.57. - Global panels and firm-level averages: - Global panel: about 60 thousand firms from 20 AEs and 20 EMEs. - Average monthly US dollar excess return in full sample: about 0.5 percent (0.4 percent for AEs; 0.7 percent for EMEs). - Share of firms in sample situated in countries involved in an international military conflict: about one percent. - Share facing major geopolitical risk events other than international military conflicts: 2.6 percent. ### Case studies — Russia’s invasion of Ukraine and US–China trade tensions - Russia–Ukraine impacts (exact magnitudes preserved): - Firms in EMDEs: more negative impact of -1.1 percentage points than those in AEs. - Emerging Europe: stock market decline of -9.0 percentage points. - Defense sector: experienced positive stock returns; defense firms with subsidiaries in Russia and Ukraine benefited. - US–China trade tensions (event dates preserved): - Event dates used: March 22, 2018; June 15, 2018; May 6, 2019; August 1, 2019; August 23, 2019; October 11, 2019; May 14, 2024 (selection excludes retaliatory announcements within few days of initial announcements as specified). - Tariff coverage and sectoral impacts: - Total sectors by 4-digit SIC: 479 sectors. - US tariff announcements impacted an average of 234 sectors; Chinese announcement impacted 254 sectors. - In impacted sectors, on average 37.9 percent of products appear in US tariff lists; 22.8 percent appear in Chinese retaliation lists. - Event-window results: - US tariff announcements: mixed effects on Chinese firms over 3-day window; consistently negative effects on US firms across windows. - Tariff reduction on October 11, 2019: divergent direct effects—Chinese firms positive from outset; US firms initially negative then effect diminished. ### Sovereign risk, long-term yields, and cross-border amplification - Sovereign CDS premia (sample: 20 AEs and 21 EMEs, Jan 2002–Dec 2023): - Average sovereign CDS premium: - Full sample: 176 basis points. - AEs: 55 basis points. - EMEs: 279 basis points. - Major domestic GPR events raise sovereign CDS premia by 16 to 27 percent. - Evaluated at means: about 44 basis points increase for AEs and 182 basis points for EMEs. - Foreign-conflict trade-linkage amplification: - For full sample, trading partner with 10 percent higher trade share in international military conflict → about 40 basis increase in sovereign CDS premia for AEs. - Extreme observed spikes (context): - Russia’s 5-year sovereign CDS exceeded 900 basis points (and later over ten thousand basis points) on first trading day after invasion; Ukrainian 5-year CDS jumped to over 3000 basis points. Estimation caps sovereign CDS premia at 1000 basis points to avoid bias. - Sovereign yields: - AEs: long-term (10-year local-currency) yields decline after major domestic GPR events (safe-haven effects). - EMEs: long-term yields increase after major domestic GPR events and after major foreign conflicts. ### Asset pricing, GPR betas, and option markets - GPR betas and cross-sectional pricing: - GPR factor shocks extracted from AR(1) of global GPR; GPR-beta estimated per stock via 48-month rolling OLS controlling for market excess returns; GPR premiums estimated via Fama‑MacBeth monthly cross-sectional regressions. - Unconditional correlations of excess returns and excess market returns with GPR factor: -0.02 and -0.06, respectively. - First-order autocorrelation of GPR betas across samples: 0.97. - Decile portfolio and factor-mimicking results: - Long-short decile portfolios (tenth minus first decile by prior-month GPR beta) used to assess risk-adjusted returns; GPR factor-mimicking portfolio constructed using Fama‑French portfolios and momentum. - Finding: GPR factor is negatively correlated with market factor; Sharpe ratio of GPR‑FMP close to efficient frontier based on standard factors in AEs. - Option premium responses to GPR factor and exposures (exact magnitudes preserved): - When GPR factor exceeds two historical standard deviations (dummy = 1): - Premiums for overall downside risk increase by approximately 4 percents. - Premiums for downside tail risk increase by approximately 6 percents. - Absolute GPR betas increase premiums for both downside risk and tail risk; magnitudes comparable to market betas after normalization. - After the Israel‑Gaza conflict onset, premiums for downside and tail risks moderately increased; firms with higher revenue exposure to Israel experienced sharp increases. - Anticipation effect: option premiums for both downside risk and downside tail risk change by approximately one percent for stocks whose excess returns change by one percent (premiums decrease when returns increase; increase when returns decrease). ### Banking and non-bank financial intermediation effects - Banking sector (sample: annual unconsolidated statements for over 6,000 banks from 21 AEs and 15 EMEs; exact coverage varies): - Major findings: - Banks’ cost of funding increases after a major GPR event. - For AEs: effect driven by non-military conflict events. - For EMEs: effect driven by military conflicts. - Bank capital on average declines, particularly for EMEs, contributing to lower lending. - NPL ratios rise, especially for EMEs following involvement in an international military conflict. - Cross-border exposures matter: banks with cross-border claims/liabilities linked to affected countries face stronger impacts, especially in EMEs. - Identification note: event indicator assumes home country not experiencing a major GPR event in same year due to low-frequency annual data. - Non-bank financial sector (sample: ≈ 35,000–40,000 funds across 62 countries, 2013Q1–2024Q2): - A 10-percentage point increase in exposure to international military conflicts: - Reduces monthly return by 0.2 percent. - Leads to a 0.5 percent monthly outflow. - A 10-percentage point increase in exposure to other GPR event types: - No significant impact on fund returns. - Leads to a 0.05 percent monthly outflow. - Case-study average exposures (selected): - 2021Q4 (Russia-Ukraine context): 0.30% of funds’ AUM domiciled in Russia and Ukraine; 22.25% AUM issued by firms with at least one subsidiary in Russia or Ukraine; 45.15% AUM had at least some revenues from Russia or Ukraine. - 2017Q4 (China context): 2.87% of assets domiciled in China; 33.60% of assets had a subsidiary in China; 42.80% had revenues from China. ### Limitations and caveats (verbatim-style preservation) - Effects capture average effects across events with varying intensity and duration. - Firms exposed through first-order and higher-order channels; supply-chain exposure only proxied via aggregated bilateral country-level import exposures (not full global supply-chain network data). - Analyses do not formally distinguish between military conflicts on home soil versus elsewhere, nor account for differences in economic and military capacity between countries involved in a conflict. - Wide uncertainty bands around median IRFs indicate substantial heterogeneity across countries, channels, and event specifics. *Italic source attribution: IMF staff calculations; April 2025 GFSR Chapter 2 (ch2annex).* ### 1. Change in Real Stock Price between the Pre-War and War Periods (Percent) ### 1. Change in Real Stock Price between the Pre-War and War Periods (Percent) ### Definitions, data, and sample - War periods used in the analysis: World War I (July 28, 1914 – November 11, 1918) and World War II (September 1, 1939 – September 2, 1945). Exceptions/adjustments: - Japan: stock market closed from September 1945 to May 1949. - Germany: imposed stock price limits on trading from January 1943 to June 1948. - Sources: Global Financial Database; Bloomberg Finance L.P.; IMF; LSEG Datastream; UN Trade and Development; Caldara and Iacoviello (2022); IMF staff calculations. - Country/sample definitions: - Sample for VAR analysis: 43 AEs and EMDEs over the period 1986 to 2024 (unbalanced panel). - Commodity-exporting countries: defined as those for which commodities constitute more than 60 percent of total merchandise exports. - Major geopolitical risk events: - Identified using Caldara and Iacoviello (2022) GPR indices; “major” = country GPR index values above the country-specific average by more than 2 standard deviations. - Total identified major events: 452 country-month observations. - Share of country-specific observations identified as major events: about 2.5 percent. - International military conflicts comprise about 15 percent of the major geopolitical risk events. ### Measurement of geopolitical risk (GPR indices) - Global and country-specific GPR indices based on Caldara and Iacoviello (2022). - Indices measure the share of articles in ten major news outlets in the US, the U.K., and Canada that discuss rising geopolitical risks (daily and monthly frequencies; historical global GPR available from 1900 with fewer newspapers). - Major global events (post-WWII) identified where monthly global GPR index > 2 standard deviations above historical average; examples listed in source (e.g., Iraq’s invasion of Kuwait (1990), Gulf War (1991), 9/11 (2001), Iraq War (2003), Russia’s annexation of Crimea (2014), Russia’s invasion of Ukraine (2022), Israel-Gaza conflict (2023)). ### Empirical methodology - Benchmark model: panel VAR with country and pandemic country-time fixed effects. - Estimation: Bayesian estimation using a Gibbs sampler; priors set according to Minnesota procedure. - Baseline specification: - Endogenous monthly variables (Z_it): GPR, industrial production index, consumer price index (CPI), policy and long-term interest rates, real equity prices (CPI-deflated stock market indices in USD), real price of oil (US CPI-deflated WTI), and the VIX. - Variables sampled at monthly frequency and entered in log levels, except interest rates (not logged). - Number of lags P = 2 (Bayes Information Criterion). - Observations above (below) the highest (lowest) 1.25th percentile of empirical distributions are dropped. - Pandemic-priors approach used to account for abnormal COVID-19 data fluctuations (Cascaldi-Garcia (2024) approach introduced via exogenous V_t variables). - Identification: recursive (Cholesky) ordering with GPR first (structural shocks to GPR affect other variables contemporaneously; remaining shocks do not affect GPR contemporaneously). ### Key empirical results and statistics - Average aggregate stock market response to average country-specific GPR shocks: ca. -0.3% at peak. - Stock market response to large country-specific GPR shocks: ca. -2% at peak. - Comparative literature: Caldara and Iacoviello (2022) and Fernandez-Villaverde and others (2024) find stock price responses between ca. 0% to ca. -6% across specifications and identification strategies. - Oil price response: - While oil prices fluctuate in the first month after geopolitical shocks, the cumulative effect on oil prices peaks at ca. -1 percent several months after the shock (larger for global or large country-specific GPR shocks). - VAR impulse responses (IRFs) — median behaviors reported: - Equity prices: negative response on average. - Option-implied volatility: spike contemporaneously. - Oil prices: persistent declines on average. - Industrial production: contraction. - Inflation: modest upward pressure. - Yield curve: bear flattens (consistent with more proactive monetary policy). - Heterogeneity and cross-country patterns: - Stock markets in G7 economies react more negatively for longer relative to the average; other AEs and EMEs broadly align with the average effect. - Equities in commodity-exporting economies suffer larger price declines relative to commodity non-exporting economies — reflecting the negative oil price response weighing more on commodity-exporting economies. ### Firm-level analysis (event regression) - Firm-level monthly excess returns (USD, in excess of monthly US Treasury yields) are regressed on: - Dummy for domestic major geopolitical risk event (1 in the month of event, 0 otherwise). - Weighted dummy for trading-partner events (weighted by previous-year cross-border trade exposures). - Event types disaggregated into international military conflicts and other events (diplomatic tensions, domestic unrest, terrorist attacks). - Controls: firm size (log total assets), leverage (equity-to-total assets), return on assets, and other firm- and macro-level controls. - Model form and estimation details provided in source (equation 2.5.1). ### Robustness checks and alternative specifications - Results qualitatively robust to: - Increasing lag order to 3 (AIC suggestion). - Replacing VIX with risk-aversion and uncertainty measures. - Dropping long-term interest rate variable. - Switching stock market index denomination from US dollar to local currency. - Considering pre-COVID-19 pandemic period only. - Excluding US data from the cross-section. - Wide uncertainty bands around median IRFs indicate substantial heterogeneity in responses depending on country characteristics, transmission channels, and event specificity. *Source: April 2025 GFSR Chapter 2 — Geopolitical Risks: Implications for Asset Prices and Financial Stability; IMF staff calculations.* ### 1. Cumulative change in Real Aggregate Stock Price after ### 1. Cumulative change in Real Aggregate Stock Price after Domestic Geopolitical Risk Shocks across Country Groupings (Percent, monthly) ### Methodology and Data - Impulse responses are from the benchmark VAR model introduced in the section; shock identified using a recursive ordering where GPR comes first. - Geopolitical risk indicator: country GPR index by Caldara and Iacoviello (2022). - IRFs reported are derived from models estimated separately on the designated country groupings. - Solid lines and round markers indicate periods where the effect is statistically significant (68 percent credible set around the IRF does not cross the x-axis). ### Firm-level panel regressions (equations and identification) - Primary specification for firm-level monthly returns (notation preserved from source): - 푦푦푖,푡 = 훼 + 훽 퐼(퐸퐸퐸퐸퐸퐸퐸퐸퐸퐸)푐,푡 + 훾 ∑ 푤푖,푐′,푡−12 (퐼(퐸퐸퐸퐸퐸퐸퐸퐸퐸퐸)푐′,푡) + 휃 퐶퐶퐶퐶퐸퐸퐸퐸 퐶퐶퐶퐶퐶퐶퐶퐶 푖,푡−1 + 휇푖 + 휈푐,푠,푡 + 퐶퐶푐′∈퐶 휖푖,푡 - 푤푖,푐′,푡−12 denote (i) firm i’s revenue derived from country c′ in percent of total revenues, or (ii) whether firm i has a subsidiary in country c′, measured in previous year. - Country-(4-digit)sector-month fixed effects (휈푐,푠,푡) absorb time-varying country- and sector-specific factors. - Firm controls lagged by 1 quarter; macro controls lagged by 1 year. ### Sample characteristics (exact figures preserved) - Global panel: about 60 thousand firms from 20 AEs and 20 EMEs. - Sample size for analyses based on geographical distribution of firm revenues and subsidiary presence: up to 39 countries, including about three thousand and twenty thousand firms, respectively. - Average monthly US dollar excess return in the full sample: about 0.5 percent (0.4 percent for AEs, and 0.7 percent for EMEs). - Share of firms in sample situated in countries involved in an international military conflict: about one percent. - Share facing major geopolitical risk events other than international military conflicts: 2.6 percent. ### Aggregate IRF notes (panels referenced) - Panels 1 and 2 in the figure correspond to country groupings and commodity dependence status; both are impulse responses from the benchmark VAR. *Italic source attribution: IMF staff calculations; April 2025 GFSR Chapter 2.* ### 2. Empirical Results — Average Effects on Firm Stock Returns ### Main estimated effects (exact magnitudes preserved) - Home-country major geopolitical risk event: - Firm stock returns decline by 0.7 percentage points in local-currency terms. - Firm stock returns decline by 1 percentage point in excess US dollar terms. - Magnitude context: average monthly stock return, in excess US dollar terms, about 0.6 percent in the sample. - Comparison to prior literature: Berkman et al. (2011) estimate average 0.4 percentage points decline in global stock returns at start of international conflicts (from different measure and longer sample). ### Trade-linkage transmission (exact figures preserved) - Involvement in a military conflict of a major trading partner with 10 percent weight in total trade: - Decline in firms’ stock returns by about 0.4 percentage points in AEs. - Decline in firms’ stock returns by about 0.7 percentage points in EMEs. - Note: A 10 percent share in cross-border trade corresponds to a country with a share that is 2½ standard deviations above the mean. ### Home-country military conflict effects by country type (exact phrasing) - Home country involvement in an international military conflict has more adverse effect on stock returns for EMEs: by more than 4.5 percentage points on average. - The impact for firms in AEs does not appear to be statistically significant (text explanation retained). ### Firm-level exposure results (exact magnitudes preserved) - Revenue exposure: - Firms within same country-sector that derive a greater share of revenues from countries involved in an international military conflict: estimated average decline about 0.2 percentage points for firms with a two-standard-deviation higher ex-ante revenue exposure. - Subsidiary presence: - Having a subsidiary in countries experiencing a major geopolitical risk event: estimated impact average decline of 0.5 percentage points on average; appears driven mainly by AE firms. - Parent company effects: - Having a parent company in an affected country matters, particularly for EM firms and following a major non-war conflict in the parent company’s country. - These are additional impacts beyond country- and sector-wide effects. ### Anticipatory effects (exact magnitudes preserved) - Analyses examine contemporaneous impact of geopolitical risk events occurring in the following month (controlling for current-month events). - Example: firms’ stock returns in AEs appear to have declined by about 5 percentage points, on average, a month before the country’s involvement in an international military conflict (panel 2). - Anticipation of a trading partner’s involvement in a military conflict also appears to weigh on contemporaneous stock returns, especially if the trading partner is a major export destination or import source, and particularly for EMEs (panel 3). ### Persistence and exchange rate contribution (exact figures preserved) - Impact persistence: expanding returns horizon implies impact persists for at least 6 months for EMEs. - Exchange rate contribution: - About a third of the contemporaneous impact appears to be driven by exchange rate movements. - About one-fifth of the impact six months after appears driven by exchange rate movements. *Italic source attribution: IMF staff calculations; April 2025 GFSR Chapter 2.* ### 3. Regression Outputs and Robustness Notes ### Regression table excerpts (preserved numeric entries) - Weight for Foreign GPR (firm level) — W. Aveg. Foreign GPR (international military conflict): - Columns show: -9.707**, -9.656**, -10.350*, -2.321*, -3.587*, -0.284, 1.166, 1.213, -1.225 - Standard errors in parentheses: (4.378), (4.539), (5.809), (1.240), (1.887), (0.665), (1.031), (1.047), (1.202) - W. Aveg. Foreign GPR (others): - Coefficients: -0.639, -0.328, -1.116, -0.188, -0.269, -0.055, -0.297**, -0.173, -0.612*** - Standard errors in parentheses: (0.775), (0.934), (1.080), (0.131), (0.178), (0.142), (0.132), (0.181), (0.177) - Controls: Included in all reported specifications. - Country x Sector x Month fixed effects: Yes in all reported specifications. - Number of Firms reported across columns: 2,829; 1,636; 1,193; 25,142; 19,283; 5,859; 23,644; 17,218; 6,426. - Number of Countries reported across columns: 37; 20; 17; 40; 20; 20; 40; 20; 20. - Total Obs. (Firm-Month): 312,897; 172,895; 140,002; 1,764,153; 1,357,934; 406,219; 684,736; 517,208; 167,528. - R2 reported across columns: 0.58; 0.56; 0.60; 0.35; 0.31; 0.49; 0.43; 0.39; 0.57. - Columns correspond to different weighting and exposure measures (Shareholders Revenue Exposure, Subsidiary Presence), and country group splits (All, Advanced Economies, Emerging Markets) as reflected in the source table structure. ### Standard error and significance details - Dependent variable in these regressions: total return from holding the stock of a firm from month t-1 to t in US dollars in excess of monthly US Treasury yields over same horizon. - Standard errors are double clustered at firm and month level. - ***, **, * indicate statistical significance at 1, 5, and 10 percent, respectively. *Italic source attribution: IMF staff calculations; April 2025 GFSR Chapter 2.* ### 4. Case Studies: Russia’s Invasion of Ukraine and US-China Trade Tensions ### Russia–Ukraine invasion — regional and sectoral impacts (exact magnitudes preserved) - Differential impacts across country groups: - Firms in EMDEs: more negative impact of -1.1 percentage points than those in AEs. - Emerging Europe: most pronounced stock market decline of -9.0 percentage points. - Emerging Asia and Latin America: relatively moderate decline (text description). - Emerging Africa: effects insignificant. - Sectoral heterogeneity: - Defense sector experienced positive stock returns. - Firms with subsidiaries in Russia and Ukraine: defense sector firms benefited. ### US–China trade tensions — event selection and windowing (exact dates preserved) - Event dates identified based on earliest publicly available announcements of tariff increases introducing new waves of tariffs: - March 22, 2018; June 15, 2018; May 6, 2019; August 1, 2019; August 23, 2019; October 11, 2019; and May 14, 2024. - Selection excludes retaliatory tariff announcements within few days of an initial government announcement to avoid confounding effects. ### Event-study specifications (preserved equations) - Aggregate event-study model: - 풚풚푓,푗,푐,푒 = 훼 + 훽⋅퐸퐸퐸퐸퐸퐸 퐶퐶퐶퐶푢푢퐶퐶 퐸퐸 푗/푐,푒 + 훾⋅퐶퐶퐶퐶퐸퐸퐸퐸 퐶퐶퐶퐶퐶퐶퐶퐶 푓 + 휈푐 + 휖푓,푗,푐,푒 - 풚푓,푗,푐 is cumulative US dollar return of firm f in industry j in country c within a narrow daily window τ starting from day before event (τ = {[-1,0], [-1,1], ... , [-1,20]}). - More granular model: - 풚풚푓,푗,푐τ = 훼 + 훽⋅퐸퐸퐸퐸퐸퐸 퐶퐶퐶퐶푢푢퐶퐶 퐸퐸 푓,푐′ + 훾⋅퐶퐶퐶퐶퐸퐸퐸퐸 퐶퐶퐶퐶퐶퐶퐶퐶 푓 + 휈푐,푗 + 휖푓,푗,푐 - 퐸퐸퐸퐸퐸퐸퐶퐶퐶퐶푢푢퐶퐶 퐸퐸 푓,푐′ is measured ex ante as (i) share of revenue of firm f attributed to country c′ to total revenue, measured year prior to event, or (ii) subsidiary presence dummy as of end of year preceding event. - Models include country-sector fixed effects (휈푐,푗). Standard errors clustered at sector level. *Italic source attribution: IMF staff calculations; April 2025 GFSR Chapter 2.* ### 5. Limitations and Caveats (verbatim-style preservation) - Effects identified capture average effects across events with varying degrees of intensity or duration. - Firms are exposed to conflict zones through first-order and higher-order exposures (e.g., revenue exposure to a country whose key trading partners are affected). - Supply chain exposure is only accounted for based on aggregated bilateral country-level import exposures, not global supply chain network data. - Analyses do not formally distinguish between military conflicts on the home soil versus elsewhere, nor differences in economic and military capacity between countries involved in a particular conflict. *Italic source attribution: IMF staff calculations; April 2025 GFSR Chapter 2.* ### 3. Effect of Subsidiary Presence and ### 3. Effect of Subsidiary Presence and Industrial Sectors on Cumulative Stock Returns ### Effect on cumulative stock returns (event-window measurement) - Cumulative returns are measured in US dollar terms for the next 7 days after the event date. - Panel 1 compares effects of Russia’s invasion of Ukraine on cumulative returns across EMDEs by region, relative to AEs; regression includes a dummy variable equal to 1 for EMDEs and 0 otherwise. Country-specific fixed effects are accounted for. - The analysis reports sectoral effects that are statistically significant at a 10 percent level or below. ### US–China trade tensions: trade policy uncertainty and GPR - Both the trade policy uncertainty index (Caldara and others, 2020) and the GPR index for China rose from March 2018, indicating trade tensions were a source of geopolitical risk. - Tariff coverage and sectoral impact: - Total sectors defined by 4-digit SIC: 479 sectors. - US tariff announcements impacted an average of 234 sectors over the five announcements considered. - Chinese tariff announcement impacted 254 sectors. - In sectors impacted by tariff announcements, on average: - 37.9 percent of products in a given sector appear in the tariff product list across US announcements. - 22.8 percent of products appear in Chinese retaliation tariff lists. ### Impact of tariff announcements on firm stock returns - Panel 1 (Online Annex Figure 2.6.3): US tariff announcements had significant but mixed effects on Chinese firms over the 3-day event window; impact on US firms was consistently negative across different time windows. - Response to China's tariff announcements: - US firms initially experienced a decline in cumulative returns over the 3-day event window but showed an upward trend over the 21-day event window. - Effects on Chinese firms remained statistically significant. - Panel 2 (third-country effects across US tariff announcements): - Firms in Mexico display a significant positive effect in the short event window (3-day). - Firms in Korea, Canada, Japan, Germany, the UK, and India generally experienced negative stock market reactions. - Panels 3 and 4 (tariff reduction event on October 11, 2019): - The tariff reduction announcement on October 11, 2019, had divergent average direct effects on cumulative stock returns of Chinese and US firms. - US firms whose products were subject to tariff reductions initially experienced negative stock returns relative to unaffected firms; this negative effect diminished over time. - Chinese firms exhibited positive returns from the outset. - Firms’ cumulative stock returns are measured over 3-day, 7-day, and 21-day windows after the event. ### Effect of subsidiary presence and sectoral exposures - Panel 2 and Panel 3 present the effect of revenue exposure and subsidiary presence in Russia and Ukraine across sectors, reporting sectors with statistically significant impacts at a 10 percent level or below. - Panel 4 (tariff reduction, subsidiary presence): - Chinese firms with subsidiaries benefited significantly from the tariff reductions. - The 7-day window effects for Chinese firms were statistically insignificant in some instances. - US firms exhibited an insignificant and more varied response (blue dotted bars), indicating the impact on US firms was more uncertain and less pronounced. - Sectors highlighted in figures with noticeable effects (examples shown in source figures): Defense; Health Care; Aerospace; Real Estate; Telecom.; Technology; Energy; Industrials; Cons. Staples. ### Chronology of major US–China tariff announcements (as recorded) - March 22, 2018 — US increase: US imposed tariffs on $50-60 billion worth of Chinese goods, including aircraft and weapon parts, batteries, televisions, medical devices, and satellites. - June 15, 2018 — US and China increase: US imposed an additional 10% tariffs on $200 billion worth of Chinese goods. As retaliation, China imposes tariffs on $50 billion worth of US goods. - May 6, 2019 — US increase: The previous tariff of 10% on $200 billion worth of Chinese goods was raised to 25%. - August 1, 2019 — US increase: US imposed tariffs of 15% on $300 billion worth of Chinese goods. - August 23, 2019 — China increase: China announced a new round of retaliative tariffs on $75 billion worth of US goods, including soy and auto parts. - October 11, 2019 — US and China reduction: United States and China reached a tentative agreement for the "first phase" of a trade deal. US reduced tariffs announced on 2nd August 2019, whereas China reduced tariffs announced on 23rd August 2019. - May 14, 2024 — US increase: US imposed tariffs on various Chinese products, including steel, aluminum, medical equipment, solar cells, electric vehicles, and batteries. ### Sovereign risk premia and long-term yields: response to major geopolitical risk events - Sample and measurement: - Sample: 20 AEs and 21 EMEs for the period January 2002 to December 2023. - Average sovereign CDS premium: - Full sample: 176 basis points. - AEs: 55 basis points. - EMEs: 279 basis points. - Sovereign CDS premia: - Major domestic geopolitical risk events raise sovereign CDS premia in both advanced economies and EMEs. - Impacts are economically sizeable: a 16 to 27 percent increase in sovereign CDS premia. - Evaluated at respective means: about 44 basis points increase for AEs and 182 basis points for EMEs. - Trade linkages amplify transmission of foreign geopolitical risk events: - For the full sample, involvement of a trading partner with 10 percent higher trade share (corresponding to a 2 ½-standard-deviation higher trade share) in an international military conflict appears to induce about 40 basis increase in sovereign CDS premia for AEs. - Impact is larger when the trading partner is a main export destination or main import source, particularly for EMEs. - Heterogeneity by fundamentals: - EMEs with public-debt-to-GDP ratios above the median EME, or international reserves adequacy or institutional quality below the median EME, experience a larger and significant increase in sovereign CDS premia following a major foreign geopolitical risk event. - Extreme observed CDS spikes (contextual observations): - On the first trading day after Russia’s invasion of Ukraine, Russia’s 5-year sovereign CDS premia reached over 900 basis points, and soon after, over ten thousand basis points. - Ukrainian 5-year sovereign CDS premia jumped to over 3000 basis points after the invasion. - To avoid biasing estimates, sovereign CDS premia are assumed to be at most 1000 basis points in the empirical work. - Sovereign yields (10-year local-currency government bond yields): - AEs: decline in long-term government bond yields following major domestic geopolitical risk events, particularly after involvement in an international military conflict (safe-haven effects). - EMEs: increase in long-term government bond yields following major domestic geopolitical risk events; EMEs also experience a rise in long-term yields following major foreign conflicts. ### Pricing of geopolitical risk in cross-sectional stock returns - Methodology (GPR beta estimation): - Global GPR index shocks estimated with an AR(1) model to obtain geopolitical risk shocks (the “GPR factor”). - For each stock, time-series OLS regressions (48-month rolling window) estimate GPR-beta controlling for excess market returns: - Equation (2.8.2) relates stock excess returns to the GPR shock and market excess returns; 훽훽_i,GPR is the GPR-beta. - Excess returns measured in US dollar terms in excess of one-month US T-bill rate. - Empirical observations: - Unconditional correlations of excess returns and excess market returns with the GPR factor are modestly negative, -0.02 and -0.06, respectively. - The GPR beta for each stock is generally stable; first-order autocorrelation of all samples is estimated as 0.97. _International Monetary Fund | April 2025 — Online annex content from April 2025 GFSR Chapter 2 (figures, tables, and notes as provided)._ ### 1. The Number of Sample Firms ### ch2annex - 1. The Number of Sample Firms ### Sample composition and distributions - Panels report: - Country Distribution (In percent) - Industry Distribution (In percent) - Note: Panels 2 and 3 respectively represent the share of each country and industry in the sample for the period of January 1989-September 2024. - Data sources: Caldara and Iacoviello (2022); LSEG Datastream and Worldscope Fundamentals database; and IMF staff calculations. ### Estimation of GPR beta premiums — cross-sectional pricing (Fama‑MacBeth) - Method: - Two-step approach: estimate betas from equation (2.8.2), then estimate premiums via Fama‑MacBeth (1973) monthly cross-sectional regressions (equation (2.8.3)). - Equation (2.8.3) (as presented): - 퐶퐶푖,푐,푡+1 = 훾푐 + 훾푡 퐺푃푅 훽̂푖,푐,푡,퐺푃푅 + 훾푚,푡 훽̂푖,푐,푡,𝑀𝑘𝑘 + 훾푡 𝑋𝑋𝑖,𝑐,𝑡 + 휀푖,𝑐,𝑡+1 - Variables: - 퐶퐶푖,푐,푡+1: excess return of stock i in country c from month t to t+1. - 훾푐: country fixed effects. - 훽̂푖,푐,푡,퐺푃푅 and 훽̂푖,푐,푡,𝑀𝑘𝑘: estimated GPR beta and market beta from equation (2.8.2). - 𝑋𝑋𝑖,𝑐,𝑡: controls including: - size: natural logarithm of previous month’s market capitalization; - book-to-market ratios; - momentum: cumulative return for month t–12 to month t–1. - Time-series average of 훾̂𝑡𝐺𝑃𝑅, 훾̂𝐺𝑃𝑅 indicate GPR beta premiums. Non-zero 훾̂𝐺𝑃𝑅 implies investors require a premium for exposure to the GPR factor. - Standard errors: Newey West (1987) estimators. - Implementation details: - Robust regressions applied to address outliers. - Dependent and explanatory variables winsorized at the 5th and 95th percentiles to mitigate outlier impact. - Exclusions: countries with limited number of stocks (less than 100) excluded in some estimations. ### Decile portfolio analysis (complementary test) - Procedure: - In each country, all stocks sorted by prior-month GPR beta and divided into equal-weighted deciles. - First decile: lowest GPR beta; tenth decile: highest GPR beta. - Construct long-short portfolio: long tenth decile, short first decile. - Calculate average excess returns of the portfolio 퐶퐶𝑑,𝑐,𝑡. - Regression for risk-adjusted average return (equation (2.8.4)): - 퐶퐶𝑑,𝑐,𝑡 = 훼𝑑 + 휸𝑑 𝑋𝑋𝑖,𝑐,𝑡 + 휀𝑑,𝑐,𝑡 - 훼̂𝑑 (risk-adjusted average return): if statistically different from zero → investors demand a premium for GPR exposure. - Standard errors: clustered at the country-level. - Advantages and disadvantages: - Advantage: avoids errors-in-variables from volatile individual stock returns (portfolio-level analysis). - Disadvantage: loses information from individual stock returns. - Both Fama‑MacBeth and decile portfolio approaches are employed. ### Additional analyses: factor‑mimicking portfolio, efficient frontier, and Sharpe ratios - GPR factor-mimicking projection (equations (2.8.5)–(2.8.6)): - Project non-traded GPR factor 휀𝑡𝐺𝑃𝑅 on return space consisting of standard factors (six Fama‑French benchmark portfolios and momentum). - Equation (2.8.5): 휀𝑡𝐺𝑃𝑅 = 훼 + 휸 [SL𝑡, SM𝑡, SH𝑡, BL𝑡, BM𝑡, BH𝑡, Mom𝑡] + 휀𝑖,𝑡 - GPRMP: 퐺𝑃𝑅𝑀𝑃𝑡 = 휸̂ [SL𝑡, SM𝑡, SH𝑡, BL𝑡, BM𝑡, BH𝑡, Mom𝑡] (equation (2.8.6)) - Sharpe ratio analysis: - Calculate Sharpe ratios for: - Fama‑French (1993) three factors (market, size, book-to-market); - momentum factor; - GPRMP; - optimized portfolios with four factors (Mkt, Size, BM, Mom). - Weights optimization: - Weights 푊𝑡(𝐸) = 𝑤𝑡(𝑥) / ∑𝑤𝑡(𝑥′) for factors in {Mkt, Size, BM, Mom}. - Grid search intervals: 0.05 within range 푤𝑡(𝐸) ∈ [-0.5 0.5]. - Findings summarized: - Online Annex Figure 2.8.2 indicates: - GPR factor is negatively correlated with the market factor. - Sharpe ratio of GPR‑FMP is close to the efficient frontier based on standard factors in AEs. - Sample periods for Panels 2 and 3: February 1985 to September 2024. ### Predictability of aggregate (market) returns by GPR factor - Monthly panel regression (equation (2.8.7)): - 퐶퐶𝑐,𝑡+1 = 훿𝑐 + 훿𝐺𝑃𝑅 휀𝑡𝐺𝑃𝑅 + 휸 𝑋𝑋𝑐,𝑡 + 휀𝑐,𝑡+1 - 휀𝑡𝐺𝑃𝑅: GPR factor in period t. - 퐶퐶𝑐,𝑡+1: excess market return over next month (t+1). - Controls 𝑋𝑋𝑐,𝑡 include: - country-level: realized daily stock return volatility (past three months), price-to-earnings ratios, dividend yields, three-month and 10-year government bond yields, industrial production (yoy changes), inflation (yoy changes); - global factors: global economic policy uncertainty (Baker and others 2016), US macroeconomic uncertainty (Jurado and others 2015), real economic uncertainty and financial uncertainty (Ludvigson and others 2021). - Results: - Online Annex Figure 2.8.3 presents estimates of 훿𝐺𝑃𝑅 for full sample (1989-2024) and for AEs and EMEs under three specifications: - (i) Single: only the GPR factor. - (ii) GPR + macro controls. - (iii) GPR + uncertainty controls. - The results indicate that the GPR factor generally predicts one-month ahead excess market returns. ### GPR premiums conditional on sign of GPR factor and hedging analysis - GPR premiums under positive vs negative GPR factor: - Theoretical expectation: - GPR premiums should be negative in normal times and positive when geopolitical risk materializes. - Online Annex Figure 2.8.4: - Presents estimated average coefficients for GPR betas when GPR factor is positive or negative and decile‑portfolio alphas. - Sample period: May 1990 to July 2024. - Bars indicate statistical significance at the 10 percent level or below. - Hedging geopolitical risk — factor mimicking panel (equation (2.8.8)): - 휀𝑡𝐺𝑃𝑅 = 휂𝑐 + 휂𝐺𝑃𝑅 𝑍𝑡−1𝐺𝑃𝑅 𝐶𝑖,𝑐,𝑡 + 휂𝑀𝑀𝑡 𝑍𝑡−1𝑀𝑀 𝐶𝑖,𝑐,𝑡 + 휂𝑆𝑖𝑆 𝑍𝑡−1𝑆𝑖𝑆 𝐶𝑖,𝑐,𝑡 + 휂𝐵𝑀 𝑍𝑡−1𝐵𝑀 𝐶𝑖,𝑐,𝑡 + 휀𝑐,𝑡 - Transformations and constructs: - GPR factor converted to dummy: 1 if GPR factor > one historical standard deviations, 0 otherwise (focus on major geopolitical events). - 𝑍𝑡−1𝐺𝑃𝑅: weight constructed by ranking firms cross-sectionally on GPR betas, then standardizing rankings to range between -0.5 and +0.5. - Interest on sign and significance of estimated coefficient 휂𝐺𝑃𝑅 controlling for Fama‑French three factor sorted portfolios. - Estimation sample restriction: only countries with more than 100 stocks included. - Results: - Online Annex Figure 2.8.5 (sample April 1990 to June 2024): GPR beta sorted portfolios have positive and statistically significant coefficients, with and without controlling for Fama‑French 3 factors. - Advanced Economies vs Emerging Market Economies: - Pricing of geopolitical risk significantly observed mainly in AEs (likely due to higher market liquidity or data availability). - Online Annex Figure 2.8.6 compares GPR premiums in AEs and EMEs (sample May 1990 to July 2024). Estimation with stocks in “EMs” exclude the book-to-market factor. ### Heterogeneity across GPR sub-components - GPR index sub-components considered: - Broad categories: “threat” and “act”. - Threat sub-components: war threats, peace threats, military buildups, nuclear threats, terror threats. - Act sub-components: the beginning of war, escalation of war, terror acts. - Each sub-component represents the percentages of articles that include relevant words; sub-components for equation (2.8.1) normalized to a mean of 100. - Correlations with overall GPR factor: - Threats: 0.90 - Acts: 0.82 - Sub-components correlations: - war threats: 0.55 - peace threats: 0.11 - military buildups: 0.61 - nuclear threats: 0.33 - terror threats: 0.52 - the beginning of war: 0.54 - escalation of war: 0.38 - terror acts: 0.61 - Online Annex Table 2.8.1 (GPR Beta Premiums of Sub-Components, 1990-2024): - Presents Fama‑Macbeth regression and Decile portfolio estimates across time windows (1990-2011; 2012-21; 2022-24). - Notable pattern: For both threats and acts indices, patterns about GPR premiums are similar, except for terror threats and acts where estimates for 2012-21 are positive (not negative), suggesting wars and terrorism may be priced differently by investors. - Selected numeric entries (as reported): - Threats index (Fama‑Macbeth): 0.007-0.020 0.012 - War threats (Fama‑Macbeth): 0.004-0.003 0.001 - Terror threats (Fama‑Macbeth): 0.000-0.006 0.006 - Acts index (Fama‑Macbeth): 0.015 0.003 0.045 - Acts index (Decile Portfolio) (1990-2011 / 2012-21 / 2022-24): -0.053 -0.205 1.239 - War threats (Decile Portfolio): -0.022 -0.292 0.844 - Terror threats (Decile Portfolio): 0.168 -0.180 -0.591 - Terror Acts (Decile Portfolio): -0.135 -0.085 -0.514 - Note: Estimates statistically significant at the 10 percent level or below are in bold in the original table. ### Robustness checks - Main results (i) industry-level heterogeneity in GPR betas and (ii) negative premiums for high GPR beta stocks since the global financial crisis until Russia’s invasion of Ukraine are robust to: - Longer sample windows for equation (2.8.2): 48 months to 120 months. - Robust regressions for equations (2.8.1) and (2.8.2). - Shocks to GPR index estimated using a GARCH model. - Using only positive shocks to the GPR index for estimating GPR betas. - Using shocks to country-level GPR indices (estimating equation (2.8.1) country-by-country). On average, correlation between home country GPR factor and global GPR factor is about 0.42, with a maximum of 0.98 and a minimum of 0.13. - Excluding countries with fewer than 100 stocks from Fama‑MacBeth and decile portfolio analyses. - Excluding country effect from Fama‑MacBeth and forming groups across all samples in decile portfolio analysis. - Allowing coefficients of Fama‑French three factors and momentum to be heterogeneous across sample countries in Fama‑MacBeth and decile portfolio analyses. - Estimating premiums for absolute values of GPR betas (following Zhang and others 2023): positive premiums for stocks with lower absolute GPR betas are robustly observed; stocks with high absolute GPR betas have higher excess return volatility, possibly reflecting the “low volatility anomaly”. ### Pricing of protection in options markets — methodology and variables - Objective: quantify prices for protection against downside risk and downside tail risk using one-month-ahead put options on individual stocks, evaluated daily. - Proxies: - Downside risk: average implied volatility across out-of-the-money deltas close to being in-the-money (deltas {40, 45}). - Downside tail risk: slope of implied volatility curve across out-of-the-money deltas (deltas {15,20,25,30,35,40,45}). - Empirical approach (equations (2.8.9)–(2.8.16)): - Estimate average level of implied volatility by regressing IV at deltas {40,45} on a constant (equation (2.8.9)). - Variations include adding country fixed effects (훼𝑐), state fixed effects (훼𝑠), exposures (훼𝐸𝑋𝑃), and slope regressions that include delta series and explanatory variables (equations (2.8.10)–(2.8.16)). - Assumptions: - Implied volatility derived from option prices using Black‑Scholes (log-normal) despite recognition of fatter tails in actual return distributions; steeper negative slopes imply higher premiums for downside tail risk. - Conceptual framework visualized in Online Annex Figure 2.8.7: Put Option Delta and Implied Volatility. - Samples and additional figures summarized in Online Annex Figure 2.8.8. *Source: April 2025 GFSR Chapter 2 annex (ch2annex - 1. The Number of Sample Firms), International Monetary Fund | April 2025* ### 1. The Number of Sample Firms ### 1. The Number of Sample Firms ### Sample composition and data sources - Sample period: January 2005 through January 2025. - Data sourced from Refinitiv (available daily from January 2005 through January 2025), LSEG Datastream and Worldscope Fundamentals database; and IMF staff calculations. - Total sample size: about 2,450 firms as of 2024. - Firms with country and industry information: about 800 firms. - All sample firms are included in the MSCI indexes. - Firms in the sample are predominantly concentrated in AEs (advanced economies). - Event dates used: - Russia’s invasion of Ukraine: February 24, 2022. - US-China trade tensions: nine tariff announcement events by the US (March 22, 2018; June 15, 2018; May 6, 2019; August 1, 2019) and by China (March 23, 2018; June 15, 2018; August 3, 2018; May 13, 2019; August 23, 2019). Retaliatory tariff announcements are included; non-bilateral tariff hikes against all countries are excluded. ### Implied volatility estimation and normalization - Implied volatility (IV) for firm i in country c at delta d in period t denoted as IV_{d,i,c,t}. - Intercept and slope of implied volatility curves estimated using equations (2.8.9)-(2.8.16) with daily data over a one-week (five-business-day) window. - Estimation approaches: - Equations (2.8.9)-(2.8.12): Ordinary Least Squares with implied volatility for higher deltas {40,45}; standard errors clustered at the firm-level. - Equations (2.8.13)-(2.8.16): robust regression with implied volatility for deltas {15,20,25,30,35,40,45}. - Normalization: - For equations (2.8.9)-(2.8.12): each firm’s implied volatility normalized to a range of 0 to 1 within each delta based on historical values. - For equations (2.8.13)-(2.8.16): normalization across all deltas based on historical values. - For equations (2.8.19)-(2.8.20) and (2.8.21)-(2.8.22): each firm’s implied volatility is normalized to a range from 0 to 1 (within each delta for some equations, across deltas for others) and winsorized at the 5th and 95th percentiles. - Frequency for GPR beta analysis: monthly (GPR beta at monthly frequency); monthly averages of implied volatility used when appropriate. ### Measures of firm exposure and model controls - Measures of exposure to Russia and Ukraine: - revenue shares from Russia and Ukraine; - asset size of subsidiaries in Russia and Ukraine, relative to parent company’s total assets; - number of subsidiaries in Russia and Ukraine. - Regressions include period effects (α_t, β_t) and country dummies (α_c, β_c) as specified in the equations. - GPR factor (ε_{t}^{GPR}) extracted from equation (2.8.1); transformed into a dummy equal to one if the GPR factor is higher than two historical standard deviation and zero otherwise (monthly frequency). ### Key empirical findings on option premiums, GPR betas, and GPR factor - GPR betas and option premiums: - Equations (2.8.17) and (2.8.18) relate IV_{d,i,c,t} to firm-level GPR betas (β̂_{i,c,t,GPR}) and market betas (β̂_{i,c,t,MKT}). - Estimation method: Ordinary Least Squares with firm-level cluster-robust standard errors for these equations; implied volatility is not normalized in these regressions. - Result: The absolute value of GPR betas lead to an increase in premiums for both overall downside risk (panel 1) and tail risk (panel 2), with the magnitude being comparable to that of market betas. Coefficients for absolute GPR betas are normalized to a scale comparable to market betas by multiplying the estimates by the ratio of the standard deviation of the GPR betas to that of market betas. - GPR factor and option premiums: - Equations (2.8.19) and (2.8.20) relate IV to the GPR factor and its interaction with delta. - When the GPR factor exceeds two historical standard deviations (dummy = 1), option premiums tend to increase: - premiums for overall downside risk increase by approximately 4 percents. - premiums for downside tail risk increase by approximately 6 percents. - These percent changes are calculated as (α̂_{GPR}/ᾱ)*100 and (β̂_{GPR}/β̄)*100, where ᾱ and β̄ are estimated firm-average values of implied volatility and slopes. - Exposures to Israel-Gaza conflict: - After the onset of the Israel-Gaza conflict, premiums for both downside and downside tail risks moderately increased. - Firms with higher revenue exposure to Israel experienced a sharp increase in premiums (left and right panels of Online Annex Figure 2.8.11 correspond to different equation specifications: (2.8.9)/(2.8.13) and (2.8.12)/(2.8.16), respectively). - Stock option markets and stock markets (anticipation effects): - Equations (2.8.21) and (2.8.22) test whether IV_{d,i,c,t} is correlated with simultaneous stock excess returns C_{i,c,t}. - Finding: Option premiums for both downside risk and downside tail risk decrease (increase) by approximately one percent for the stocks with excess returns that increase (decrease) by one percent, implying anticipation effects. ### Additional methodological notes - Implied volatility estimation windows: daily data over a one-week (five-business-day) window for slope/intercept estimation. - Robust regression used for slope estimates across deltas {15,20,25,30,35,40,45}. - Winsorization: implied volatilities winsorized at the 5th and 95th percentiles for some normalized specifications. - Figures referenced (Online Annex Figures 2.8.8–2.8.12, Online Annex Figure 2.8.9, Online Annex Figure 2.8.10, Online Annex Figure 2.8.11, Online Annex Figure 2.8.12) present coefficient estimates, percent-change illustrations, and event-window indices consistent with the described estimates and results. *Source: LSEG Datastream and Worldscope Fundamentals database; Refinitiv; Caldara and Iacoviello (2022); and IMF staff calculations (April 2025 GFSR Chapter 2 Annex).* ### 1. Global ### 1. Global ### Firms with Revenue Exposures to Israel - Data sources: Factset; LSEG Datastream and Worldscope Fundamentals database; and IMF staff calculations. - Measures: - “Downside risk” and “Downside tail risk” represent estimates of the average levels and the slopes of implied volatility curves for firm-level stock put options for one-month ahead prices, estimated over a one-week window (the respective date and past four business days). - Event week represents the week of October 7, 2023, and the next four business days. - Empirical indication: - The right panel (described) shows the increase in downside risk and tail risk, measured by the average levels and slopes of implied volatility curves, by an increase in exposures to Israel, relative to all firm averages. - Related figure: - Online Annex Figure 2.8.12. Stock Returns and Option Premiums, 2005-2025 — shows percent changes in premiums when the simultaneous stock excess returns increase by one percent. Changes are calculated by dividing estimated coefficients for stock excess returns and the interaction term between returns and deltas by estimated firm-average values of implied volatility and slopes. Bars indicate statistical significance at the 10 percent level or greater. ### Banking Sector: Model, Data, and Key Findings - Model specification highlights: - Outcome variable y_{b,t} modeled as function of domestic major geopolitical event indicator and control variables (bank- and country-level), bank fixed effects (μ_b), and time fixed effects (ν_t). Standard errors clustered at the bank level. - Bank-level controls (lagged by 1 year): total assets (in US dollars, logs), capital ratio (equity-to-total assets), liquidity ratio (liquid assets-to-total assets), asset quality (non-performing loans-to-gross loans ratio), profitability (operating profits-to-total assets). - Country-level controls include: real GDP growth, log nominal GDP (in US dollars), CPI-based annual inflation, net capital flows-to-GDP, short-term deposit rates, long-term government bond yields, and the institutional quality index (average of bureaucracy quality, corruption, democratic accountability, government stability and law and order from the ICRG database). - Foreign shock extension (equation 2.9.2): - Incorporates cross-border banking claims from the BIS Locational Banking Statistics database. - Uses weights w_{c,c',t-1} equal to the share of banking sector claims on country c’ in total cross-border banking claims of country c’s banking sector in year t-1. Alternative specifications weight by cross-border liabilities share. - Standard errors clustered at the bank level; bank and year fixed effects included. - Sample: - Annual unconsolidated bank-level financial statements for over 6,000 banks from 21 AEs and 15 EMEs. Exact coverage depends on specification. - Key empirical results: - Banks’ cost of funding increases after a major geopolitical risk event. - For AEs, this effect is driven by non-military conflict events. - For EMEs, this effect is driven by military conflicts. - Impact on bank capital on average is negative, particularly for EMEs, contributing to lower lending. - NPL ratios rise, especially for EMEs following involvement in an international military conflict. - Cross-border exposures matter: banks are exposed to major foreign geopolitical risk events through cross-border claims and liabilities, with impacts appearing stronger for EMEs. - Banks in EMEs, on average, experience higher funding costs and a decline in their capital relative to lagged assets, especially if their funding sources are involved in an international military conflict. - Due in part to deteriorated risk-taking capacity, bank lending declines. - Identification note: - Conditional on the home country not experiencing a major geopolitical risk event in that year, i.e., I(EVENT)_{c,t} = 0. This assumption is due to the low frequency of the underlying data (annual) which makes it challenging to identify the impact of domestic and foreign events occurring in the same year jointly. - Additional point: - Full set of results are available upon request. ### Non-bank Financial Sector: Coverage and Methods - Sample coverage: - Approximately 35,000 to 40,000 funds (exchange-traded funds, mutual funds, insurance funds, pension funds, and hedge funds) from 62 countries, covering 2013Q1 to 2024Q2. - By fund type: bond, equity, mixed asset, and other funds. - Main empirical model for monthly returns and flows (equation 22.111.11): - Y_{i,c,t} = α + β Exposure_{i,c',K-1} + γ Controls_{i,t} + υ_{c,f,t} + ε_{i,t} - Y_{i,c,t} is monthly return or monthly flows (normalized by AUM at t-1) for fund i domiciled in country c in month t; T denotes event month. - Exposure variable represents the weighted average of holdings where the issuer is domiciled in countries c’ that experience geopolitical risk events in quarter T-1. - Controls for return regressions: fund size and cash holdings. - Controls for flow regressions: fund size, cash holdings, and one-month lagged fund returns. - Fixed effects: country-fund-type-month fixed effects (υ_{c,f,t}); fund fixed effects added for robustness. - Standard errors two-way clustered by fund and domicile-month. ### Non-bank Financial Sector: Key Findings on Exposures, Returns, and Flows - Overall: - Investment funds with significant exposure to geopolitical risks, especially international military conflicts, experience lower returns and outflows. - Magnitudes: - A 10-percentage point increase in exposure to international military conflicts: - Reduces monthly return by 0.2 percent. - Leads to a 0.5 percent monthly outflow. - A 10-percentage point increase in exposure to other types of GPR events: - Does not have a significant impact on fund returns. - Leads to a 0.05 percent monthly outflow (modest impact on flows). - Case study aggregate exposures (average as of specified quarters): - As of 2021Q4 (Russia-Ukraine context): - 0.30% of funds’ assets under management were domiciled in Russia and Ukraine. - 22.25% of assets were issued by non-Russian and non-Ukrainian firms with at least one subsidiary in Russia or Ukraine. - 45.15% of assets had at least some revenues from Russia or Ukraine. - As of 2017Q4 (China context): - 2.87% of assets were domiciled in China. - 33.60% of assets had a subsidiary in China. - 42.80% had revenues from China. - Russia-Ukraine War empirical setup: - Cumulative returns and cumulative flows regressions start at month of the invasion; cumulative flows normalized by fund size one month prior to event. - Exposure measures (one quarter prior) defined as: - D_i: value-weighted average holding of assets with issuers domiciled in event countries. - R_i: value-weighted average indicator that issuer derives revenues from country c’ (not domiciled there) and issuer’s revenue percentage is higher than country-sectoral median. - A_i: weighted average indicator that issuer has at least one subsidiary in country c’ and is not domiciled there. - Controls: for cumulative returns — fund size and cash holdings; for cumulative flows — fund size, cash holdings, one-month lagged fund returns. - Fixed effects: country-fund-type; standard errors clustered by fund and domicile country. - Russia-Ukraine War empirical results: - Ex-ante more exposed funds experience lower returns and outflows after Russia’s invasion of Ukraine. - Direct exposure has the largest negative impact on returns and flows; indirect exposures (revenues and subsidiaries) are less important. - US-China Trade Tensions empirical setup: - Model (equation 22.111.33) decomposes exposure into: Chinese firms impacted by tariffs, US firms impacted by tariffs, and RoW firms in affected sectors with revenues from tariff-imposing country. - Cumulative flows normalized by fund size one month prior to event. - For cumulative return regressions, controls include fund size, cash holdings, exposure to impacted RoW firms without revenues from tariff-imposing country, and overall exposure to the country subject to tariffs. For cumulative flow regressions, controls include fund size, cash holdings, one-month lagged fund returns, exposure to impacted RoW firms that do not derive revenue from tariff-imposing country, and overall exposure to the country subject to tariffs. - Fixed effects: country-fund-type; standard errors clustered by fund and domicile country. - US-China Trade Tensions empirical results: - On average, funds with a one-standard deviation (about 2.3 percent) higher exposure to Chinese firms operating in sectors subject to US tariffs experienced: - a 0.01 standard deviation (equivalent to 0.03 percent) lower cumulative returns in the month following the US tariff announcement. - The effect on flows is generally not significant. - Robustness: results hold using alternative mappings from tariffed product lists to firm sectors. - Trade agreement note: On January 15th, 2020, US and China signed a trade deal that lifted certain tariffs previously imposed. Investment funds holding Chinese firms that benefited from lower US tariffs experienced mild gains, but funds holding US firms experienced lower returns. - Figures and visualization notes: - Online Annex Figure 2.10.1: Sample coverage by domicile distribution, distribution by assets, and fund total assets and fund numbers (Mil USD, Unit). - Online Annex Figure 2.10.2: Change in investment fund cumulative returns around geopolitical events (Russia-Ukraine war and US-China trade disputes) — shows relative cumulative returns between 75th and 25th percentiles; references: Russia-Ukraine cumulative returns relative to 2020M9; US-China cumulative returns relative to 2017M9. - Online Annex Figure 2.10.3: Indirect effects of Russia-Ukraine conflict on investment funds’ cumulative returns and cumulative flows — cumulative flows and returns relative to 2022M2; model controls include investment fund size, fund liquidity, one-month lagged fund return (for flow regressions), and fund type-domicile fixed effects. Shaded area represents 90% confidence interval. - Online Annex Figure 2.10.4 and 2.10.5: Effects of US-China trade disputes on investment fund returns and flows — show standardized coefficient ranges per tariff announcement; solid dots indicate results significant at 90% confidence level; solid diamonds indicate at least half of regression coefficients statistically significant at 90% confidence level. *April 2025 GFSR Chapter 2—Geopolitical Risks: Implications for Asset Prices and Financial Stability. International Monetary Fund | April 2025* ### References ### References ### Geopolitical risk, trade policy, war, and stock/bond markets - Acemoglu, Daron, Tarek A. Hassan, Ahmed Tahoun. 2018. “The Power of the Street: Evidence from Egypt’s Arab Spring.” Review of Financial Studies 31(1): 1-42. - Afonso, Antionio, Jose Alves, Sofia Monteiro. 2024. “Beyond Borders: Assessing the Influence of Geopolitical Tensions on Sovereign Risk Dynamics.” European Journal of Political Economy, 83: 102550. - Biermann, Marcus, and Elsa Leromain. 2024. “The Indirect Effect of the Russian-Ukrainian War through International Linkages: Early Evidence from Stock Market.” CEPR Discussion Paper No. 1899. - Federle, Jonathan, Andre Meier, Gernot J. Muller, and Victor Sehn. 2024a. “Proximity to War: The Stock Market Response to the Russian Invasion of Ukraine.” Journal of Money, Credit, and Banking, forthcoming. - Federle, Jonathan, Andre Meier, Gernot J. Muller, Willi Mutschler, and Moritz Schularick. 2024b. “ The Price of War.” KIEL Working Paper No. 2262, KIEL Institute for the World Economy. - Fernández-Villaverde, Jesús and Mineyama, Tomohide and Song, Dongho. 2024. “Are We Fragmented Yet? Measuring Geopolitical Fragmentation and its Causal Effect.” NBER Working Paper No. 32638. - Franconi, Alessandro. 2024. Central Banking in Times of High Geopolitical Risk. Job Market Paper. - Merics (Mercator Institute for China Studies.) 2023. “How China Imposes Sanctions -A guide to the Evolution of Beijing’s New Policy Tool.” Merics Report (June 06, 2023). - Metiu, Norbert, Global financial transmission of geopolitical risk shocks (March 27, 2025). Available at SSRN - Pinchetti, M., 2024. “Geopolitical Risk and Inflation: The Role of Energy Markets.” Discussion Papers 2431, Centre for Macroeconomics (CFM). - Shpak, S., John S. Earle, Scott Gehlbach, and Mariia Panga. 2023. “Damaged Collateral and Firm-Level Evidence: Evidence from Russia’s War in Ukraine.” Journal of Comparative Economics, 51: 1334-1343. - Tanyeri, Basak, Tanseli Savaser, and Naime Usul. 2022. “The Stock and CDS Market Consequences of Political Uncertainty: The Arab Spring.” Emerging Market Finance and Trade 58(7): 1821-1837. - Vayanos, Dimitri. 2004. “Flight to Quality, Flight to Safety and the Pricing of Risk.” NBER Working Paper 10327. - Zaremba, Adam, Nusret Cakici, Ender Demir, and Huaigang Long. 2022. “When Bad News is Good News: Geopolitical Risk and the Cross-Section of Emerging Market Stock Returns.” Journal of Financial Stability, vol. 58(C). - Zhang, Yaojie, Yuxuan Zhang, Xinrui Ren, and Meichen Jin. 2024. “Geopolitical Risk Exposure and Stock Returns: Evidence from China,” Finance Research Letters, vol. 64(C). ### Measurement, indices, and methods for geopolitical and policy uncertainty - Baker, Scott, Nicholas Bloom, Steven Davis. 2016. “Measuring Economic Policy Uncertainty,” The Quarterly Journal of Economics, 131, 4, pp. 1593–1636, - Caldara, Dario, and Matteo Iacoviello. 2022. “Measuring Geopolitical Risk.” American Economic Review, 112 (4): 1194–1225. - Cheng, D., Y. Liao, and Z. Pan. 2023. “The Geopolitical Risk Premium in the Commodity Futures Market,” Journal of Futures Markets, 43: 1069–1090. - Hyeyoon, Jung, Rober F. Engle, and Richard Berner. 2023. “CRISK: Measuring the Climate Risk Exposure of the Financial System.” FRB of New York Staff Report No. 977, Rev. March 2023. - Jurado, Kyle, Sydney Ludvigson, and Serena Ng. 2015. “Measuring Uncertainty.” American Economic Review 105, 3, pp. 1177–1216. - Ludvigson, Sydney, Sai Ma, and Serena Ng. 2021. “Uncertainty and Business Cycles: Exogenous Impulse or Endogenous Response?” American Economic Journal: Macroeconomics 13(4), pp. 369–410. - Caldara, Dario, Matteo Iacoviello, Patrick Molligo, Andrea Prestipino, and Andrea Raffo, 2020. “The Economic Effects of Trade Policy Uncertainty,” Journal of Monetary Economics, 109(C), pp. 38-59. - Antolín-Díaz, Juan, and Juan F. Rubio-Ramírez. 2018. “Narrative Sign Restrictions for SVARs.” American Economic Review, 108 (10): 2802–29. ### Asset pricing, funds, intermediation, and portfolio effects - Adrian, T., E. Etula, and T. Muir. 2014. “Financial Intermediaries and the Cross-Section of Asset Returns.” Journal of Finance, 69: 2557-2596. - Adrian, Tobias, Richard Crump, and Erik Vogt. 2019. “Nonlinearity and Flight-to -Safety in the Risk-Return Trade-Off for Stocks and Bonds.” Journal of Finance, 74: 1931-1973. - Caballero, R.J. and Kamber, G. 2019. “On the Global Impact of Risk-Off Shocks and Policy-Put Frameworks.” NBER Working Paper 26031. - Carhart, Mark M. 1997. “On Persistence in Mutual Fund Performance.” Journal of Finance, vol. 52(1): 57-82. - Kelly, Bryan, Lubos Pastor, and Pietro Veronesi. 2016. “The Price of Political Uncertainty: Theory and Evidence from the Option Market,” Journal of Finance, 71(5), 2417-2480. - Pastor, Lubos, and Pietro Veronesi, 2013. “Political Uncertainty and Risk Premia,” Journal of Financial Economics 110, 520–545. - Wang, Albert Y., and Michael Young. "Terrorist Attacks and Investor Risk Preference: Evidence from Mutual Fund Flows.” Journal of Financial Economics 137, no. 2 (2020): 491-514. - Online Annex Figure 2.10.5. Effect of US-China Trade Agreement on Investment Fund Returns and Flows - Average effect on fund cumulative returns of the exposure to companies impacted by US-China Trade Agreement (Standard deviation) - Average effect on fund cumulative flows of exposure to companies impacted by US-China Trade Agreement (Standard deviation) - Sources: FactSet, Lipper, LSEG Datastream, and IMF staff calculations. - Note: The y-axis represents standardized coefficients. Cumulative flows and returns are relative to 2020M1. Exposure measures are derived by calculating the weighted averages of an indicator variable, indicating if the security issuer is i) benefited from the tariff agreement as the counterparty country agrees to reduce tariffs, and ii) domiciled in a given country. Benefitted companies are defined as those operating within sectors that produce products subject to the tariff agreement. The model controls for investment fund size, fund liquidity, one-month lagged fund return (for flow regressions only), fund overall exposure to China, fund overall exposure to the US, fund exposure to RoW impacted companies that i) have revenues derived from China, ii) have revenues derived from the US, and iii) do not have revenues derived from the US or China, and fund type-domicile fixed effects. Standard errors are clustered by fund and domicile. The weights reflect the holding percentage of each security one quarter prior to the event. Shaded area represents 90% confidence intervals. ### Commodities, oil markets, and inventories - Bakshi, Gurdip, Xiaohui Gao, and Alberto G. Rossi. 2019. “Understanding the Sources of Risk Underlying the Cross Section of Commodity Returns.” Management Science, 65(2): 619-641. - Cheng, D., Y. Liao, and Z. Pan. 2023. “The Geopolitical Risk Premium in the Commodity Futures Market,” Journal of Futures Markets, 43: 1069–1090. - Ferrari Minesso, Massimo, Lappe, Marie-Sophie, and Roessler, Denise. (2023). “Geopolitical Risk and Oil Prices.” ECB Economic Bulletin, Issue 8/2023. - Kilian, L. and Murphy, D.P. 2014. “The Role of Inventories and Speculative Trading in the Global Market for Crude Oil.” Journal of Applied Econometrics, 29: 454-478. - Mumtaz, H., & Pirzada, A., Theodoridis, K. 2018. “Non-Linear Effects of Oil Shocks on Stock Prices.” Working Papers 865, Queen Mary University of London, School of Economics and Finance. ### Sovereign debt, crises, reserves, and macro-financial transmission - Aguiar, Mark, Satyajit Chatterjee, Harold Cole, and Zachary Stangebye. 2016. “Quantitative Models of Sovereign Debt Crises.” in Handbook of Macroeconomics, vol. 2, John B. Taylor and Harald Uhlig, eds. (St. Louis, MO: Elsevier:. 1697–1755. - International Monetary Fund (IMF). 2016. “Guidance Note on the Assessment of Reserve Adequacy and Related Considerations.” IMF Policy Paper, Washington, DC. - Kalemli-Ozcan, S., Carmen Reinhart, and Kenneth Rogoff. 2016. “Sovereign Debt and Financial Crises – Theory and Historical Evidence.” Journal of the European Economic Association, 14(1): 1-6. - Kaminsky, Graciela Laura and Pablo Vega-Garcia. 2016. “Systematic and Idiosyncratic Sovereign Debt Crises.” Journal of the European Economic Association, 14: 80–114. - Meyer, Josefin, Carmen M. Reinhart, and Christoph Trebesch. 2022. “Sovereign Bonds Since Waterloo.” Quarterly Journal of Economics: 1615-1680. ### Financial econometrics, risk, uncertainty, and behavioral foundations - Alessandri, P. and Mumtaz, H., 2019. “Financial Regimes and Uncertainty Shocks..” Journal of Monetary Economics, 101:31-46. - Bekaert, Geert, Hoerova, M. and Duca, M.L. 2013. “Risk, Uncertainty and Monetary Policy,” Journal of Monetary Economics, 60(7): 771-788. - Engle, Robert. 2016. “Dynamic Conditional Beta,” Journal of Financial Econometrics, 14, issue 4, pp. 643-667. - Engle, Robert F, Stefano Giglio, Bryan Kelly, Heebum Lee, Johannes Stroebel, 2020. “Hedging Climate Change News.” The Review of Financial Studies, 33(3), pp. 1184–1216. - Ilhan, Emirhan, Zacharias Sautner, and Grigory Vilkov. 2021. “Carbon Tail Risk.” Review of Financial Studies 34, 1540-1571. - Maćkowiak, Bartosz, Filip Matějka, and Mirko Wiederholt. 2023. “Rational Inattention: A Review.” Journal of Economic Literature, 61 (1): 226–73. - Mumtaz H, Sunder-Plassmann L. 2020. “Nonlinear Effects of Government Spending Shocks in the USA: Evidence from State-Level Data.” Journal of Applied Econometrics, 36: 86–97. - Ohnsorge, Franziska, Marcin Wolski, and Y. Sophia Zhang, 2014. “Safe Havens, Feedback Loops, and Shock Propagation in Global Asset Prices.” IMF Working Paper No. 14/81. - Pinchetti, M., 2024. “Geopolitical Risk and Inflation: The Role of Energy Markets.” Discussion Papers 2431, Centre for Macroeconomics (CFM). - Zaremba, Adam, Nusret Cakici, Ender Demir, and Huaigang Long. 2022. “When Bad News is Good News: Geopolitical Risk and the Cross-Section of Emerging Market Stock Returns.” Journal of Financial Stability, vol. 58(C). ### Classic empirical and behavioral references - Dimson, Elroy. 1979. “Risk Measurement When Shares are Subject to Infrequent Trading.” Journal of Financial Economics, Volume 7, Issue 2: 197-226. - Fama, Eugene F. Fama, and Kenneth R. French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, Volume 33, Issue 1: 3-56. - Fama, Eugene F., James D. MacBeth, 1973. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, Vol. 81, No. 3: 607-636. - Hirshleifer, David, Dat Mai, and Kuntara Pukthuanthong. 2023. “War Discourse and the Cross Section of Expected Stock Returns.” No 31348, NBER Working Papers, National Bureau of Economic Research, Inc. - Tversky, Amos, Daniel Kahneman. 1974. “Judgment under Uncertainty: Heuristics and Biases”. Science, vol. 185(4157): 1124-1131. - Wang, Albert Y., and Michael Young. "Terrorist Attacks and Investor Risk Preference: Evidence from Mutual Fund Flows.” Journal of Financial Economics 137, no. 2 (2020): 491-514. April 2025 GFSR Chapter 2—Geopolitical Risks: Implications for Asset Prices and Financial Stability International Monetary Fund | April 2025 --- _Source: https://www.imf.org/-/media/files/publications/gfsr/2025/april/english/ch2annex.pdf_