## wp1814

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### Overview and purpose of SyRIN
- SyRIN is a reduced-form, top-down framework to assess systemic risk across banks and nonbanks by modeling a financial system as a portfolio of financial entities/sectors and recovering a financial system multivariate density (FSMD).
- The FSMD characterizes:
  - individual firm value distributions in marginal densities, and
  - the association across firm values (interconnectedness structure) in its copula function.
- The Consistent Information Multivariate Density Optimizing (CIMDO) approach is used to infer multivariate densities consistent with empirically observed probabilities of distress (PoDs).
- SRMs (systemic risk metrics) are derived from statistical moments of the common FSMD and are therefore consistent across perspectives (tail risk, interconnectedness, entity/sector contributions).
- SyRIN can be implemented with market-based data or supervisory data and is adaptable to institutional granularity and data availability.
- SyRIN is informative for identifying vulnerable sectors and guiding deeper analysis, but cannot identify specific causal channels due to its reduced-form nature.

### Systemic-risk transmission mechanisms (direct and indirect)
- Two primary channels of contagion:
  - Direct interlinkages: contractual obligations between financial entities (direct exposure channel).
  - Indirect interlinkages: exposures to common risk factors and market price channels, including asset fire sales and sell-offs (asset liquidation channel).
- Indirect interconnectedness can be non-linear and self-reinforcing; copula functions (not just correlation) are used to capture linear and non-linear dependence.

### Investment funds — vulnerabilities, empirical findings, and key statistics
- Transmission channels:
  - Asset liquidation channel: redemptions → fire sales → price dislocations.
  - Direct exposure/funding channel: funds reduce exposures to risky issuers → funding and counterparty stress.
- Structural vulnerabilities:
  - Open-end funds face redemption risk and maturity/liquidity mismatches.
  - Closed-end funds face higher liquidity risk, higher volatility risk, more derivatives, more leverage, and may trade at a discount between NAV and share price.
- Key statistics and holdings (as of 2016Q4 and end-2015 where noted):
  - Open-end funds and ETFs held $17.5 trillion of equities and fixed-income instruments as of 2016Q4.
  - Their share of the US equity market amounted to 34 percent as of 2016Q4.
  - Their holdings of different debt market sectors ranged from 11 to 24 percent as of 2016Q4.
  - By end-2015, assets under management of closed-end funds were less than 2 percent of the U.S. fund industry.
- Empirical evidence on asset-liquidation effects:
  - Hau and Lai (2012): distressed selling by mutual funds accounted for 10 percent of the 52 percent crisis-related decline in the US stock market during July 2007–June 2009.
  - Coval and Stafford (2007): widespread selling by distressed funds led to increased illiquidity and downward pressure on individual stocks.
  - Manconi and others (2012): in June–December 2007, funds investing in securitized assets liquidated corporate bonds first, spreading the crisis.
  - Anand and others (2013): institutional investors reduced liquidity provision at crisis peak (September 2008–March 2009), surging illiquidity especially for risky stocks.
- Money market funds (MMFs) — post-2016 reforms and funding role:
  - After reforms in 2016, commercial paper holdings of MMFs fell by 70 percent between 2016Q1 and 2016Q4.
  - MMFs were still the main providers of repo funding in the US, accounting for around $800 billion as of 2016Q4 (23 percent of the repo market per US Flow of Funds).
  - Broker-dealers were receiving $1.3 trillion of repo funding as of end-2016.
- Sponsor support channel: sponsors sometimes purchase troubled fund assets or guarantee NAV; cited examples resulted in material losses in past episodes.

### Hedge funds — structure, transmission channels, and empirical outcomes
- Structural features and risks:
  - Hedge funds employ derivatives, margin, short-selling, leverage, and invest in illiquid assets.
  - Leverage sources include margin accounts, derivatives, repos, and short sales.
  - Margin and collateral dynamics can amplify stress via increased margin requirements and decreased collateral value.
- Transmission channels:
  - Asset liquidation channel: fire sales and amplified price impact due to illiquidity and leverage.
  - Direct exposure channel via prime brokerage: top prime brokers were highly concentrated (top 10 serviced 84 percent of hedge fund AUM as of end-2006).
  - Rapid tactical shifts and crowded strategies can amplify market gyrations.
- Empirical outcomes:
  - Credit strategies lost: 19 percent (distressed) and 26 percent (convertible bond arbitrage) in 2008 (Le Sourd 2009).
  - Emerging markets hedge funds lost 30 percent in 2008 (Le Sourd 2009).
  - Khandani and Lo (2011): August 2007 losses in long/short equity hedge funds were amplified by sudden liquidations and funds implementing similar strategies.
  - Historic failures include Long-Term Capital Management (LTCM) and Amaranth Advisors.

### Insurance sector — business model, risks, holdings, and systemic role
- Business model and risks:
  - Insurance business model likened to a swap: insurers receive fixed premiums and pay floating benefits; pooling and diversification reduce idiosyncratic risk.
  - Key financial risks: interest rate risk, credit risk, equity/property/infrastructure exposure, inflation and FX risk, concentration risk, liquidity risk, and technical risks (underwriting/reserving).
  - Insurers hold long-term assets funded by short-term liabilities; prepaid funding provides cushion against short-term liquidity needs.
- Non-traditional and bank-like activities:
  - Increasing engagement in corporate financing, securities financing transactions, securities lending, derivatives writing, and collateral management — creating potential direct exposure and asset liquidation channels.
  - Insurers have increasingly dominated the supply side of the derivative market and can write non-standardized, long-term derivatives.
- Channels of distress and contagion (summary):
  - Margin calls related to derivatives, non-traditional insurance operations, major catastrophes, and waves of lapses/surrenders can trigger fire sales.
  - Large aggregate claim events can deplete reserves, eat into regulatory capital buffers, and force sales of illiquid, long-term assets at discounts.
  - Policyholder lapses/surrenders can reduce business volume and expose minimum guarantees in adverse markets; empirical evidence of bank-run-like behavior is limited.
  - Intragroup leverage (loans, off-balance-sheet instruments) can amplify shocks and spread contagion; group supervision (Solvency II example) is important.
  - Banking–insurance “flow of funds nexus”: inability of insurers to finance corporates via bond markets may force corporates to draw on bank lines of credit, amplifying banking-sector liabilities.
- Key asset statistics (as of end-2016):
  - Life insurance companies held almost $6.8 trillion in total assets.
  - Property and casualty firms held $1.9 trillion in total assets.
  - Insurance sector was the largest U.S.-based corporate bond investor, with 25 percent of total holdings (as of end-2016 context).

### Pension funds — structure, risks, holdings, and systemic relevance
- Pension plan types and features:
  - Defined Benefit (DB): benefits guaranteed; sponsor may need to inject capital; corrective measures include increasing contributions or reducing benefits.
  - Defined Contribution (DC): liability limited to individual account value; fully funded by definition.
  - Hybrid plans: features of both DB and DC.
- Systemic relevance and risks:
  - DB plans generally unlikely to produce major contagion channels because they hold long-term assets, limit derivatives to hedging, are prevented from borrowing, and can rely on sponsor contributions and benefit reductions.
  - Uncertainties exist about sponsors’ ability to inject capital during wider market distress.
  - Potential channels: herd behavior, procyclical asset-liability management strategies, waves of redemptions or drops in contributions forcing liquidation of illiquid assets, and minimum guarantees becoming in the money without adequate backing.
  - Mitigant: steep penalties for abrupt withdrawals before retirement limit contagion from pre-retirement withdrawals.
- Trend (as of 2016Q4):
  - Since 2008, holdings of riskier securities by pension funds, particularly equities, have decreased significantly in aggregate, while investments in risk-free assets such as US treasuries have increased moderately.
  - Some US public pension funds may have increased risk taking due to regulatory linking of liability discount rates to expected return on assets.
- Indirect systemic impact:
  - Evidence that pension funds (alongside insurance companies) may be playing less of a countercyclical role, making liquidity provision in times of stress more difficult.

### Definition and estimation of PoD for investment funds; PoD methods for banks and insurers
- PoD for investment funds:
  - Defined as the probability of events that would require funds to liquidate assets to meet redemption demands.
  - Estimation uses a Value at Risk (VaR) approach with asset returns information:
    - Compute daily returns r_t = log(P_t) – log(P_{t-1}); standardize using full sample mean and standard deviation.
    - Determine γ as the 1st percentile of standardized returns (analogous to 99 percent VaR).
    - Compute rolling PoDs using six-month trailing sample mean and standard deviation and assuming a Normal distribution to obtain the probability returns fall below γ.
  - Implementation notes: returns can be estimated using mark-to-market asset value data or reconstructed portfolios if mark-to-market data unavailable.
- PoDs for banks and insurance companies:
  - Estimated using CDS spreads with a recovery rate assumption R = 40 percent.
  - CDS data: five-year CDS spreads from CMA retrieved through Datastream (or Bloomberg).
  - PoD formula presented in source (symbolic form).
  - Entities included (coverage approximate):
    - Banking: Bank of America, Capital One Financial, Citigroup, Goldman Sachs, JPMorgan, Morgan Stanley, and Wells Fargo — covering approximately 67 percent of total US banks’ assets.
    - Insurance: AIG, Allstate, Berkshire Hathaway, Hartford Financial Services, MetLife, Prudential, and Travelers Companies — covering approximately 50 percent of total U.S. insurance sector assets.

### SyRIN indicators, CIMDO framework, and systemic metrics
- CIMDO framework (Kullback minimum cross-entropy approach) recovers a posterior multivariate density j(x,y) that:
  - Minimizes the Kullback "entropy distance" from a prior p(x,y) while satisfying consistency constraints given observed marginal PoDs P^obs.
  - Prior typically a parametric multivariate T distribution; posterior takes the form j^(x,y) = p(x,y) exp{−[1 + μ̂ + λ1̂ 1_{x ≤ x̄_i} + λ2̂ 1_{y ≤ ȳ_j}]}.
- Systemic-risk indicators derived from the FSMD:
  - Financial Stability Index (FSI): expected number of entities becoming distressed given at least one distressed entity.
  - Distress Dependence Matrix (DiDe) and Vulnerability Index (VI): interconnectedness indicators.
  - Marginal Contribution to Systemic Risk (MCSR) and Systemic Risk Index: systemic loss indicators using expected shortfall and Shapley-value-based attribution.
- Interpretation and use:
  - DiDe entries are pairwise conditional probabilities of distress (row: PoD of entity in row given column entity distressed).
  - VI maps joint probabilities into [0, 1] for vulnerability interpretation.
  - MCSR requires Monte Carlo simulations of system losses and uses expected shortfall at the 1percent tail (footnote: ES represents the (average) extreme loss to the system that occurs with a probability of 1percent (or less)).
  - Systemic Risk Index normalized by the maximum observed ES to lie between zero and unity.

### Key SyRIN empirical findings (selected)
- Aggregate and sectoral contributions (as of 2013Q4):
  - Marginal contributions to systemic risk (MCSR) by sector amounted to 73 percent in total:
    - Banks: 32 percent
    - Insurance sector: 25 percent
    - Pension funds: 16 percent
- High Yield (HY) sector findings:
  - Twelve-month rolling correlation of returns of the top 10 global high yield mutual funds vs. High Yield Index: average correlation over the entire period was 0.93.
  - The level of interconnectedness of the HY sector relative to size (Ratio = MCSR/Size) exceeds unity and has been on an upward trajectory since early 2012; this ratio currently stands close to its level leading up to the financial crisis.
  - Vulnerability of banking and insurance sectors to shocks from the HY sector has been increasing dramatically in recent years.
- Time-series linkages:
  - Contributions to banking sector distress vulnerability from insurance and HY sectors trended upward over most of the sample and increased fairly steeply since early 2012, while aggregate systemic risk declined.
  - Between January 2008 and March 2014, percentage contribution by bond mutual funds (aggregate of Sov, HY and IG bond mutual fund sectors) to vulnerability of banking and insurance sectors increased; the upward trend is steeper for banking sector distress vulnerability.
  - Evidence of convergence of business models: the insurance sector becoming more “bank-like” over time.
- Systemic risk level:
  - The level of systemic risk at the time of analysis was contained and lower than historical peaks around the financial crisis and the European sovereign crisis.
  - Both the Systemic Risk Index and the FSI Index display peaks at Lehman collapse (September 2008) and the initial stages of the European sovereign debt crisis (May–June 2010) and subsequent intensification after spreading to Italy and Spain.

### Liquidity, dealer inventories, and days-to-liquidate metrics for HY funds
- Days to liquidate metric:
  - Computed as the ratio of assets of US high-yield mutual funds and ETFs per daily dealer inventories.
  - Data limitation: no dealer inventory data before April 2013; dashed red line in source assumes a constant ratio of this amount to total corporate bonds before this date.
  - SEC seven-day limit for redemption payments (Investment Company Act of 1940, Section 22e) highlighted against increasing days required for full liquidation.
- Practical observation:
  - Mutual fund growth and declining dealer inventories in less liquid markets increase the number of days required to fully liquidate holdings if all investors redeem at once.

### Policy recommendations and supervisory implications (summarized)
- Tailored liquidity assessment:
  - Regulators should assess relative liquidity of asset classes versus redemption terms of pooled vehicles; less frequently traded markets (e.g., HY bonds) may warrant lower frequency redemption terms.
  - The seven-day maximum to pay redemptions in US mutual funds (Investment Company Act of 1940, Section 22e) may be insufficient during stress.
- Enhance liquidity risk management oversight:
  - Continue improvements and adopt initiatives such as IOSCO consultation on liquidity risk management recommendations (July 2017) and UK FCA discussion paper (February 2017).
  - Areas for improvement: greater flexibility in redemptions and dealing frequencies, treatment of institutional investors, guidance on risk management tools, enhanced disclosure requirements.
- Improve NAV accuracy and redemption-term alignment:
  - For less liquid assets where a large share of bonds do not trade daily, daily NAV relying on matrix-pricing can be misleading.
  - Recommendation: where transactions are infrequent, mutual funds should adopt less frequent NAV pricing aligned with lower-frequency redemption terms that match underlying liquidity.
- ETF approvals and underlying asset liquidity:
  - Regulatory authorities should make underlying asset liquidity a major criterion when approving new ETFs.
- Insurance-product hedging:
  - Insurance products that provide protection against market moves should be fully hedged with exchange- or platform-traded derivatives.
- Asset manager communication and investor disclosure:
  - Emphasize clearer communication to investors about liquidity and volatility risks inherent in funds invested in less liquid markets.
- Global coordination:
  - Regulators should pursue harmonized global efforts to examine mutual funds, develop best practices for addressing redemption risks, and supervise liquidity and pricing of illiquid securities.
- Notes on redemption frequency flexibility:
  - European UCITS Directive permits redemption frequencies of up to twice a month; only a small proportion of funds invested in illiquid assets offer redemption terms less frequent than daily.

### Implementation inputs, data sources, and aggregation
- Data sources and aggregation:
  - Bank and insurance sector data: US Flow of Funds (FoF).
  - Fund-type data (equity, bond funds, and MMFs): ICI.
  - Hedge funds: Barclayhedge data on global HF with a 75 percent weight for the US (weight derived from 2013 IOSCO survey).
  - Frequency: quarterly via Datastream or Bloomberg; linear interpolation used when annual data only.
- Portfolio reconstruction mappings (selected):
  - Equity funds portfolio: 75% MSCI US index, 25% MSCI World index (tickers: MSUSAM$, MSWRLD$).
  - Bond funds indices: BofA Merrill Lynch US Corporate & Government Index, BofA Merrill Lynch US High Yield Index, BofA Merrill Lynch US Corporate Index (tickers: B0A0, C0A0, H0A0).
  - MMF portfolio weights: 40% 3M Certificate of Deposits, 20% O/N repo, 20% 3M Commercial Paper, 10% Asset-Backed Commercial Paper, 10% T-Bills.
  - Pension funds portfolio: 50% domestic equities, 25% foreign equities, 25% bonds (tickers: MSUSAM$, MSWRLD$, B0A0).
- Appendix Table 2 selected tickers and mappings:
  - Banks: Private depository institutions (Table L.109) — Ticker US70PDTAA.
  - Insurance: Life insurance (L.115) + other insurance Corporations (L.114) — Tickers US54XXXAA, US51XXXAA.
  - Equity funds: ICI—all equity funds — Ticker USFANEQ.A.
  - Bond funds (incl. HY and IG): ICI—All bond and income funds TNA — Ticker USFANBI.A.
  - MMF: ICI MMFs TNA — Ticker USFANMM.A.
  - Pension funds: Private and public pension funds (L.116) — Ticker US59TOFAA.
  - Hedge funds: AuM of hedge funds—weight 75% — Ticker Barclayhedge website.

### Conclusions on SyRIN’s role
- SyRIN provides a comprehensive, top-down assessment of systemic risk across banks and other financial intermediaries by quantifying amplification mechanisms from interconnectedness.
- The tool produces metrics for tail risk, interconnectedness, and contributions to systemic risk across entities and sectors.
- SyRIN is implementable with publicly available data and adaptable to different institutional granularity and data availability.
- SyRIN is intended to identify vulnerabilities that warrant deeper sector-specific scrutiny and to inform policy formulation to minimize systemic vulnerabilities.

*Source: wp1814 — IMF Working Paper (excerpts from "2. Input Series for Total Asset Data", Box 1, Section II, Appendix I and selected figures/tables referenced in the source).*

### References .............................................................................................................

### References

### Tables
- 1. Distress Dependence Matrix ................................................................................................25

### Figures
- 1. Asset Liquidation and Direct Exposure Channels ...............................................................10
- 2. Asset Liquidation and Direct Exposure Channels ...............................................................11
- 3. Holdings of Nonbank Financial Institutions as of 2016 ......................................................11
- 4. US Funds as of 2016Q4 .......................................................................................................12
- 5. Channels for Hedge Fund Distress Transmission ................................................................16
- 6. Holdings of US Insurance Companies as of 2016Q4 ..........................................................19
- 7. US Pension Fund Holdings ..................................................................................................22
- 8. SyRIN: A Comprehensive Multi-Sector Tool .....................................................................24
- 9. Correlation of Returns: High Yield Mutual Funds and ETFs vs. the High Yield Index .....29
- 10. PoDs Funds ........................................................................................................................31
- 11. Systemic Risk Index ..........................................................................................................32
- 12. Financial Stability Index ....................................................................................................32
- 13. Marginal Contribution to Systemic Risk as of 2013Q4 .....................................................33
- 14. Increase in MCSR ..............................................................................................................34
- 14. Contributions to Distress Vulnerability of the Banking Sector .........................................34
- 16. Contributions to Banking Sector Distress Vulnerability as of 1Q2014 .............................35
- 17. Contributions to Insurance Sector Distress Vulnerability .................................................36
- 18. Contributions to Distress Vulnerability of the Banking (left) and Insurance (right) Sectors 
  as at January 2008 and March 2014 .........................................................................................37
- 19. Comparison of Systemic Risk Level with Contribution to Banking Sector Distress 
  Vulnerability ............................................................................................................................38
- 20. Comparing Aggregate Systemic Risk level with Contribution to Insurance Sector Distress 
  Vulnerability ............................................................................................................................38
- 21. Accommodative Monetary Policies Have Encouraged Greater Risk-Taking ...................40
- 22. Days Required for Full Liquidation ...................................................................................41
- 23. The Rise of Passive Investment in US Equity Markets .....................................................45

### Appendix
- I. Inputs for Implementation ....................................................................................................50

### Appendix Tables
- 1. Input Series for Portfolio Reconstruction ............................................................................51

*Source: wp1814 - References*

### 2. Input Series for Total Asset Data ...................................................................................

### 2. Input Series for Total Asset Data

### Overview and purpose of SyRIN
- SyRIN is a reduced-form, top-down framework to assess systemic risk across banks and nonbanks by modeling a financial system as a portfolio of financial entities/sectors and recovering a financial system multivariate density (FSMD).
- The FSMD characterizes (i) individual firm value distributions in marginal densities and (ii) the association across firm values (interconnectedness structure) in its copula function.
- The Consistent Information Multivariate Density Optimizing (CIMDO) approach is used to infer multivariate densities consistent with empirically observed probabilities of distress (PoDs).
- SRMs (systemic risk metrics) are derived from statistical moments of the common FSMD and are therefore consistent across perspectives (tail risk, interconnectedness, entity/sector contributions).
- SyRIN can be implemented with market-based data or supervisory data, and is adaptable to institutional granularity and data availability.
- SyRIN is informative for identifying vulnerable sectors and guiding deeper analysis, but cannot identify specific causal channels due to its reduced-form nature.

### Systemic-risk transmission mechanisms (direct and indirect channels)
- Two primary channels of contagion across financial intermediaries and markets:
  - Direct interlinkages: contractual obligations between financial entities (direct exposure channel).
  - Indirect interlinkages: exposures to common risk factors and market price channels, including asset fire sales and sell-offs (asset liquidation channel).
- Indirect interconnectedness can be non-linear, self-reinforcing, and may be latent in calm periods but become significant in high volatility periods.
- Copula functions (not just correlation) are used to capture linear and non-linear dependence in interconnectedness.

### Investment funds — vulnerabilities and transmission channels
Findings and characteristics:
- Investment funds (open-end funds/mutual funds, closed-end funds, ETFs, money market funds) transmit shocks primarily through:
  - Asset liquidation channel (redemptions → fire sales → price dislocations).
  - Direct exposure/funding channel (funds reduce exposures to risky issuers → funding and counterparty stress).
- Open-end funds face redemption risk and maturity/liquidity mismatches; closed-end funds face higher liquidity risk, higher volatility risk, more derivatives, more leverage, and may trade at a discount between NAV and share price.
- Open-end funds and ETFs held $17.5 trillion of equities and fixed-income instruments as of 2016Q4 (Federal Reserve data).
- Their share of the US equity market amounted to 34 percent as of 2016Q4.
- Their holdings of different debt market sectors ranged from 11 to 24 percent as of 2016Q4.
- By end-2015, assets under management of closed-end funds were less than 2 percent of the U.S. fund industry.
- The importance of mutual funds has been growing significantly since 2006, especially for corporate and municipal securities.

Empirical evidence on asset-liquidation effects:
- Hau and Lai (2012): distressed selling by mutual funds accounted for 10 percent of the 52 percent crisis-related decline in the US stock market during July 2007–June 2009.
- Coval and Stafford (2007): widespread selling by distressed funds led to increased illiquidity and downward pressure on individual stocks.
- Manconi and others (2012): in June–December 2007, funds investing in securitized assets liquidated corporate bonds first, spreading the crisis.
- Anand and others (2013): institutional investors reduced liquidity provision at crisis peak (September 2008–March 2009), surging illiquidity especially for risky stocks.

Money market funds (MMFs) — direct exposure and funding relevance:
- After reforms in 2016, commercial paper holdings of MMFs fell by 70 percent between 2016Q1 and 2016Q4.
- MMFs were still the main providers of repo funding in the US, accounting for around $800 billion as of 2016Q4 (23 percent of the repo market per US Flow of Funds).
- Broker-dealers were receiving $1.3 trillion of repo funding as of end-2016.
- Historical episodes: U.S. MMFs suffered massive outflows in September 2008 after one MMF “broke the buck”; U.S. MMFs cut exposures to European banks in mid-2011, contributing to dollar shortages for those banks.

Sponsor support channel:
- Sponsors sometimes purchase troubled fund assets or guarantee NAV; examples cited resulted in material losses in past episodes.

### Hedge funds — vulnerabilities, channels, and empirical outcomes
Structural and market features:
- Hedge funds are private vehicles for wealthy and institutional investors and are relatively unconstrained by regulation relative to mutual funds.
- They employ derivatives, margin, short-selling, leverage, and invest in illiquid assets, increasing vulnerability to downward price spirals.
- Leverage sources include margin accounts, derivatives, repos, and short sales.
- Margin and collateral dynamics can amplify stress: adverse prices can coincide with (i) an increase in margin requirements and (ii) a decrease in collateral value.

Transmission channels and market impact:
- Asset liquidation channel: collapse leads to fire sales and amplified price impact due to illiquidity and leverage.
- Direct exposure channel via prime brokerage: prime brokers provide margin lending and can re-pledge collateral (re-hypothecation); top prime brokers are highly concentrated (top 10 serviced 84 percent of hedge fund AUM as of end-2006).
- Hedge fund behaviors (rapid tactical shifts) can amplify market gyrations and cause dislocation in crowded markets.

Empirical outcomes:
- Credit strategies lost: 19 percent (distressed) and 26 percent (convertible bond arbitrage) in 2008 (Le Sourd 2009).
- Emerging markets HF lost 30 percent in 2008 (Le Sourd 2009).
- Khandani and Lo (2011): August 2007 losses in long/short equity HF were amplified by sudden liquidations and funds implementing similar strategies.
- Historic examples of funding/illiquidity failure: Long-Term Capital Management (LTCM) and Amaranth Advisors.

### Insurance sector — business model, risks, and expanding financial-intermediation role
Business model and risk profile:
- Insurance business model likened to a swap: insurers receive fixed premiums and pay floating benefits; pooling and diversification reduce idiosyncratic risk.
- Insurers hold long-term assets funded by short-term liabilities; prepaid funding provides cushion against short-term liquidity needs.
- Liability-driven investment tilts asset allocation toward fixed-income and hedging instruments.

Key financial risks:
- Interest rate risk (material for long-term contracts with minimum guarantees).
- Credit risk (counterparty risk in reinsurance and derivatives).
- Equity, property, and infrastructure exposures depending on business mix.
- Inflation and foreign exchange risk (mitigated by regulatory matching/hedging).
- Concentration risk on both asset and liability sides.
- Liquidity risk from unexpected claims or waves of surrenders/lapses.
- Technical risks: underwriting performance and reserving risk; systematic risks include demographic and catastrophic events.

Non-traditional activities and contagion potential:
- Insurers increasingly engage in “bank-like” activities: corporate financing, securities financing transactions, securities lending, derivatives writing, collateral management.
- These activities create potential direct exposure and asset liquidation channels in distress episodes.
- The insurance sector is a significant source of financing for other sectors via corporate bond holdings, commercial mortgages, and direct loans.

Key statistics:
- As of end-2016, life insurance companies held almost $6.8 trillion in total assets.
- As of end-2016, property and casualty firms held $1.9 trillion in total assets.
- Insurance sector was the largest U.S.-based corporate bond investor, with 25 percent of total holdings (as of end-2016 context provided).

### Implementation and policy relevance
- SyRIN supports macroprudential policy by quantifying systemic risk amplification from interconnectedness across banks and nonbanks, informing where deeper supervisory scrutiny is warranted.
- The framework can embed market-perceived changes in interconnectedness (via market-based PoDs) so SRMs reflect realistic market reactions.
- Because SyRIN is reduced-form, it is a screening and prioritization tool to guide further analysis, rather than a tool to identify specific causal channels.

*Source: IMF Working Paper — content from "2. Input Series for Total Asset Data" section of the provided document.*

### 13.5 percent of that market (Figure 6). Large-scale distress of insurance firms would inhibit

### wp1814 - 13.5 percent of that market (Figure 6). Large-scale distress of insurance firms would inhibit

### Insurance sector: channels of distress and contagion
- Insurance firms play a “bank-like” role and provide financing to the corporate sector; large-scale distress would inhibit this role.
- The asset liquidation channel can arise if insurers face liquidity needs resulting in fire sales triggered by:
  - margin calls (related to insurers’ use of derivatives),
  - non-traditional insurance operations,
  - major catastrophes and waves of lapses/surrenders of policies.
- Margin calls are typically heavy when the business mix includes investments and participating products linked with long-term guarantees.
- Insurers have increasingly dominated the supply side of the derivative market over the past decade and can write non-standardized, long-term derivatives that other financial institutions find costly to intermediate.
- Insurer activities have extended to bank-like operations, including liquidity provision via liquidity or collateral swaps; liquidity needs from such transactions could force asset sales and amplify contagion, especially where non-traditional insurance activities are significant.
- Large aggregate claim events (e.g., pandemics, earthquakes) can:
  - deplete standard reserves and extra provisions (such as resilience reserves),
  - eat into the regulatory capital buffer,
  - force insurers to sell illiquid, long-term assets at significant discounts.
- Policyholder lapses (walking away from a contract) and surrenders (withdrawing policy cash value) expose insurers to losses from lower business volume and potentially costly minimum guarantees in a deflationary environment; waves of lapses/surrenders could lead to asset fire sales, though empirical evidence of bank-run-like behavior is limited.
- Insurers may leverage capital via intragroup loans and off-balance sheet instruments, amplifying shocks and spreading contagion across sectors; international regulators are actively addressing these concerns (for example, Solvency II considers group supervision essential).
- The banking–insurance “flow of funds nexus” can transmit stress: inability of insurers to finance corporates via corporate bond markets may force firms to draw on bank lines of credit, amplifying banking-sector liabilities and distress.
- Historical note: whereas the banking sector has become better capitalized and less risky, available analysis suggests no observed decline in systemic risk of the insurance sector.

### Holdings and asset composition (as of 2016Q4)
- Figure 6: Holdings of US Insurance Companies as of 2016Q4 (in percent) — categories listed in source:
  - Domestic & Foreign Bonds
  - Commercial Mortgages
  - AgenciesTreasuries (Marketable)
  - Equities
- Figure 7: US Pension Fund Holdings (in $ bn), as of 2016Q4 — categories listed in source:
  - Global Equities
  - U.S. Treasuries
  - U.S. Corporate and Foreign Bonds

### Pension funds: structure, risks, and systemic relevance
- Pension plans types:
  - Defined Benefit (DB): benefits guaranteed; plan may not need to be fully funded; sponsor may need to inject capital if funding inadequate; corrective measures include increasing contributions or reducing benefits.
  - Defined Contribution (DC): liability limited to individual account value; fully funded by definition; risk borne by members.
  - Hybrid plans: present features of both DB and DC.
- DB plans generally unlikely to produce major contagion channels because they:
  - hold long-term assets,
  - limit derivatives to hedging,
  - are prevented from borrowing,
  - can rely on sponsor contributions and benefit reductions if necessary.
- Uncertainties remain about DB plans’ ability to rely on sponsor contributions or benefit reductions during wider market distress.
- Potential contributions to systemic risk under certain conditions:
  - Herd behavior can exacerbate asset price swings and contribute to downward price pressure in market distress.
  - Some asset-liability management strategies are inherently procyclical and may affect bond and equity markets.
  - Waves of redemptions or drops in contributions may force liquidation of illiquid assets at large discounts, depressing valuations and prompting member exits.
  - Effects amplified where minimum guarantees become in the money without adequate backing.
- Mitigating factors: abrupt withdrawals before retirement are typically prevented or discouraged by steep penalties, limiting this contagion channel.
- Trend: since 2008, holdings of riskier securities by pension funds, particularly equities, have decreased significantly in aggregate, while investments in risk-free assets such as US treasuries have increased moderately (as of 2016Q4); some US public pension funds may have increased risk taking due to distinct regulatory linking of liability discount rates to expected return on assets.
- Indirect systemic impact: emerging evidence that pension funds (alongside insurance companies) may be playing less of a countercyclical role, making liquidity provision in times of stress more difficult; increased regulatory emphasis on asset-liability matching can make institutional investors more procyclical and risk averse during stress, reducing their role as shock absorbers.

### SyRIN: a comprehensive multi-sector systemic risk tool
- Motivation:
  - Most empirical systemic risk work has focused on the banking sector; recent research has begun analyzing nonbank financial institutions (insurance, mutual funds, hedge funds).
  - SyRIN conceptualizes the financial system as a portfolio of entities spanning banks and nonbanks, incorporating the largest banks and insurance companies in a country, plus pension, mutual fund, and hedge fund sectors.
- Methodology:
  - SyRIN infers the financial system multivariate distribution (FSMD) using the CIMDO approach, a non-parametric method that enables robust inference of the CIMDO-multivariate density from minimal information on asset price returns and probabilities of distress (PoDs).
  - The FSMD permits estimation of financial stability indicators and systemic loss indicators via joint and conditional probabilities and simulation of systemic losses.
- Systemic indicators estimated:
  - Financial Stability Index (FSI): a tail risk indicator reflecting the expected number of entities becoming distressed given at least one distressed entity; embeds changes in individual PoDs and distress dependence among entities.
  - Distress Dependence Matrix (DiDe) and Vulnerability Index (VI): interconnectedness indicators.
  - Marginal Contribution to Systemic Risk (MCSR) and the Systemic Risk Index: systemic loss indicators that account for interconnectedness and relative size of entities.
- Illustrative formulation:
  - Example with three entities (random variables x, y, r) where the CIMDO-density is inferred (equation provided in source).
  - DiDe: matrix of pairwise conditional probabilities of distress (rows: PoD of entity specified in row given column entity becomes distressed).
  - Vulnerability Index (VI) for an entity is constructed from sums of joint probabilities conditional on distress of other entities and typically normalized to map into [0, 1].
- Interpretation notes:
  - FSI represents the expected number of distressed entities conditional on at least one distress event; higher FSI implies increased instability and increased distress dependence.
  - Conditional probabilities in DiDe provide insights into interconnectedness and likelihood of contagion, though they do not imply causation.

*Source: https://www.imf.org/-/media/files/publications/wp/2018/wp1814.pdf*

### Box 1. The CIMDO Framework to Model Multivariate Densities

### Box 1. The CIMDO Framework to Model Multivariate Densities

### The CIMDO objective and solution
- CIMDO is based on the Kullback (1959) minimum cross-entropy approach; original formulation in Segoviano (2006) and methodological improvements and robustness proofs in Segoviano and Espinoza (2017).
- For a portfolio with two asset types whose logarithmic returns are x and y, the CIMDO-objective function is defined as:
  - I(j,p) = ∫∫ j(x,y) ln[p(x,y)/j(x,y)] dy dx, where p(x,y) and j(x,y) ∈ ℝ+
    - (equation labeled (a) in the source)
- Prior distribution:
  - The prior density p(x,y) follows a parametric form (for example, a multivariate t distribution) chosen for economic intuition and theoretical consistency.
  - The prior p(x,y) is usually inconsistent with empirically observed measures of distress; empirical PoDs are used to recover the posterior.
- Consistency (constraint) equations imposed on the marginal densities of the posterior j(x,y):
  - ∫∫ j(x,y) 1_{x ≤ x̄_i} dy dx = P^obs_{i,x} and ∫∫ j(x,y) 1_{y ≤ ȳ_j} dx dy = P^obs_{j,y}
    - where j(x,y) is the posterior to be solved; P^obs are the empirically observed probabilities of distress (PoDs); 1_{·} are indicating functions defined with distress thresholds x̄_i, ȳ_j.
    - (equation labeled (ܾ) in the source)
- Additional required conditions for j(x,y):
  - j(x,y) ≥ 0
  - ∫∫ j(x,y) dy dx = 1
- Optimization functional including Lagrange multipliers:
  - The functional minimized is:
    - F(j,p) = ∫∫ j(x,y) ln j(x,y) dy dx − ∫∫ j(x,y) ln p(x,y) dy dx
      + λ1 [∫∫ j(x,y) 1_{x ≤ x̄_i} dy dx − P^obs_{i,x}]^2
      + λ2 [∫∫ j(x,y) 1_{y ≤ ȳ_j} dx dy − P^obs_{j,y}]^2
      + μ [∫∫ j(x,y) dy dx − 1]^2
    - where λ1, λ2 are Lagrange multipliers for consistency constraints and μ is the Lagrange multiplier for probability additivity.
    - (equation labeled (ܿ) in the source)
- Optimal posterior form obtained via calculus of variations:
  - j(x,y)^ = p(x,y) exp{−[1 + μ̂ + λ1̂ 1_{x ≤ x̄_i} + λ2̂ 1_{y ≤ ȳ_j}]}
    - (equation labeled (݀) in the source)
- Interpretation:
  - CIMDO recovers the posterior distribution that minimizes the Kullback "entropy distance" from the prior while satisfying the moment-consistency constraints offered by observed PoDs.
  - The approach transforms the problem from assuming parametric probabilities to an inference problem: inferring the unknown multivariate density consistent with observed marginal PoDs.
- Implementation note from the updated methodology:
  - The current CIMDO uses a multivariate T prior to improve robustness and includes a computational algorithm allowing estimation of CIMDO densities of large dimensions.

### Contributions to Distress Vulnerability
- Percentage contribution metric example:
  - Contribution of entity Y to distress dependence of entity X:
    - [P(X ≥ x̄_i | Y ≥ ȳ_j) · P(Y ≥ ȳ_j)] / P(X ≥ x̄_i) × 100%
    - (equation labeled (5) in the source)
- Monitoring these percentage contributions over time provides a metric of how distress dependence between entities or sectors evolves.

### Systemic Loss Indicators
- Marginal Contribution to Systemic Risk (MCSR):
  - Requires simulation of the distribution of losses at the system level.
  - Systemic tail risk measure used: “expected shortfall” (ES).
    - Footnote: The ES represents the (average) extreme loss to the system that occurs with a probability of 1percent (or less).
  - MCSR for each sector/entity is backed out from the system ES using a Shapley-value-based risk attribution methodology (Tarashev, Borio, and Tsatsaronis (2010)).
- Systemic Risk Index:
  - Constructed using the systemic ES recorded at each point in time.
  - Series is bounded between zero and unity by deflating by the max ES recorded over the period (or sub-period).
  - Normalization illustrates the relative position of systemic risk with respect to a reference point.
- Purpose of indicators:
  - Analyze complex interlinkages and quantify vulnerability to distress risks between entities, within and across sectors.
  - Address key questions:
    - (i) How is systemic risk evolving and what is its current level?
    - (ii) What institutions/sectors contribute most to systemic risk?
    - (iii) How vulnerable are specific institutions/sectors to distress in other institutions/sectors?

### Implementation and aggregation in SyRIN (tool context)
- Overview of implementation steps:
  - Determine asset sizes, recovery rates, and PoD of financial intermediaries and sectors to include.
  - Use PoDs as input to CIMDO to infer the FSMD (the multivariate density describing interconnectedness across entities and sectors).
  - Obtain two types of measures from the FSMD:
    - Financial stability measures estimated by sliding the FSM into different joint and conditional probabilities.
    - Loss metrics obtained by Monte Carlo simulations based on the FSMD.
  - Metrics are consistent because they derive from statistical moments of a common FSMD.
- Aggregation recommendations:
  - Include at the individual level: major banks and insurance companies (significant share of financial intermediation by asset size; entity-level data more available).
  - Include at the sector level: mutual funds, hedge funds, and pension funds aggregated by common categories (benchmarking within sector, common business strategies and risk factors).
  - Example taxonomy suggestions: HF, PF, MMF, EF, HY, Sov, IG (adaptable to country circumstances and data availability).
- Empirical note (High Yield example):
  - Twelve-month rolling correlation of returns of the top 10 global high yield mutual funds vs. High Yield Index: the average correlation over the entire period was 0.93.

### Probabilities of Distress (PoDs)
- SyRIN is a structural risk model based on firms’ distress; PoDs can be estimated using market-based and supervisory information.
- Meaning of distress:
  - Usually includes default but can encompass debt restructuring, government intervention, recapitalization, credit agencies’ downgrades, etc.; common feature is significant decrease in firms’ asset values.
- PoDs for banks and insurance companies:
  - Market-based information methods:
    - Merton type: distress ≡ default (Merton 1974) focusing on capability to service debt obligations.
    - CDS spreads: PoDs estimated using credit default swap spreads; distress defined by the CDS trigger event.
    - Bond spreads: PoDs estimated via no-arbitrage relationships between bond yields and default probabilities.
  - Supervisory information:
    - Used when market-based data are unavailable or inadequate (e.g., subsidiaries without market indicators).
    - PoDs constructed from supervisory information can indicate probability that losses would violate a supervisory-defined capital buffer (Segoviano and Padilla 2006).

*Source: wp1814 - Box 1. The CIMDO Framework to Model Multivariate Densities (excerpt).*

### Section II, we define the PoD for investment funds as the probability of events that would

### wp1814 - Section II, we define the PoD for investment funds as the probability of events that would

### Definition and estimation of PoD for investment funds
- PoD for investment funds is defined as the probability of events that would require funds to liquidate assets to meet redemption demands.
- Estimation approach:
  - Follow a Value at Risk (VaR) approach using asset returns information for the fund types under analysis.
  - Define a threshold related to periods of significant outflows; PoD is the probability that returns would be lower than the threshold.
  - See Appendix 1 for technical details (as referenced in the source).

### PoD consistency with business models and risk factors
- PoDs should reflect differences in leverage, liquidity, and maturity mismatches across financial intermediaries; entities with higher leverage, liquidity, and/or maturity mismatches should exhibit higher PoDs.
- Empirical finding (as shown in Figure 10):
  - Hedge funds show higher PoDs than MMFs and bond funds, and became significantly higher in periods of distress.
  - Open-end bond funds (especially those investing in less liquid assets such as high yield) showed larger PoDs than MMFs.

### Systemic risk level and measurement tools
- Two measures of systemic risk presented: the Systemic Risk Index (Figure 11) and the FSI Index (Figure 12).
- Key finding:
  - The level of systemic risk at the time of analysis was contained and lower than historical peaks around the financial crisis and the European sovereign crisis.
  - Both indices display peaks at well-documented systemic episodes: Lehman collapse (September 2008); initial stages of the European sovereign debt crisis (May–June 2010); and subsequent intensification after spreading to Italy and Spain.

### Sectoral contributions to systemic risk (MCSR) and vulnerability
- As of 2013Q4, marginal contributions to systemic risk (MCSR) by sector amounted to 73 percent in total:
  - Banks: 32 percent
  - Insurance sector: 25 percent
  - Pension funds: 16 percent
- Certain sectors (HY and IG) exhibit interconnectedness measures that dominate their relative size (Ratio = MCSR/Size greater than unity).
- Time-series findings:
  - Increase in absolute MCSR relative to 2007Q1 highlights the steepest increase in MCSR for the HY sector as of 2013Q4.
- Contributions to banking sector distress vulnerability:
  - Contributions from hedge fund and insurance sectors tend to increase prior to periods of heightened distress.
  - Contributions from the insurance sector have been steadily increasing over time.
  - By 1Q2014, HY sector was the most important contributor to banking sector distress vulnerability, followed by insurance and hedge funds.
- Contributions to insurance sector distress vulnerability:
  - Banking sector’s contributions to insurance vulnerability have shown a steady increase, tracking the reverse direction as well.
  - As of 3/24/2014, the banking sector’s contribution dominates, followed by HY and HF sectors.
- Linkages and trends:
  - Linkages between banking, insurance, and bond mutual fund sectors have increased in recent years.
  - Between January 2008 and March 2014, percentage contribution by bond mutual funds (aggregate of Sov, HY and IG bond mutual fund sectors) to vulnerability of banking and insurance sectors increased; the upward trend is steeper for banking sector distress vulnerability.
  - Evidence of convergence of business models: the insurance sector becoming more “bank-like” over time.

### Systemic risk level versus distress vulnerability
- Although aggregate systemic risk was contained (falling to a low level comparable to 2007Q1), contributions to distress vulnerability from certain sectors increased since early 2012.
- Specific observations:
  - Contributions to banking sector distress vulnerability from insurance and HY sectors trended upward over most of the sample and increased fairly steeply since early 2012, while aggregate systemic risk declined.
  - Increases in aggregate systemic risk are typically preceded by a buildup of distress vulnerability of the banking sector to shocks from the hedge fund sector.
  - Hedge fund sector’s contribution to banking sector distress exhibits more pronounced cyclicality than its contribution to insurance sector distress, which is generally stable.

### SyRIN findings and focus on High Yield (HY) mutual funds
- SyRIN identified the HY mutual fund sector as having potentially high systemic risk impact.
- Key conclusions:
  - The level of interconnectedness of the HY sector relative to size (ratio) exceeds unity and has been on an upward trajectory since early 2012; this ratio currently stands close to its level leading up to the financial crisis.
  - Vulnerability to distress of banking and insurance sectors to shocks from the HY sector has been increasing dramatically in recent years.
- Structural drivers behind HY trends:
  - Increasing flows into mutual fund and ETF investments, particularly into riskier, less liquid asset classes such as high yield.
  - Monetary policy and regulatory stance interaction:
    - Near-zero short-term interest rates and unconventional monetary policy removed low-risk, longer-duration assets from the market and impelled investors toward riskier asset classes.
    - Regulatory tightening and higher capital standards on banks reduced banks’ ability to absorb risk, shifting risk to nonbank financial sector.
  - Resulting dynamics:
    - Nonbank financial sector became a substantial holder of risk, with increasing ownership of corporate and riskier foreign debt.
    - Average holdings by market makers (broker-dealers) decreased sharply.
    - Growth particularly strong in less liquid fixed income markets, such as high yield, as low rates also led to increased supply of bonds by riskier companies.

### Liquidity and redemption risks for HY mutual funds
- Mutual funds and ETFs engage in liquidity transformation, offering demandable equity backed by less liquid underlying investments; fund inflows can reverse quickly during stress.
- Redemption risk drivers:
  - Mutual fund growth and declining dealer inventories in less liquid markets increase the number of days required to fully liquidate holdings if all investors redeem at once.
  - SEC regulation permits funds to delay paying redemptions for a maximum of seven days under the Investment Company Act of 1940 (Section 22e).
  - Example: The Third Avenue Focused Credit Fund suspended redemptions on December 9, 2015, blocking future investor redemptions after large losses and outflows—showing that the suspension mechanism has not been tested at scale.
- Figure 22 metrics:
  - Days to liquidate is computed as the ratio of assets of US high-yield mutual funds and ETFs per daily dealer inventories.
  - Data limitations: no dealer inventory data before April 2013; dashed red line assumes a constant ratio of this amount to total corporate bonds before this date.
  - The SEC seven-day limit for redemption payments is highlighted against increasing days required for full liquidation.

### Policy recommendations to mitigate risks (summarized)
- Tailored liquidity assessment:
  - Regulators should assess relative liquidity of asset classes versus redemption terms of pooled vehicles; less frequently traded markets (e.g., HY bonds) may warrant lower frequency redemption terms.
  - The seven-day maximum to pay redemptions in US mutual funds (Investment Company Act of 1940, Section 22e) may be insufficient during stress given liquidity mismatches and low dealer inventories.
- Enhance liquidity risk management oversight:
  - Continue improvements and adopt initiatives such as IOSCO consultation on liquidity risk management recommendations (July 2017) and UK FCA discussion paper (February 2017).
  - Areas for improvement: greater flexibility in redemptions and dealing frequencies, treatment of institutional investors, guidance on risk management tools, enhanced disclosure requirements.
- Improve accuracy of NAV calculations:
  - SEC Rule 22c-1 requires open-end funds to compute NAV at least once daily, Monday through Friday; for less liquid assets where a large share of bonds do not trade daily, daily NAV relying on matrix-pricing can be misleading.
  - Recommendation: where transactions are infrequent, mutual funds should adopt less frequent NAV pricing aligned with lower-frequency redemption terms that match underlying liquidity.
- ETF approvals and underlying asset liquidity:
  - Regulatory authorities should make the liquidity profile of underlying assets a major criterion when approving new ETFs.
- Insurance products with market protection:
  - Insurance products that provide protection against market moves should be fully hedged with exchange- or platform-traded derivatives; single-factor insurance (mortgage or bond insurance) should also be hedged with such derivatives.
- Asset manager communication and investor disclosure:
  - Emphasize clearer communication to investors about liquidity and volatility risks inherent in funds invested in less liquid markets.
- Global coordination:
  - Regulators should pursue harmonized and coordinated global efforts to examine mutual funds, develop best practices for addressing redemption risks, and supervise liquidity and pricing of illiquid securities.
- Note on UCITS:
  - Greater flexibility in redemption and dealing frequency under the European Union’s UCITS Directive allows funds to have redemption frequencies of up to twice a month; however, only a small proportion of funds invested in illiquid assets offer redemption terms less frequent than daily.

### Broader vulnerabilities and forward-looking observations
- SyRIN can assist policy formulation by identifying vulnerabilities related to:
  - Increased sensitivity of capital markets to the exit from unconventional monetary policies, potentially making exits more volatile.
  - The rise of passive investment and benchmark-centric market participants, increasing procyclicality and interconnectedness:
    - Share of total U.S. public equities held by index funds and ETFs rose from 6 percent in 2007 to 16 percent by end-2016.
  - Changing cross-country financial interlinkages, increasing cross-border interconnectedness.
  - Higher vulnerabilities for emerging markets to shocks originating in advanced economies due to stronger financial links and portfolio concentration.

### Conclusions on SyRIN’s role
- SyRIN provides a comprehensive, top-down assessment of systemic risk across banks and other financial intermediaries by quantifying amplification mechanisms from interconnectedness.
- The tool produces metrics for tail risk, interconnectedness, and contributions to systemic risk across entities and sectors.
- SyRIN is implementable with publicly available data and adaptable to different institutional granularity and data availability.
- SyRIN is intended to identify vulnerabilities that warrant deeper sector-specific scrutiny and to inform policy formulation to minimize systemic vulnerabilities.

*Source: wp1814 - Section II, we define the PoD for investment funds as the probability of events that would (IMF working paper content).*

### REFERENCES

### REFERENCES

### Bibliographic references (selected)
- Acharya, V.V., and M. Richardson, 2010. “Is the insurance industry systemically risky?” In: Chapter 9 of Regulating Wall Street: The Dodd-Frank Act and the Architecture of Global Finance, ed. V. Acharya, T. Cooley, M. Richardson, and I. Walter. John Wiley & Sons. November 2010.
- Allen, F., and Gale, D., 2000. “Financial contagion,” Journal of Political Economy, 108(1), 1-33.
- Anand, A., P. Irvine, A. Puckett, and K. Venkataraman, 2013. “Institutional trading and stock resiliency: Evidence from the 2007–2009 financial crisis,” Journal of Financial Economics, Vol. 108 (3), 773–97.
- Andonov, A., R. Bauer, and M. Cremers, 2013. “Pension Fund Asset Allocation and Liability Discount Rates: Camouflage and Reckless Risk Taking by U.S. Public Plans?” SSRN Working Paper.
- Bank for International Settlements, Financial Stability Board, and International Monetary Fund, 2016, “Elements of Effective Macroprudential Policies: Lessons from International Experience”.
- Baba, N., R.N. McCauley, and S. Ramaswamy, 2009. “US dollar money market funds and non-US banks,” Bank for International Settlements Quarterly Review, 65–81. March 2009.
- Bengtsson, E., 2012. “Shadow banking and financial stability: European money market funds in the global financial crisis,” Journal of International Money and Finance, Vol. 32, 579–94.
- Billio, M., Getmansky, M., Lo, A. W., and Pelizzon, L., 2012. “Econometric measures of connectedness and systemic risk in the finance and insurance sectors,” Journal of Financial Economics, Vol. 104(3), 535-559.
- (Additional references are listed in the source document.)

### Appendix I. Inputs for implementation — overview
- Purpose: Implementation of SyRIN requires PoDs and total assets of entities and sectors under analysis.
- Dataset coverage: PoDs at the individual entity level (banks and insurance companies) and sectors (mutual funds, pension funds, and hedge funds).
- This appendix describes the method employed to estimate PoDs for each entity and sector.

### PoDs: Banks and Insurance Companies — method and coverage
- PoDs for banks and insurance companies are estimated using CDS spreads, following Segoviano and Goodhart (2009).
- Recovery rate assumption: R = 40 percent.
- PoD formula as presented in source:
  1
  t
  t
  C D S
  P oD
  R
  
  
  .
- CDS data: five-year CDS spreads from CMA retrieved through Datastream (or Bloomberg). (Footnote 49)
- Entities included:
  - Banking: Bank of America, Capital One Financial, Citigroup, Goldman Sachs, JPMorgan, Morgan Stanley, and Wells Fargo.
    - Coverage: These entities cover approximately 67 percent of total US banks’ assets.
  - Insurance: AIG, Allstate, Berkshire Hathaway, Hartford Financial Services, MetLife, Prudential, and Travelers Companies.
    - Coverage: These entities cover approximately 50 percent of total U.S. insurance sector assets.

### PoDs: Investment Funds — VaR-based approach (steps)
- Approach: VaR approach — estimate distribution of asset returns for each fund type and define a threshold related to periods of significant outflows. PoD is probability returns fall below that threshold.
- Steps:
  1. Compile daily stock price: P_t
  2. Compute daily stock price return: r_t = log(P_t) – log(P_{t-1})
  3. Standardize r_t by subtracting full sample mean ݎ̅ and dividing by full sample standard deviation σ.
  4. Standardized returns are given by: ݎ_{t}^{σ} = (r_t - ݎ̅) / σ  (as presented in source formatting)
  5. Compute distress threshold for the full-time series such that 1 percent of returns fall below this threshold (analogous to 99 percent VaR and consistent with periods of high outflows).
     - Re-order ݎ_{t}^{σ} series in ascending order—lowest to highest; i.e. ݎ_{(1)}^{σ}, … .
     - Delineate the 1st percentile of the ݎ_{(·)}^{σ} series. Call this γ.
  6. Compute time series of PoDs:
     - For each point in time r_t^{σ}—compute rolling sample mean and standard deviation for six months prior (trailing window).
     - Using these sample moments for r_t^{σ} and assuming a Normal distribution—at each point in time compute the probability that returns fall below γ.
- Notes on returns estimation:
  - Returns can be estimated using mark-to-market asset value data.
  - If data presentation requires, adjust by redemptions and subscriptions so returns reflect impact of price changes.
  - If mark-to-market data are not available, proxy by reconstructing funds’ asset portfolios and estimating market value based on individual asset prices.

### Appendix Table 1. Input series for portfolio reconstruction (fund-type mappings)
- Equity funds:
  - Portfolio: 75% MSCI US index, 25% MSCI World index. Weights derived from ICI data.
  - Ticker: MSUSAM$ (US), MSWRLD$ (World)
  - Field: MSRI
- Bond funds (including HY and IG):
  - Indices: BofA Merrill Lynch US Corporate & Government Index, BofA Merrill Lynch US High Yield Index, and BofA Merrill Lynch US Corporate Index (Investment Grade)
  - Ticker: B0A0, C0A0 (Investment Grade), and H0A0 (High Yield)
  - Field: ML: RIUSD (Price), ML: OAS (Spread)
- MMF (Money Market Funds):
  - Portfolio weights: 40% 3M Certificate of Deposits, 20% O/N repo, 20% 3M Commercial Paper, 10% Asset-Backed Commercial Paper, and 10% T-Bills
  - Ticker: FRCDW3M (CDs), USORGCP (O/N repo), FRCPN3M (CP), USCPA3M (ABCP), and FRTBS3M (T-Bills)
  - Field: Price (Yield)
- Pension funds:
  - Portfolio: 50% domestic equities (MSCI US index), 25% foreign equities (MSCI World index), and 25% bonds (BofA Merrill Lynch US Corporate & Government Index). Weights derived from ICI data [1].
  - Ticker: MSUSAM$ (US), MSWRLD$ (World), and B0A0
  - Fields: MSRI, ML: RIUSD (Price), ML: OAS (Spread)
- Hedge funds:
  - Index: HFR index
  - Ticker: HFRXHF$
  - Field: RI

### Data on total assets per sector — sources and aggregation
- Bank and insurance sector data source: US Flow of Funds (FoF).
- Fund-type data (equity, bond funds, and MMFs): ICI.
- Size of each fund: estimated by applying relative weights derived from ICI to the FoF data.
- Frequency and retrieval:
  - Data retrieved using Datastream or Bloomberg at a quarterly frequency.
  - When data are annual, a linear interpolation to obtain quarterly data is used.
- Hedge funds (HF): use Barclayhedge data on global HF and apply a 75 percent weight for the US, where the weight is derived from the 2013 IOSCO survey. (Footnotes 50, 51)
- Appendix Table 2. Input series for total asset data (selected entries)
  - Banks: Private depository institutions (Table L.109) — Ticker US70PDTAA
  - Insurance: Life insurance (L.115) + other insurance Corporations (L.114) — Ticker US54XXXAA, US51XXXAA
  - Equity funds: ICI—all equity funds — Ticker USFANEQ.A
  - Bond funds (incl. HY and IG): ICI—All bond and income funds TNA — Ticker USFANBI.A
    - IG and HY bond funds are a subset of bond funds; relative shares derived using ICI yearly figures.
  - MMF: ICI MMFs TNA — Ticker USFANMM.A
  - Pension funds: Private and public pension funds (L.116) — Ticker US59TOFAA
  - Hedge funds: AuM of hedge funds—weight 75% — Ticker Barclayhedge website
- Notes:
  - [1] http://www.ici.org/research/stats/retirement
  - [2] TNA refers to total net assets.
  - [3] We used Table 4, available at http://www.icifactbook.org/2013/fb_data.html#section5.

*Source: wp1814 - REFERENCES (IMF PDF).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp1814.pdf_