## ch1annex

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### Modeled Weekly Basis Trade Returns and 95th Percentile Value at Risk
- Panel 1:
  - Shows model basis trade returns and 95th percentile value-at-risk (VaR).
  - Returns = gross basis (price differential between cash bonds and futures contracts, adjusted for futures conversion factors and optionality but not coupons) − repo rates matching the basis trade.
  - Returns are scaled by an index of aggregate basis trade growth since 2019 based on CFTC data on levered funds’ net short positions in Treasury futures.
  - VaR computed in‑sample using a GARCH (1,1) model with t-distributed errors.
- Panel 2:
  - Shows incidence of returns breaching the VaR, by year.
  - Reported as (Percent annualized) with an expectation: 5 percent per year.
- Data sources and notes:
  - Sources: Bloomberg Finance L.P.; Commodities and Futures Trading Commission (CFTC); Office of Financial Research; and IMF staff calculations.
  - Gross basis adjusted for futures conversion factors and optionality but not coupons.
  - See Online Annex 1.10 for details.

### Online Annex 1.4 — Modeling Distress in Direct Lending
- Objective:
  - Assess performance of direct lending under counterfactual shocks via simulation of a stylized private equity-sponsored leveraged buyout (LBO) originated in Q4 2021.
- Sample and post-LBO structure:
  - LBO targets: subset of U.S. publicly traded small-cap firms within the S&P SmallCap 600.
  - Enterprise Value (EV) = 12×EBITDA.
  - Unitranche loan finances 50 percent of EV → 50 percent loan-to-value (LTV).
  - Total leverage = 6.0× EBITDA with a SOFR+5 percent coupon (reflecting Q4 2021 market terms).
- Liquidity and cash-flow mechanics:
  - Quarterly cash-flow simulation: EBITDA inflows; interest expense outflows.
  - Liquidity reserves capped at origination as share of initial EBITDA; cap uniformly distributed between 0.25x and 0.75x of initial EBITDA across scenarios.
  - If quarterly EBITDA < interest expense → gap absorbed by liquidity reserves; if reserves exhausted and shortfall persists → borrower in distress.
  - Adverse counterfactual SOFR path: benchmark rate set at twice the realized historical SOFR path.
  - Quarterly interest expense = applicable rate path × outstanding debt balance.
- Firm cohorts and scenarios:
  - 2021–2025 cohort: firms continuously listed over the recent tightening cycle.
  - 2006–2010 cohort: firms operating through the Global Financial Crisis.
  - Scenarios:
    - “baseline”: historical SOFR path + 2021–2025 EBITDA.
    - “stressed rates”: adverse counterfactual SOFR (twice realized SOFR) + 2021–2025 EBITDA.
    - “stressed earnings”: historical SOFR + 2006–2010 EBITDA.
- Simulation details:
  - For “stressed rates”: 10,000 simulations; in each simulation liquidity reserve cap drawn uniformly between 0.25x and 0.75x of EBITDA at origination; 100 firms randomly sampled from 2021–2025 cohort; construct time series of share of distressed borrowers under baseline and stressed rates; compute ratio (stressed rates relative to baseline); Figure 1.16, panel 4 depicts median and interquartile range of this ratio across simulations.
  - For “stressed earnings”: 10,000 simulations with randomly drawn liquidity caps; sample 100 firms from 2006–2010 cohort; compute median share of distressed borrowers over the time series; Figure 1.16, panel 4 reports ratio of this median to corresponding median in the baseline scenario.
- Attribution: Prepared by Dmitry Yakovlev.

### Online Annex 1.5 — Modeling Liquidity in Perpetual Non‑Traded BDCs
- Motivation and objective:
  - Evaluate time to a liquidity shortfall for perpetual non-traded (PNT) BDCs under various scenarios.
  - Estimate duration BDCs could meet 5 percent quarterly redemption requests under varying market dislocation and constrained funding access.
- Principal outflows and available liquidity:
  - Outflows: (i) investor redemptions; (ii) maturities of unsecured debt; (iii) borrower drawdowns on previously extended revolving credit facilities (“dash-for-cash”).
  - Available liquidity: beginning-of-period cash balances and undrawn capacity under secured credit facilities.
- Simulation framework and key assumptions:
  - Quarterly frequency; initialized using end-2025 balance sheets for each of the largest PNT BDCs.
  - No assets sold or matured during the shock (borrowers roll over via amend-and-extend).
  - Partial drawdown of undrawn revolvers by borrowers.
  - Maturing unsecured debt can’t be refinanced under severe stress.
  - Quarterly redemptions fixed at 5 percent of NAV; no new shareholder inflows.
  - Regulatory distribution requirement (≥90 percent of net investment income) limits income retention.
  - Asset valuation shocks applied via stressed indices for leveraged loans and direct lending.
  - Utilization of credit facilities constrained to maintain compliance with the BDC Asset Coverage Requirement (ACR); breaching the ACR terminates the simulation.
- Model equations (symbols preserved):
  - TOTA_t = C_t + TT*PT_t + NT*PN_t
  - TOTL_t = UNK_t + OTH_UNK_t + MISC_t
  - NAV_t = TOTA_t − TOTL_t
  - R_t = 5% * NAV_{t−1}
  - TLA_0 = C_0 + TAU_0 − UDC_0
  - UTIL_t = R_t + MAT_maturing_t
  - TLA_t = TLA_{t−1} − UTIL_t + RETAINED_INCOME_t
- Interpretation:
  - Results are stress simulations (not baseline projections). Relaxing assumptions (partial proceeds from maturing assets, limited asset sales, access to funding) materially extends time to first liquidity gap.

### Online Annex 1.6 — Artificial Intelligence Stack and Balance Sheet Vulnerabilities
- Scope and sample:
  - Sample of 73 public and private firms across multiple jurisdictions.
  - Segment counts: 22 builders and energizers; 19 chip developers and hardware; 20 data managers and software.
  - Hyperscalers: seven U.S. firms and three Chinese firms; CoreWeave included in panel 2.
- Key exposures and capital plans:
  - Chip developers and hyperscalers account for more than 70 percent of the stack’s revenue and outstanding debt (as reported).
  - Hyperscalers’ future capital expenditures estimated at around $3 trillion through 2029.
- Vulnerability indicators and thresholds (Table 1.6.1 values preserved):
  - Leverage (Debt-to-equity (percent)): Top quartile <47 ; Bottom quartile >140
  - Liquidity (Current assets to Current liability ratio): Top quartile <1.2 ; Bottom quartile >1.9
  - Profitability (Operating profit margin (percent)): Top quartile >20 ; Bottom quartile <10
  - Capex intensity (Capex to Revenue (percent)): Top quartile <3.6 ; Bottom quartile >35.9
  - Valuations (Price-to-equity ratio): Top quartile <22x ; Bottom quartile >31x
- Visualization notes:
  - Figure 1.6.1 panels summarize capex growth, capex as percent of operating cash flows, and cash balance estimates for hyperscalers with scenarios for unchanged dividend payout and dividend payout reduced by 50 percent.
- Attribution: Prepared by Yingyuan Chen, Deepali Gautam, and Aki Yokoyama.

### Online Annex 1.7 — Banking Sector Analysis (Lending, Risk Indicators, and Capital Distribution)
- Lending conditions and loan growth (1.7.1):
  - Lending conditions broadly stable; perceived credit risk has not increased materially overall.
  - In some countries lending conditions gradually tightening as risk tolerance declines, while loan demand rises.
- Key risk indicators (1.7.2):
  - Number of banks on monitoring list has broadly declined since 2022, but analysts’ forecasts point to near-term deterioration in earnings and lower returns on equity.
  - Market pressures: lower price-to-book ratios, higher market leverage, tightening liquidity conditions (higher net loan to deposit ratios and quarterly loan growth).
- Dataset and summary statistics (400 banks, 52 countries; 1996–2025):
  - CE Tier1 Ratio (%): Obs. 4427, Mean 13, Std. Dev. 5, Min 4, Max 168
  - Total Capital Ratio (%): Obs. 8348, Mean 15, Std. Dev. 6, Min 5, Max 183
  - CET1 Capital Buffer (%): Obs. 2094, Mean 5, Std. Dev. 3, Min 0.3, Max 28
  - Total Capital Buffer (%): Obs. 2176, Mean 5, Std. Dev. 5, Min 0, Max 160
  - Asset growth (y-o-y) (%): Obs. 9492, Mean 11, Std. Dev. 15, Min -31, Max 99
  - Loan growth (y-o-y), gross (%): Obs. 9246, Mean 12, Std. Dev. 16, Min -49, Max 98
  - Cash to Total Assets (%): Obs. 9928, Mean 6, Std. Dev. 5, Min 0.1, Max 65
  - Loans to total Assets (%): Obs. 9678, Mean 62, Std. Dev. 15, Min 2, Max 94
  - RWA Density (%): Obs. 7793, Mean 65, Std. Dev. 18, Min 4, Max 128
  - Dividend Payout Ratio (%): Obs. 8006, Mean 40, Std. Dev. 28, Min 0, Max 297
  - Share Buyback Ratio (%): Obs. 4700, Mean 18, Std. Dev. 16, Min 0, Max 221
  - Salary to Net Income (%): Obs. 8795, Mean 141, Std. Dev. 5, Min -89, Max 149
  - Release of capital: Obs. 162, Mean 0.7, Std. Dev. 0.94, Min 0.01, Max 7.8
- Descriptive findings:
  - Capital accumulation mainly from retained earnings; strong post-GFC, slowed after COVID-19; some emerging markets showed negative accumulation as leverage increased.
  - Shareholder payouts declined during 2008–2011; typically within 40–80 percent of annual net income in most cases; US saw increased prominence of share buybacks post-2017.
  - Decrease in RWAs reflected higher holdings of cash and sovereign bonds during/after COVID.
  - Loan growth returned to pre-crisis levels despite higher regulatory requirements; small positive correlation between RWA density and loan growth.
- Econometric analysis (difference-in-difference; 2018–2025):
  - Dependent variable: Loan growth (percent).
  - Selected regression coefficients:
    - Post: Model (1) 1.191; Model (2) -1.250
    - Total shareholder payout ratio: 0.002 (Model (1))
    - Post * Total shareholder payout ratio: -0.003 (Model (1))
    - CET1 buffers: -0.501*** (Model (2))
    - Post * CET1 buffers: -0.008 (Model (2))
    - Log of assets: -0.580*** (Model (1)), -0.814*** (Model (2))
    - Return on Equity: 0.241*** (Model (1)), 0.280*** (Model (2))
  - Fixed effects: Country — Yes; Year — Yes
  - Observations: Model (1) 1648; Model (2) 1838
  - R2: Model (1) 0.198; Model (2) 0.213
- Interpretation and conclusions:
  - Marginal impact of shareholder payout ratio post capital release on credit growth is inconclusive.
  - Interaction of capital release and capital buffers statistically insignificant on global sample but negative sign is consistent with prior studies.
  - Lowering capital requirements may allow higher leverage and boost ROE short term but increase procyclicality; mixed evidence that lowering capital and liquidity requirements leads to significant long-term credit growth.
  - Key drivers of capital ratio changes over past 20 years: retained earnings, declining RWA density (especially in the EU), shareholder payouts.
- LLM analysis of capital distribution strategies:
  - Textual analysis of >1,000 earnings transcripts from 78 banks in 26 countries using LLMs with a four-step validated workflow.
  - Findings:
    - More than two-thirds of management teams expect to maintain or increase capital return to shareholders heading into 2026.
    - Shift in North America toward greater M&A (inorganic growth) activity.
    - A few banks in Europe and North America disclosed likely plans to further reduce internal CET1 target levels.
  - Sample: 78 publicly traded banks with total assets > $100 billion; 31 banks excluded from original 109.
- Disclosure of forward guidance on capital distribution (sample and results):
  - Sample: 78 banks (from an initial 109); 1,068 English-language earnings transcripts for 109 banks reviewed (Q1 2023–Q4 2025, availability as of February 22, 2026).
  - Across sample: estimated total assets of $79 trillion, weighted average CET1 of 13.5, ROE of 11.8 in 3Q25.
  - Key findings:
    - In 3Q25, 92 percent of banks disclosed CET1 ratios/trends.
    - About half disclosed internal CET1 targets in 3Q25; disclosures concentrated in Europe and North America.
    - CET1 capital buffers above internal targets ranged from 43 to 140 basis points (Figure 1.7.6, panel 2).
    - Two-thirds of G-SIBs disclosed internal CET1 targets in 3Q25; buffers above internal targets ranged from 50 to 150 basis points for nearly all G-SIBs.
    - Capital distribution hierarchy: Asia — dividend payments and organic growth primary; Europe/North America — dividends first, then share repurchases, organic growth, inorganic growth.
    - North America in 2025 shifted priorities toward organic growth and dividend payouts ahead of buybacks; more banks disclosed inorganic growth plans.
    - Forward guidance suggests banks expect to maintain or increase capital returns to shareholders into 2026.
  - G-SIB metrics reported:
    - Reported total assets of $79 trillion for the sample.
    - Weighted average CET1 ratios of 13.53 percent in 3Q25.
    - Reported ROE of 11.8 in 3Q25.

### Frontier Market Resilience Index (FMRI) — design and scope
- Purpose and coverage:
  - FMRI assesses macroeconomic and institutional resilience across 43 frontier and low-income economies.
  - Regional composition: Sub-Saharan Africa 17 countries (about 40 percent); Latin America and the Caribbean 11 countries (about 24 percent); Europe and Central Asia 6 countries (about 13 percent); Southeast Asia 5 countries; Middle East and North Africa 4 countries (about 9 percent).
- Structure and construction:
  - Resilience modeled as multi-dimensional: external buffers, fiscal space, debt sustainability, price stability, institutional capacity.
  - Indicators aggregated into buckets; all indicators within a bucket and all buckets equally weighted.
  - Quarterly frequency; structural indicators included at quarterly frequency using most recent values (all inputs annual; values repeated quarterly).
  - Baseline normalization window: 2010Q1 to 2019Q4.
  - Minimum data requirements: minimum of eight quarterly observations in baseline; for sparse indicators threshold of three observations; pooled baseline moments as fallback where needed.
  - Indicator signs adjusted so higher z-scores indicate stronger resilience.
  - Headline index: sum of bucket scores (unbalanced-panel approach).
- Interpretation and historical movement:
  - Increases indicate improvements in resilience relative to a country’s own historical norms.
  - Sharp decline in 2020 driven by COVID-19; improvement between end-2022 and end-2024 driven by external liquidity and inflation stabilization; public debt vulnerabilities remained elevated.

### Depreciation and Credit Spreads — structural framework overview
- Objective:
  - Map economic depreciation and capital obsolescence into credit risk and credit spreads, focusing on capital‑intensive technology firms (e.g., hyperscalers).
- Key premises:
  - Rapid technological advancement can shorten economic life of capital (e.g., GPUs’ effective useful lives could be as short as one year or less in some views).
- Modeling approach and elements:
  - Replacement-cost valuation linked to Merton-style structural credit model and residual-income/accounting valuation concepts.
  - Notation highlights:
    - Economic useful life of capital: 휏휏.
    - Productive capital: 퐾퐾_{productive} comprised of depreciable and non-depreciable capital.
    - Cash buffers: 퐵퐵_t.
    - Economic IRR on productive assets: r^{dep}_den (notation preserved as in text).
  - Market dynamics:
    - Physical drift of firm assets interpreted as economic IRR; market price of asset risk parameter θ̄ defined as (r^{dep}_0 − μ̂_A^Q)/σ̂_A.
  - Counterfactual scenarios:
    - For scenario s with shorter economic life τ_s or higher replacement needs compute r^{dep}_s and derive scenario risk‑neutral drift and distance to default.
- Mechanism and implications:
  - Shorter economic lives → lower economic returns → reduced risk‑neutral asset drifts → shorter distances to default → increased default probabilities and credit spreads even without immediate revenue or accounting deterioration.
  - Particularly relevant for hyperscalers with large capital stocks vulnerable to obsolescence.
- Caveats:
  - Obsolescence may be offset by higher-performing chips and productivity gains; investment can raise revenue and earnings.
  - Financial statement approximations: depreciable capital proxied by property and equipment and operating lease asset; cash buffers = cash and cash equivalents + short‑term securities; straight-line depreciation assumed.
- Data sources and references noted in the annex.

*Source: IMF staff; Bloomberg Finance L.P.; CFTC; Office of Financial Research; ch1annex (IMF | April 2026).*

### 1. Modeled Weekly Basis Trade Returns and 95th Percentile

### 1. Modeled Weekly Basis Trade Returns and 95th Percentile Value at Risk

### Panel descriptions and methodology
- Panel 1 shows model basis trade returns and 95th percentile value-at-risk (VaR).
- Returns are calculated as the difference between the gross basis (the price differential between cash bonds and futures contracts, adjusted for futures conversion factors and optionality but not coupons) and repo rates matching the basis trade.
- Returns are scaled by an index of aggregate basis trade growth since 2019, based on CFTC data on levered funds’ net short positions in Treasury futures.
- A GARCH (1,1) model with t-distributed errors is used to compute the VaR in-sample.
- See Online Annex 1.10 for details.

### Panel 2: breach-frequency metric
- Panel 2 shows incidence of returns breaching the VaR, by year.
- (Percent annualized) (Percent; expectation: 5 percent per year)

### Data sources
- Sources: Bloomberg Finance L.P.; Commodities and Futures Trading Commission (CFTC); Office of Financial Research; and IMF staff calculations.

### Notes and interpretation
- The gross basis is adjusted for futures conversion factors and optionality but not coupons.
- Returns are matched to repo rates that correspond to the basis trade.
- VaR is estimated in-sample using the specified GARCH (1,1) model with t-distributed errors.
- Scaling uses an index of aggregate basis trade growth since 2019 derived from CFTC levered funds’ net short positions in Treasury futures.
- Panel 2’s breach incidence is reported as percent annualized with an expectation of 5 percent per year.

*Source: IMF staff; Bloomberg Finance L.P.; CFTC; Office of Financial Research (from the provided content).*

### References

### ch1annex - References

### References
- Cheng, Minder and Madhavan, Ananth, The Dynamics of Leveraged and Inverse Exchange-Traded Funds (January 19, 2010). Journal Of Investment Management (JOIM), Fourth Quarter 2009
- Barbon, Andrea & Heiner Beckmeyer & Andrea Buraschi & Mathis Moerke, 2022. “Liquidity Provision to Leveraged ETFs and Equity Options Rebalancing Flows: Evidence from End-of-Day Stock Prices,” Swiss Finance Institute Research Paper Series 22–40, Swiss Finance Institute.
- Shum, Pauline, Walid Hejazi, Edgar Haryanto, Arthur Rodier, “Intraday Share Price Volatility and Leveraged ETF Rebalancing,” Review of Finance, Volume 20, Issue 6, October 2016, Pages 2379–2409
- Ivanov, Ivan T., Stephen L. Lenkey. “Do leveraged ETFs really amplify late-day returns and volatility?” Journal of Financial Markets, Volume 41, 2018
- Sirri, Erik R., and Peter Tufano. “Costly Search and Mutual Fund Flows.” The Journal of Finance, vol. 53, no. 5, 1998, pp. 1589–622. JSTOR, http://www.jstor.org/stable/117418. Accessed 9 Feb. 2026.

### Online Annex 1.4 — Modeling Distress in Direct Lending
- Objective: Assess performance of direct lending under counterfactual shocks via simulation of a stylized private equity-sponsored leveraged buyout (LBO) originated in Q4 2021.
- Sample construction:
  - LBO targets drawn from a strict subset of U.S. publicly traded small-cap firms within the S&P SmallCap 600 index.
  - Historical quarterly Adjusted EBITDA time series used; actual liability structure replaced with modeled post-LBO leveraged capital structure.
  - Industry filtering: exclude highly cyclical sectors and industries not representative of sponsor-backed direct-lending transactions.
  - Profitability screening: retain only firms with sustained profitability during the two years preceding simulated debt issuance.
- Post-LBO capital structure assumptions:
  - Enterprise Value (EV) = 12×EBITDA.
  - Unitranche loan finances 50 percent of EV → 50 percent loan-to-value (LTV).
  - Total leverage equals 6.0× EBITDA with a SOFR+5 percent coupon (reflecting Q4 2021 market terms).
- Liquidity and cash-flow mechanics:
  - Quarterly cash-flow simulation: EBITDA inflows; interest expense outflows.
  - Liquidity reserves (cash balances and revolving facility) capped at origination as a share of initial EBITDA; cap uniformly distributed between 0.25x and 0.75x of initial EBITDA across scenarios.
  - If quarterly EBITDA < interest expense → gap absorbed by liquidity reserves; if reserves exhausted and shortfall persists → borrower considered in distress.
  - Adverse counterfactual SOFR path: benchmark rate set at twice the realized historical SOFR path.
  - Quarterly interest expense = applicable rate path × outstanding debt balance.
- Firm cohorts:
  - 2021–2025 cohort: firms continuously listed over the recent tightening cycle; realized EBITDA paths reflect current-cycle dynamics.
  - 2006–2010 cohort: firms operating through the Global Financial Crisis; EBITDA trajectories proxy severe macro-financial stress.
- Scenarios:
  - “baseline”: historical SOFR path + 2021–2025 EBITDA.
  - “stressed rates”: adverse counterfactual SOFR (twice realized SOFR) + 2021–2025 EBITDA.
  - “stressed earnings”: historical SOFR + 2006–2010 EBITDA.
- Simulation details:
  - For “stressed rates”: 10,000 simulations; in each simulation liquidity reserve cap drawn uniformly between 0.25x and 0.75x of EBITDA at origination; 100 firms randomly sampled from 2021–2025 cohort; construct time series of share of distressed borrowers under baseline and stressed rates; compute ratio (stressed rates relative to baseline); Figure 1.16, panel 4 depicts median and interquartile range of this ratio across simulations.
  - For “stressed earnings”: 10,000 simulations with randomly drawn liquidity caps; sample 100 firms from 2006–2010 cohort; compute median share of distressed borrowers over the time series; Figure 1.16, panel 4 reports ratio of this median to corresponding median in the baseline scenario.
- Attribution: This annex was prepared by Dmitry Yakovlev.
- Reference: Ferreira, Martell, and Yakovlev (2026) “Modeling Distress in Direct Lending” forthcoming 2026.

### Online Annex 1.5 — Modeling Liquidity in Perpetual Non-Traded BDCs
- Motivation:
  - Evaluate time to a liquidity shortfall for perpetual non-traded (PNT) BDCs under various scenarios.
  - Estimate duration BDCs could meet 5 percent quarterly redemption requests under varying market dislocation and constrained funding access.
- Principal liquidity outflows modeled:
  - (i) investor redemptions;
  - (ii) maturities of unsecured debt (rolled over in milder scenarios, not under severe stress);
  - (iii) borrower drawdowns on previously extended revolving credit facilities (“dash-for-cash” dynamic).
- Available liquidity:
  - Beginning-of-period cash balances and undrawn capacity under secured credit facilities (may be increased in milder scenarios conditional on eligible collateral; not in severe stress).
- Simulation framework:
  - Quarterly frequency; computes number of quarters until BDC cannot meet projected redemption requests.
  - Conducted for each of the largest PNT BDCs; initialized using end-2025 balance sheets; liquidity, debt, and NAV evolve endogenously over time.
  - Output: final quarter in which a BDC maintains sufficient liquidity to cover the subsequent quarter’s projected cash outflows.
- Key assumptions:
  - No assets sold or matured during the shock (borrowers rolling over debt via amend-and-extend).
  - Partial drawdown of undrawn revolvers by borrowers previously granted such revolvers.
  - Maturing unsecured debt can’t be refinanced under severe stress (unsecured debt markets shut down).
  - No borrowing-base reductions modeled for liability-side credit facilities.
  - Quarterly redemptions fixed at 5 percent of NAV. No new inflows of shareholder capital from investors.
  - Regulatory distribution requirement (≥90 percent of net investment income) limits income retention.
  - Asset valuation shocks applied via stressed indices for leveraged loans and direct lending.
  - Utilization of credit facilities constrained to maintain compliance with the BDC Asset Coverage Requirement (ACR); breaching the ACR terminates the simulation.
  - Relaxing assumptions (partial proceeds from maturing assets, limited asset sales, access to additional secured/unsecured funding) would materially extend the horizon to the first observed liquidity gap.
- Model equations and interpretations (symbols preserved as in source):
  - TOTA_t = C_t + TT*PT_t + NT*PN_t
    - Total assets (TOTA_t) comprise cash balances (C_t) and traded and non-traded loans (TT, NT), marked to prices (PT_t, PN_t).
  - TOTL_t = UNK_t + OTH_UNK_t + MISC_t
    - Total liabilities (TOTL_t) consist of unsecured debt (UNK_t), outstanding amount of secured debt (OTH_UNK_t), and miscellaneous liabilities (MISC_t).
  - NAV_t = TOTA_t − TOTL_t
    - Net asset value (NAV_t) equals total assets minus liabilities.
  - R_t = 5% * NAV_{t−1}
    - Quarterly redemptions (R_t) fixed at 5 percent of prior-quarter NAV.
  - TLA_0 = C_0 + TAU_0 − UDC_0
    - Initial available liquidity (TLA_0) consists of initial cash balances (C_0) and initial available undrawn secured debt (TAU_0), net of initial borrower revolver drawdowns under the “dash-for-cash” shock (UDC_0).
  - UTIL_t = R_t + MAT_maturing_t
    - Liquidity utilized in quarter t (UTIL_t), spent on redemptions (R_t) and unsecured debt maturing in quarter t (MAT_maturing_t). In unsecured rollover scenario, MAT_maturing_t = 0.
  - TLA_t = TLA_{t−1} − UTIL_t + RETAINED_INCOME_t
    - Available liquidity declines with projected outflows, marginally replenished by retained income (mostly insignificant).
- Note: Results should be interpreted as stress simulations rather than baseline projections.

### Online Annex 1.6 — Artificial Intelligence Stack and Balance Sheet Vulnerabilities
- Key points and exposures:
  - Chip developers and hyperscalers are systemically vital and collectively account for more than 70 percent of the stack’s revenue and outstanding debt (as shown in Figure 1.17).
  - Hyperscalers’ future capital expenditures estimated at around $3 trillion through 2029, creating potential funding gaps warranting balance-sheet vulnerability assessment.
- Sample and segmentation:
  - Sample of 73 public and private firms across United States, United Kingdom, Canada, the Netherlands, Chinese mainland, Taiwan POC, Korea, Hong Kong SAR, and Australia.
  - Segment counts: 22 firms in builders and energizers; 19 in chip developers and hardware; 20 in data managers and software.
  - Hyperscalers represented by seven U.S. firms (Alphabet, Amazon, Apple, IBM, Meta, Microsoft, and Oracle) and three Chinese firms (Alibaba, Baidu, and Tencent); CoreWeave included in panel 2.
- Comparative historical context:
  - Dot-com period investments in fiber networks, data centers, server farms, and undersea cables led to realized revenues falling short of expectations; current risks could arise through circular financing structures, monetization challenges, supply-side constraints (power generation), and heightened cybersecurity risks.
- Vulnerability assessment indicators and thresholds:
  - Five indicators: leverage (debt-to-equity ratio), liquidity (current assets-to-current liabilities ratio), profitability (operating profit margin), capex intensity (capex-to-revenue ratio), valuation (price-to-equity ratio).
  - Threshold derivation: based on average of within-segment and across-segment top and bottom quartiles using latest available annual financial data; profitability metric bounded at 10 percent (lower bound) and 20 percent (upper bound).
- Table 1.6.1. Thresholds for Vulnerability Assessment Indicators (values preserved)
  - Indicator metrics and quartile thresholds:
    - Leverage (Debt-to-equity (percent)): Top quartile <47 ; Bottom quartile >140
    - Liquidity (Current assets to Current liability ratio): Top quartile <1.2 ; Bottom quartile >1.9
    - Profitability (Operating profit margin (percent)): Top quartile >20 ; Bottom quartile <10
    - Capex intensity (Capex to Revenue (percent)): Top quartile <3.6 ; Bottom quartile >35.9
    - Valuations (Price-to-equity ratio): Top quartile <22x ; Bottom quartile >31x
- Visualization notes:
  - Figure 1.6.1 panels summarize capex growth, capex as percent of operating cash flows, and cash balance estimates for hyperscalers with scenarios for unchanged dividend payout and dividend payout reduced by 50 percent.
- Attribution: This annex was prepared by Yingyuan Chen, Deepali Gautam, and Aki Yokoyama.

### Online Annex 1.7 — Banking Sector Analysis (Sections 1.7.1 and 1.7.2)
- 1.7.1 Lending Conditions and Loan Growth:
  - Summary: Lending conditions remain broadly stable; perceived credit risk has not increased materially overall.
  - Caveat: In some countries lending conditions are gradually tightening as risk tolerance declines, even as loan demand continues to rise.
  - Figure 1.7.1: Lending Standards and Loan Growth — lending standard series normalized by jurisdictional standard deviations; positive values indicate looser standards; negative values indicate tighter standards.
  - Section prepared by Yiran Li and Silvia Ramirez.
- 1.7.2 Key Risk Indicators:
  - Monitoring: Number of banks on monitoring list has broadly declined since 2022, but analysts’ forecasts point to near-term deterioration in earnings and lower returns on equity.
  - Market pressures: lower price-to-book ratios and higher market leverage, alongside tightening liquidity conditions (higher net loan to deposit ratios and quarterly loan growth), likely to further pressure the weaker tail of banks.
  - Figure 1.7.2: Monitoring or vulnerable banks characterized by lower profitability, higher market leverage, lower Tier capital ratios, and higher loan growth compared to non-monitoring banks.

*Source: ch1annex - References (IMF | April 2026).*

### 1. Comparison of Monitoring List and Non–Monitoring List Banks in 1Q26

### 1. Comparison of Monitoring List and Non–Monitoring List Banks in 1Q26

### Context: Global Changes in Capital Requirements
- Primary purpose of capital requirements: ensure banks maintain buffers sufficient to absorb unexpected losses.
- Post-GFC reforms introduced tighter minimum capital rules and new liquidity and resolvability requirements; accounting moved from incurred-loss to expected-loss models.
- Finding: reforms strengthened the financial system, increased bank resilience, supported lending, and helped banks weather subsequent crises including the COVID-19 shock.
- Selected announcements about changes in prudential requirements:
  - ECB (SSM): CCB / P2G / CCyB — March 2020
  - Euro Area NCA: CCyB → 0% — Mar–Apr 2020
  - Bank of England: CCyB 1% → 0% — March 2020
  - Federal Reserve: SCB — September 2025
  - US Agencies: eSLR buffer — November 2025
  - Bank of England: SW Tier 1 14% → 13% — December 2025
- Risks motivating modernization: elevated market volatility, rising geopolitical risks, growing bank exposure to unregulated nonbank financial sector, and strengthening bank–sovereign nexus driven by widening fiscal deficits and higher public debt.

### Data Description
- Dataset: 400 banks across 52 countries covering a 30-year period (1996–2025), including major economies (EU, USA, China, Canada, Australia, India, Brazil, South Africa).
- Annual data used; extreme observations related to mergers excluded.
- Capital buffer ratios constructed by subtracting actual capital ratios from minimum requirements as reported by S&P Capital IQ; limitation: undisclosed requirements (pillar 2, distribution restrictions) not captured.
- Summary statistics (Table 1.7.2.):
  - CE Tier1 Ratio (%): Obs. 4427, Mean 13, Std. Dev. 5, Min 4, Max 168
  - Total Capital Ratio (%): Obs. 8348, Mean 15, Std. Dev. 6, Min 5, Max 183
  - CET1 Capital Buffer (%): Obs. 2094, Mean 5, Std. Dev. 3, Min 0.3, Max 28
  - Total Capital Buffer (%): Obs. 2176, Mean 5, Std. Dev. 5, Min 0, Max 160
  - Asset growth (y-o-y) (%): Obs. 9492, Mean 11, Std. Dev. 15, Min -31, Max 99
  - Loan growth (y-o-y), gross (%): Obs. 9246, Mean 12, Std. Dev. 16, Min -49, Max 98
  - Cash to Total Assets (%): Obs. 9928, Mean 6, Std. Dev. 5, Min 0.1, Max 65
  - Loans to total Assets (%): Obs. 9678, Mean 62, Std. Dev. 15, Min 2, Max 94
  - RWA Density (%): Obs. 7793, Mean 65, Std. Dev. 18, Min 4, Max 128
  - Dividend Payout Ratio (%): Obs. 8006, Mean 40, Std. Dev. 28, Min 0, Max 297
  - Share Buyback Ratio (%): Obs. 4700, Mean 18, Std. Dev. 16, Min 0, Max 221
  - Salary to Net Income (%): Obs. 8795, Mean 141, Std. Dev. 5, Min -89, Max 149
  - Release of capital: Obs. 162, Mean 0.7, Std. Dev. 0.94, Min 0.01, Max 7.8

### Findings from Descriptive Analysis
- Capital accumulation:
  - Most capital used to increase buffers came from retained earnings.
  - Capital accumulation was strong immediately after the GFC but slowed markedly after the COVID-19 crisis; in many emerging markets accumulation was negative as banks increased leverage and expanded loan portfolios.
- Shareholder payouts:
  - Payouts declined during 2008–2011 following the GFC; typically remained within the range of 40–80 percent of annual net income in most cases.
  - Recent US exceptions: share buybacks became more prominent; 2017–2019 optimization and regulatory tailoring in the US contributed to increased payouts.
  - EU and some other countries reduced buffers post-COVID but imposed binding requirements or recommendations on payout restrictions.
- Asset and RWA composition:
  - Banks’ payouts relative to net income exceeded market averages.
  - Decrease in Risk-Weighted Assets (RWAs) has been an important trend; reduction in RWAs reflected higher holdings of cash and cash-like instruments (deposits at central banks) and increased holdings of sovereign bonds coinciding with fiscal expansion during and after COVID.
- Loan growth:
  - After initial fall during the GFC, average loan growth rates across regions returned to pre-crisis levels despite higher regulatory and capital requirements.
  - Small positive correlation between RWA density and loan growth; banks with higher RWA density tend to have slightly higher loan growth, though this also implies higher capital costs and higher required returns for higher-risk assets.

### Findings from Econometric Analysis: Empirical Design
- Methodology: difference-in-difference (DiD) approach to assess impact of shareholder payouts and capital buffers post capital release on credit growth.
- Two main specifications estimated; dependent variable is loan growth (levels). Treatment variable identifies years of and following a reduction in CET1 requirement.
- Interaction variables:
  - Total payout ratio demeaned and interacted with the post-release indicator.
  - CET1 buffer (actual CET1 ratio minus CET1 requirement from S&P Capital IQ) interacted with the post-release indicator.
- Controls include RWA density, return on equity, and log of total assets.
- Time horizon for econometric analysis: 2018–2025 (shorter than full dataset due to data availability).

### Results (Table 1.7.3 and interpretation)
- Regression outputs (selected coefficients; dependent variable: Loan growth, percent):
  - Post: Model (1) 1.191; Model (2) -1.250
  - Total shareholder payout ratio: 0.002 (Model (1) column present)
  - Post * Total shareholder payout ratio: -0.003 (Model (1))
  - CET1 buffers: -0.501*** (Model (2))
  - Post * CET1 buffers: -0.008 (Model (2))
  - Log of assets: -0.580*** (Model (1)), -0.814*** (Model (2))
  - Return on Equity: 0.241*** (Model (1)), 0.280*** (Model (2))
- Fixed effects: Country — Yes; Year — Yes
- Fit statistics:
  - Observations: Model (1) 1648; Model (2) 1838
  - R2: Model (1) 0.198; Model (2) 0.213
- Interpretation:
  - Marginal impact of shareholder payout ratio post capital release on credit growth is inconclusive.
  - Interaction coefficient of capital release and capital buffers is statistically insignificant on the global sample but bears a negative sign, consistent with other studies.
  - Inferences about shareholder payouts are challenging due to data limitations: short sample for capital release observations (most start in 2020) and bias toward the EU where reductions occurred and payout restrictions were applied.
  - After COVID restrictions were lifted, banks tended to increase payouts to compensate for previous limits; capital distributions to shareholders likely to remain elevated per earnings-transcript analysis.

### Conclusions
- Mixed evidence that lowering capital and liquidity requirements would lead to a significant increase in long-term credit growth.
- Lowering capital requirements would allow banks to increase leverage and use cheaper debt funding instead of equity, potentially boosting ROE in the short term but increasing procyclicality of credit over time.
- Key drivers of changes in capital ratios over the past 20 years:
  - Internally generated capital (retained earnings)
  - Declining RWA density (especially in the EU)
  - Shareholder payouts
- Empirical relationships:
  - Capital buffers and annual credit growth show little correlation, even after controlling for lags.
  - Banks with lower capital buffers may increase credit growth due to lower minimum capital constraints; banks with high existing buffers would not necessarily expand credit supply.

### Searching for Capital Distribution Strategies using Large Language Models (LLMs)
- Data and method:
  - Textual analysis of more than 1,000 earnings transcripts from 78 banks in 26 countries using LLMs.
  - Four-step process: Data dictionary and prompts → Earnings transcript review and upload → Human and statistical validation → Identify key findings.
  - Data dictionary standardized variable definitions and terminology (e.g., “excess capital” synonyms) to ensure consistent extraction.
- Key LLM-derived findings:
  - More than two-thirds of bank management teams in the sample expect to maintain or increase capital return to shareholders, supported by strong profitability and solid capital positions heading into 2026.
  - Shift in North America toward greater merger & acquisition (inorganic growth) activity compared to prior years.
  - A few banks in Europe and North America disclosed likely plans to further reduce their internal CET1 ratio target levels going forward.
- Sample note: 78 publicly traded banks with total assets exceeding $100 billion across 26 countries; 31 banks excluded from original 109 due to earnings transcript availability, data content, or coverage (including two G-SIBs in Japan and two in China).

*Source: IMF staff estimates, S&P Capital IQ, Bloomberg LP, Visible Alpha SP Global Market Intelligence (Global Financial Stability Report Online Annex, April 2026).*

### 6. Disclosure of Forward Guidance on Capital Distribution

### 6. Disclosure of Forward Guidance on Capital Distribution

### Tools and Sample
- Sample size included 78 banks, including 22 G-SIBs in Asia, Europe, North America, and the United Kingdom and excluded Agricultural Bank of China, Bank of China, Bank of Communications, Mitsubishi UFJ Financial Group, and Sumitomo Mitsui Financial Group due to data unavailability.
- The project evaluated transcripts and sourced 1,068 English-language earning transcripts for 109 banks from the first quarter of 2023 to the fourth quarter of 2025, subject to availability as of February 22, 2026.
- Across this sample, these banks had estimated total assets of $79 trillion, weighted average CET1 of 13.5, ROE of 11.8 in the third quarter of 2025.
- Limitations related to transcript availability and data coverage on capital distribution strategies reduced the sample from 109 to 78 banks.
- Panel reporting: Panel 1, panel 3 to 6 show results as percent of total respondents in each quarter. Panel 2 shows the average CET1 capital above disclosed CET1 target ratio (lower bound).

### Methodology and Prompt Engineering
- Prompts were designed to support specific analytical objectives; to ensure auditability, prompts included instructions for retrieval of direct quotes and transcript sections as evidence.
- The prompt formulation process involved multiple iterations. Initial versions were drafted with assistance from an LLM and then refined through human review (Figure 1.7.7.).
- Prompt engineering strategies included zero-shot, one-shot and few-shot prompting, reflection, decomposition, and chain-of-thought approaches.
- The workflow used a Question-and-Answer agent-based framework:
  - Agent 1 monitored a designated file directory, retrieved uploaded earnings transcripts, and extracted text.
  - Agent 2 answered the full set of questions and provided supporting evidence for each response.
- Validation: Each answer was reviewed alongside the evidence provided. Numerical outputs were cross-checked against external data sources or the original earnings transcript. In some cases, the same question was posed in two different ways to assess consistency.

### Data Dictionary (selected fields and examples)
- Buyback_Guidance (String): Forward guidance on buyback volume or pace.
  - Example: "we are guiding to over $8 billion between '24 and '26."
- Buyback_Status (Categorical): Status of the buyback program (Active, Paused, Accelerated).
  - Example: "The EUR 2 billion share buyback we announced in November is still ongoing"
- Buyback_Volume_Qtr (Currency): Total value of shares repurchased in the quarter.
  - Example: "we also repurchased approximately 408,000 shares this quarter, or $67 million."
- CET1_buffer (Basis Points): The target buffer held above regulatory minimums.
  - Example: "The CET1 ratio is at 13.3% in Q4. This is around 310 basis points above the MDA buffer."
- CET1_Current (Decimal %): The reported Common Equity Tier 1 ratio.
  - Example: "ended 2024 with a CET1 ratio of 13.6%, approximately 150 bps above our regulatory capital requirement."
- CET1_manage_down (Categorical): Manage excess capital buffers down?
  - Example: "you'll see us continue to manage down to that 13.1%."
- CET1_Target_Range (String Range): Management's stated target range for CET1 capital.
  - Example: "We're not changing our target of over 12% we are now closing at 12.8%"
- Distribution_Goal (Currency): Total capital committed to be returned over a specific period.
  - Example: "our Board authorized a $20 billion share repurchase program."
- Dividend_amount (Currency): Total common dividends paid in the quarter.
  - Example: "EUR 4.79 per share (FY24 dividend per share)"
- Dividend_Guidance (String): Forward guidance on dividend or pace.
  - Example: "we plan to accrue for an increase in our dividend of around 10%."
- Hierar_strategy (Categorical): Hierarchy of capital redeployment.
  - Example: "We will continue to prudently grow the dividend, continue to invest ... and continue to opportunistically repurchase the stock."
- Inorganic_Spend (Currency): Capital allocated to acquisitions or M&A.
- Inorganic_Spend_Guidance (String): Forward guidance on capital allocated to acquisitions or M&A.
- Model_Impact (Basis Points): Capital impact from internal model updates or regulatory floors.
- Organic_RWA_Deploy (Currency): Capital deployed into business growth (loans, trading assets).
- Reg_Basel_Regime_Status (String): Status of major rules (e.g., Basel III Endgame).
- RoTE_Target (Decimal %): Target Return on Tangible Equity.
- RWA_Total (Currency): Total Risk-Weighted Assets reported.
- Strategy (Categorical): Capital redeployment strategy.
- Total_Payout_Ratio (Decimal %): Percentage of earnings returned via dividends and buybacks.

### Key Findings on Disclosures and Forward Guidance
- Banks disclosed CET1 ratios and trends in their earning transcripts as part of prepared remarks or Q&A session. In 3Q25, 92 percent of the banks in the sample disclosed this information.
- About half of the banks in the sample disclosed internal CET1 targets. In the third quarter of 2025, disclosures were concentrated among banks in Europe and North America.
- On average, CET1 capital buffers above internal targets ranged from 43 to 140 basis points (Figure 1.7.6., panel 2).
- Two-thirds of G-SIBs disclosed internal CET1 target ratios in the third quarter of 2025; comparisons with current CET1 levels suggested capital buffers above internal targets ranged from 50 to 150 basis points for nearly all G-SIBs.
- Banks, including G-SIBs, provide a high-level overview of their capital distribution strategies and disclose a hierarchy among these strategies:
  - In Asia: dividend payments and organic growth are the primary approaches.
  - In Europe and North America: dividends rank first, followed by share repurchases, organic growth, and inorganic growth (Figure 1.7.6., panel 3 and 4).
- In North America, banks including G-SIBs shifted their capital distribution hierarchy in 2025, prioritizing organic growth and dividend payouts ahead of share repurchases and inorganic growth; a greater number also disclosed inorganic growth plans compared with previous quarters.
- Forward guidance on capital distributions suggests that banks including G-SIBs expect to maintain or increase capital returns to shareholders, supported by continued profitability and solid capital positions heading into 2026 (Figure 1.7.6., panel 5 and 6).
- A small number of banks in Europe and North America disclosed information in the third and fourth quarters of 2025 indicating a potential further reduction in their internal CET1 target ratio ranges.
- Overall, banks in Europe, North America, and the United Kingdom—including G-SIBs—provided more extensive disclosures on capital distribution strategies than other banks and G-SIBs in Asia.

### G-SIB Characteristics (selected reported metrics)
- Reported total assets of $79 trillion for the sample (Figure 1.7.10).
- Weighted average CET1 ratios of 13.53 percent in 3Q25.
- Reported ROE of 11.8 in the third quarter of 2025.
- Profitability trends have supported elevated total payout ratios since 2023.

*Source: IMF staff estimates. Global Financial Stability Report Online Annex, IMF | April 2026.*

### References

### ch1annex - References

### Frontier Market Resilience Index (FMRI) — design and scope
- Purpose:
  - Provides a systematic and transparent assessment of macroeconomic and institutional resilience across frontier and lower-income emerging market economies.
  - Evaluates resilience relative to a country’s own historical experience rather than cross-country level comparisons.
  - Designed as contemporaneous and intended as a near-real time summary measure of underlying resilience (not a predictive model of stress episodes).
- Coverage and sample composition:
  - Covers 43 frontier and low-income economies.
  - Regional composition:
    - Sub-Saharan Africa: 17 countries (about 40 percent).
    - Latin America and the Caribbean: 11 countries (about 24 percent).
    - Europe and Central Asia: 6 countries (about 13 percent).
    - Southeast Asia: 5 countries.
    - Middle East and North Africa: 4 countries (about 9 percent).
  - Country list and regional classifications follow IMF WEO conventions.
- Conceptual structure:
  - Resilience modeled as multi-dimensional: external buffers, fiscal space, debt sustainability, price stability, and institutional capacity.
  - Indicators aggregated into economically coherent buckets; each bucket represents a distinct channel for shock absorption or amplification.
  - Aggregation: all indicators within a bucket, and all buckets within the index, are equally weighted (no ex ante weighting schemes).
- Indicator selection criteria:
  - Relevance for shock absorption.
  - Consistency with IMF surveillance frameworks.
  - Availability across frontier markets.
  - Interpretability.
  - Emphasis on macroeconomic and balance-sheet indicators; does not mechanically incorporate sovereign bond spreads or other financial market prices.
- Frequency and data treatment:
  - Constructed at a quarterly frequency.
  - Structural indicators (e.g., governance measures) are included at quarterly frequency using their most recently available values; all inputs annual, values repeated quarterly (note in table: "All inputs annual; values repeated quarterly").
  - Baseline normalization window for z-score computation: 2010Q1 to 2019Q4.
  - Minimum data requirements:
    - Minimum of eight quarterly observations required within the baseline period (2010Q1–2019Q4) to include a country-indicator series in z-score calculation.
    - For structurally sparse indicators, a lower threshold of three observations is applied.
    - If conditions not met, z-scores omitted for the affected country-indicator pair; pooled baseline moments may be used as fallback where sufficient cross-country data exist.
  - Indicator signs adjusted so that higher z-scores consistently indicate stronger resilience (e.g., inflation, public debt, and foreign-currency debt exposure enter with inverted signs).
- Normalization and aggregation:
  - Each indicator transformed into a standardized z-score at the country-indicator level with mean and standard deviation computed over 2010Q1 to 2019Q4.
  - Bucket scores: simple average of available indicator z-scores within each bucket (country-quarter level).
  - Global and regional bucket series: unweighted averages across countries with available data in each period; country coverage reported alongside each aggregate.
  - Headline resilience index: defined as the sum of bucket scores (unbalanced-panel approach to allow extension to most recent data without dropping countries or indicators due to reporting lags).
- Interpretation and use:
  - Increases in the index represent improvements in resilience relative to a country’s own historical norms.
  - Best interpreted as tracking changes in resilience over time within countries and across the sample rather than strict ranking of structural resilience levels.
  - Can serve as a structured diagnostic tool to identify emerging vulnerabilities, assess breadth of resilience gains, and distinguish improvements driven by cyclical external conditions from those supported by stronger fiscal or institutional fundamentals.
  - Not intended to replace existing debt sustainability or external sector assessments.
- Historical movements noted:
  - Sharp decline in 2020 driven by deterioration in external balances, fiscal positions, debt dynamics during COVID-19, heightened macroeconomic instability, and rising inflation.
  - Between end-2022 and end-2024, aggregate FMRI improved back toward average levels observed during 2010–2019, primarily due to improvements in external liquidity and stabilization of inflation.
  - Public debt vulnerabilities remained elevated; external solvency indicators remained weaker than pre-pandemic norms.

### Depreciation and Credit Spreads — structural framework overview
- Objective:
  - Show how economic depreciation and capital obsolescence map into credit risk and credit spreads, focusing on large, capital‑intensive technology firms (e.g., hyperscalers).
  - Link changes in economic depreciation and buffer policy to scenario-consistent movements in fair-value credit spreads measured relative to the baseline risk-neutral PD and valuation-multiple adjustments implied by replacement-cost economics.
  - Not intended to forecast default probabilities (PD) or predict future PD paths.
- Key premises:
  - Rapid technological advancement can shorten the economic life of capital (e.g., GPU and advanced chips), lowering true return on productive assets even if accounting profits remain strong.
  - Example assertion: GPUs’ effective useful lives could be as short as one year or less in some views.
- Modeling approach:
  - Replacement-cost perspective anchored in capital-replacement and investment literature (Jorgenson, 1963; Tobin, 1969; Hayashi, 1982) and residual-income/accounting-based valuation literature (Feltham and Ohlson, 1995; Penman, 2010).
  - Structural credit component builds on option-theoretic model of Merton (1974) and empirical implementation of Bharath and Shumway (2008).
  - Economic depreciation embedded directly into replacement-cost valuation; economic depreciation treated as determinant of sustainable productive capacity and long‑run returns.
- Core model elements and notation (select highlights as presented):
  - Economic useful life of capital: 휏휏.
  - Implied depreciation schedule: 푑푑
푡푡.
  - Reinvestment need to maintain productive capital: 퐾퐾
푝푝푝푝푝푝푝푝.
  - Cash buffers: 퐵퐵
푡푡 (cash and cash equivalents plus short‑term securities).
  - Depreciable capital proxied by property and equipment, and operating lease asset; non-depreciable capital proxied by difference between total assets and sum of depreciable assets and cash buffers.
  - Economic accounting identity (stylized): sum over depreciation and residual value after 휏휏 periods (presented as equation (1) in the text).
  - Productive capital: 퐾퐾
푝푝푝푝푝푝푝푝 = depreciable capital 퐾퐾
푝푝푑푑푝푝 + non-depreciable capital 퐾퐾
푛푛푝푝푑푑푝푝.
  - Economic IRR on productive assets: 푟푟
푑푑푒푒푝푝푛푛, derived from operating cash flows 퐶퐶
푡푡 and terminal-value component 휙휙 (presented as equation (2)).
  - If accounting useful lives exceed economic lives then 푑푑
푡푡 is understated and reported ROE may be inflated; equation (2) enforces consistency between 퐾퐾
푝푝푑푑푝푝 and 푑푑
푡푡 via equation (1).
- Structural credit linkages:
  - Market value of firm assets under risk-neutral measure follows geometric diffusion with physical drift 휇휇
퐴퐴
푃푃 and asset volatility 휎휎
퐴퐴.
  - Economic IRR interpreted as physical drift of firm assets: 휇휇
퐴퐴
푃푃 = 푟푟
푑푑푒푒 푝푝푛푛.
  - Baseline economic return: 푟푟
0
푑푑푒푒 푝푝푛푛.
  - Market price of asset risk parameter: 휃휃
� defined as (푟푟
0
푑푑푒푒 푝푝푛푛 − ˆ휇휇
퐴퐴
푄푄)/ˆ휎휎
퐴퐴, providing a bridge between economic fundamentals and risk‑neutral dynamics.
- Counterfactual scenario procedure:
  - For scenario s (e.g., shorter economic life 휏휏
푠푠, higher replacement investment needs, altered buffer policies), compute new replacement‑cost IRR 푟푟
푠푠
푑푑푒푒푝푝푛푛.
  - Scenario physical drift: 휇휇
퐴퐴,푠푠 
푃푃 = 푟푟
푠푠
푑푑푒푒 푝푝푛푛.
  - Holding market price of risk 휃휃
� fixed, scenario risk‑neutral drift: ˆ휇휇
퐴퐴,푠푠
푄푄 = 푟푟
푠푠
푑푑푒푒 푝푝푛푛 − 휃휃
� ˆ휎휎
퐴퐴.
- Distance to default and PDs (select formula relationships as presented):
  - Let 퐷퐷 denote face value of debt, T the horizon, and ˆ휎휎
퐴퐴 the asset volatility.
  - Risk-neutral distance to default at maturity T presented in formula form (as in text).
  - Associated risk-neutral default probability and model-based credit spread at maturity T presented in formula form (as in text), with LGD entering spreads as shown.
- Mechanism and implications:
  - Shorter economic lives of capital → lower economic returns → reduced risk‑neutral asset drifts → shorter distances to default → increased default probabilities and credit spreads, even without immediate revenue or accounting earnings deterioration.
  - Particularly relevant for hyperscalers with large capital stocks vulnerable to rapid obsolescence; credit risk can be sensitive to technological change and capital intensity rather than traditional leverage metrics alone.
- Conservatism and caveats:
  - Obsolescence may be accompanied by higher‑performing chips and productivity gains; obsolete chips may be repurposed.
  - If investment translates into stronger revenue and earnings growth, firms can raise equity or use cash flows to limit debt reliance.
  - Financial statement approximations and data sources: depreciable capital proxied by property and equipment and operating lease asset; cash buffers defined as cash and cash equivalents plus short‑term securities; economic useful life approximated by ratio of productive capital to annual depreciation; financial statement data from SEC Form 10-K filings or other disclosure sources; straight-line depreciation assumed as per IASB Standard 16 and ASC 360-10-35-4; framework abstracts from tax considerations for tractability.

### Key referenced empirical and methodological sources cited in the annexes (selected items as listed)
- Bharath, S. T. and Shumway, T. (2008). Forecasting Default with the Merton, Distance to Default Model. Review of Financial Studies, 21(3):1339–1369.
- Bank for International Settlements (BIS). 2026. “Financing the AI Boom: From Cash Flows to Debt.” BIS Bulletin No. 120.
- Feltham, G. A. and Ohlson, J. A. (1995). Valuation and clean surplus accounting for operating and financial activities. Contemporary Accounting Research, 11(2):689–731.
- Hayashi, F. (1982). Tobin’s Marginal Q and Average Q: A Neoclassical Interpretation. Econometrica, 50(1):213–224.
- Jorgenson, D. W. (1963). Capital Theory and Investment Behavior. American Economic Review, 53(2):247–259.
- Merton, R. C. (1974). On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. Journal of Finance, 29(2):449–470.
- Modigliani, F., and Miller, M. H. (1963). “Corporate Income Taxes and the Cost of Capital. A Correction.” American Economic Review, 53(3):433–443.
- Penman, S. H. (2010). Financial Statement Analysis and Security Valuation. McGraw–Hill, 4th edition.
- Tobin, J. (1969). A general equilibrium approach to monetary theory. Journal of Money, Credit and Banking, 1(1):15–29.

*IMF | April 2026 — ch1annex - References*

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_Source: https://www.imf.org/-/media/files/publications/gfsr/2026/april/english/ch1annex.pdf_