Motivation

• Macroprudential policy setting faces the challenge of identifying growth of financial and macroeconomic variables above and below potential.

• The gaps between actual performance and potential are crucial for policy makers but are unobserved. This is especially true for financial variables such as capital and risk of default of borrowers and lenders.

• The global financial crisis has highlighted the importance of monitoring both balance sheets of borrowers and lenders as well as the relevance of risk and uncertainty shocks as driver of the business cycle.

• If for example capital is too low and default risk is too high, policy makers could seek policies to increase the capital base of agents or to decrease debt.

• The question arises of how to quantify capital needs and risks associated to borrowers’ and lenders’ balance sheets and determine capital and risk gaps e.g., deviations of capital and risk from potential that can be used by policy makers to calibrate macroprudential tools.

Contribution

9. Against this backdrop, a macrofinancial structural model is presented that captures (i) sectoral dynamics of nonfinancial firms and financial intermediaries and feedbacks between them, (ii) default risk in each sector, (iii) capital and risk gaps, and it provides (iv) a quantitative method for measurement.

• Sectoral dynamics. The model simulates the joint balance sheet dynamics of borrowers (nonfinancial firms) and lenders (financial intermediaries). Balance sheet strength of borrowers crucially impacts balance sheet strength of lenders, and vice versa.

• Risk. The model differentiates between two types of risk originating from variation in borrowers’ asset returns: nonfinancial firm cross-sectional variation in asset returns (idiosyncratic risk), and aggregate variance in asset returns (aggregate risk). As shown below, idiosyncratic risk can be measured by default risk of nonfinancial firms derived from corporate credit spreads; aggregate risk can be measured by default risk of financial intermediaries derived from financial credit spreads.

• Gaps. The framework measures capital and risk gaps that may arise at borrowers or at lenders and are closely linked.

• Measurement. A quantitative method is provided to measure gaps in a theoretically sound framework.

Literature Review

10. The model is based on Christiano, Motto and Rostagno (2014) who focus on the balance sheet dynamics of firms and firm default. They show that variations in idiosyncratic risk are an important driver for business cycle fluctuations.

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Literature Review

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Source: IMF staff.

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11. The framework is extended with defaulting financial intermediaries, and financial intermediary debt investors. Aggregate risk is an important driver of the probability of default of financial intermediaries. In comparison to existing models with financial intermediary or bank default, default is due to aggregate risk.

12. Both frameworks follow the financial accelerator literature in that capital is accumulated mostly out of retained earnings, implying that capital is sticky. In addition, welfare-maximizing capital and risk measures are calculated that result from the optimal trade-off of the tax-benefits of debt and the cost of default and serve as a benchmark for the performance of the economy and the financial system and allow to quantify capital and risk gaps.

Core of the Model

15. The core of the model builds a standard real business cycle model (RBC model) with exogenous government spending and investment adjustment cost. It has four macroeconomic shocks: total factor productivity, government spending, investment efficiency, and labor market tightening (disutility of labor). The core of the model is augmented with a financial system.

The Financial System

16. The financial system comprises three set of agents: nonfinancial firms, financial intermediaries, and financial investors, ultimately households.

17. Financial intermediaries use own funds and funds raised from financial investors in the form of deposits and whole-sale funding to issue loans. Nonfinancial firms use the proceeds from the loans together with own funds to acquire productive assets.

• Funding constraints of nonfinancial firms and financial intermediaries:

  $$\begin{array}{cc}{q}_t{k}_t=n_t^F+b_t& b_t=n_t^B+d_t\end{array}$$

18. The acquisition of assets of nonfinancial firms gives rise to two financial shocks, as described in the following: cross-sectional return-on-asset variance of nonfinancial firms (idiosyncratic risk), and aggregate return-on-asset variance of nonfinancial firms (aggregate risk).

Nonfinancial Firms, Firm Default, and Probability of Default

19. The cashflow of nonfinancial firms consist of an initial outlay of own funds. Next period nonfinancial firms receive a return on invested assets and pay back debt. The return on assets is subject to an idiosyncratic and aggregate productivity shock. Firms’ income is taxed, and future cash-flows are discounted at a stochastic discount factor.

• Expected cashflow of nonfinancial firms:

  $E_t[-n_t^F+M_{t+1}[\max (z_{t+1}{\epsilon }_{i,t+1}{R}_{k,t+1}{k}_t-R_{b,t}{b}_t)(1-\tau ),0\left]\right]$

20. Nonfinancial firms default if the value of end-of-period assets falls below the value of liabilities, or if its idiosyncratic productivity falls below a certain default threshold.

• Nonfinancial firm default:

  $${\epsilon }_{i,t+1}<{\epsilon }_{t+1}^Z\equiv \frac{R_{b,t}{b}_t}{{}^{z_{t+1}{R}_{k,t+1}{k}_t}}$$

21. The probability of default of nonfinancial firms depends on firms’ balance sheet strength, aggregate productivity, and the cumulative distribution function of idiosyncratic productivity.

• Model-based through-the-cycle PD:

  $$P{D}^F\left({\epsilon }_{t+1}^z\right)=\mathrm{Pr}ob({\epsilon }_{i,t+1}<{\epsilon }_{t+1}^z)=F({\epsilon }_{t+1}^z,{\sigma }_{\epsilon ,t+1})$$

Financial Intermediaries, Intermediary Default and Probability of Default

22. The cashflow of financial intermediaries consist of an initial outlay of own funds. Next period financial intermediaries receive a return on the loan portfolio and pay back received funding. Income is taxed.

• Expected cashflow of financial intermediaries:

  $E_t[-n_t^B+M_{t+1}[\max (R_{B,t+1}{b}_t-R_{d,t}{d}_t)(1-\tau ),0\left]\right]$

23. The return on the loan portfolio consists of two parts. Financial intermediaries receive the interest and principal payment from non-defaulting firms and recover the assets from defaulted firms. Default is subject to screening cost.

• Return on loan portfolio at time t+1:

  $$R_{b,t}{b}_t(1-PD({\epsilon }_{t+1}^z\left)\right)+\underset{0}{\overset{{\epsilon }_{t+1}^z}{{\displaystyle \int }}}{\epsilon }_{i,t+1}{z}_{t+1}{R}_{k,t+1}{k}_{t+1}(1-\mu )dF-R_{d,t}{d}_t$$

24. The expression can be rewritten to receive model-based loss-given default (LGD) and expected losses.

• Model-based expected loss and LGD:

  $$\begin{array}{c}{B}_t(1-PD({\epsilon }_{t+1}^z\left)LGD\right({\epsilon }_{t+1}^z\left)\right)-D_t\\ \begin{array}{cc}{B}_t\equiv R_{b,t}{b}_t& D_t\equiv R_{d,t}{d}_t\end{array}\end{array}$$

• Model-based loss rate:

  $l_{t+1}=PD\left({\epsilon }_{t+1}^Z\right)LGD\left({\epsilon }_{t+1}^Z\right)$

25. Financial intermediaries default if the value of end-of-period assets falls below the value of liabilities, or if aggregate productivity falls below a certain default threshold. Hence, the probability of default of financial intermediaries depends on balance sheet strength of borrowers and financial intermediaries and the distribution function of aggregate productivity. For simplicity it is assumed that aggregate productivity takes a fixed value above and below the default threshold.

• PD of FIs depends on borrower and bank balance sheet strength and aggregate risk

  $P{D}^B\left(z_{t+1}^{*}\right)=\mathrm{Pr}ob(z_{t+1}<z_{t+1}^{*})={\pi }^D(z_{t+1}^{*},{\sigma }_{z,t+1})$

• Default threshold:

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Financial Investors

26. Financial investors (or mutual funds) hold the equity in nonfinancial firms and financial intermediaries and provide funding in the form of deposits and wholesale funding to financial intermediaries. Financial investors receive funding in case the financial intermediary doesn’t default and receive the assets of intermediaries in case of default.

• Expected cashflow of financial investors:

  $$E_t\lfloor -d_t+M_{t+1}\lfloor D_t(1-{\pi }^D\left(z_{t+1}^{*}\right))+{\pi }^D\left(z_{t+1}^{*}\right)B_t(1-l\left({\epsilon }_{t+1}^D\right))(1-{\mu }_B)\rfloor \rfloor$$

Capital Accumulation and Agents’ Optimization

27. Nonfinancial firms and financial intermediaries accumulate capital out of retained earnings, according to an exogenously given law of motion (below; derivation see Appendix I). A constant fraction of earnings is distributed as dividends, while the remainder is retained, as in the standard financial accelerator literature as in Bernanke, Gertler and Gilchrist (1999).⁴

28. Given the model set-up, the model solution is found by letting nonfinancial firms maximize their cashflow, taking the cashflows of financial intermediaries and financial investors as given, assuming both make zero profits.

29. Given an initial capital position, nonfinancial firms scale up their balance sheets (by scaling up financial-intermediaries balance sheet) financed through liabilities to maximize future profits.

30. The optimal lending rate and financial intermediaries’ cost-of-funding is determined by the trade-off between the cost-of-default and tax-benefits of debt. Consequently, nonfinancial firms maximize with respect to three choice variables: financial intermediaries’ funding and hence nonfinancial firms’ liabilities, lending rates, and financial intermediaries’ cost-of-funding.

Financial Frictions and Optimality

31. There are three financial frictions in the model:

• Income of nonfinancial firms and financial intermediaries is tax-deductible, while income of financial investors is not (see cashflows). So, more intermediated funding between financial intermediaries and financial investors results in a tax-benefit. This is called “the benefit of financial intermediation”.

• Defaults of nonfinancial corporates trigger a screening cost.

  • i. The optimal lending rate is determined trading off the benefit of financial intermediation associated to non-defaulting loans versus the cost of default.

• Defaults of financial intermediaries result in lower productivity.

  • i. Financial intermediaries’ cost-of-funding is determined by trading off the benefit of financial intermediation associated with more funding versus the productivity loss in case of default.

The Capital Gaps

32. In the model, capital is sticky, and capital is accumulated out of retained earnings, as in Christiano, Motto and Rostagno (2014). Nonfinancial firms have three choice variables.

33. In comparison to the model solution, the optimal welfare-maximizing optimal solution can be calculated, assuming a flexible capital structure and solving also for the optimal level of capital of nonfinancial firms and financial intermediaries. This maximization problem has five choice variables–two more than the model solution.

• Optimal capitalization:

  $$\max E_t[-{\lambda }_t{n}_t^F+\beta {\lambda }_{t+1}\left[\max \right(z_{t+1}{\epsilon }_{i,t+1}{R}_{k,t+1}{k}_t-R_{b,t}{b}_t)(1-\tau ),0]]\{d_t,R_{d,t},R_{b,t},n_t^F,n_t^B\}Subjectto:$$

• Funding constraints of entrepreneurs and banks:

  $$\begin{array}{cc}{q}_t{k}_t=n_t^F+b_t& b_t=n_t^B+d_t\end{array}$$

• FI participation and FI capital constraint:

  $\begin{array}{c}{E}_t[-{\lambda }_t{n}_t^B+\beta {\lambda }_{t+1}\left[\max \left(B_t\right(1-PD\left({\epsilon }_{t+1}^Z\right)LGD\left({\epsilon }_{t+1}^Z\right))-D_t(1-\tau )\right]],0\ge 0\\ B_t(1-PD({ℰ}_{t+1}^{*}\left)LGD\right({ℰ}_{t+1}^{*}\left)\right)-D_t\ge 0\end{array}$

• Wholesale FI debt investor participation constraint:

  $E_t[-{\lambda }_t{d}_t+\beta {\lambda }_{t+1}[D_t(1-{\pi }^D(z_{t+1}^{*}\left)\right)+{\pi }^D\left(z_{t+1}^{*}\right)B_t(1-l({\epsilon }_{t+1}^D\left)\right)(1-{\mu }_B)\left]\right]\ge 0$

• Default thresholds:

  $\begin{array}{ccc}{\epsilon }_{t+1}^N\equiv \frac{R_{b,t},b_t}{z^N{R}_{k,t+1}{k}_t}& {\epsilon }_{t+1}^{*}\equiv \frac{R_{b,t}{b}_t}{Z_{t+1}^{*}{R}_{k,t+1}{k}_t}& {\epsilon }_{t+1}^D\equiv \frac{R_{b,t},b_t}{z^D{R}_{k,t+1}{k}_t}\end{array}$

34. The difference between welfare maximizing optimal capital and own capital accumulated out of retained earnings, provides the deviation from potential, the capital gaps. So, similar to the well-known concept in monetary policy of output gap between sticky and flexible prices, the capital gaps between sticky and flexible capital are calculated.

Deviation of Risk from Potential: Risk Gaps

35. Deviations of capital from potential imply deviations of risk from potential, both nonfinancial firm default risk and financial intermediary default risk.

36. The solution of the model with capital accumulated out of retained earnings can be compared to the solution of the model with optimal capital. The comparison allows to determine deviations from potential of capital, default risk, lending, and funding. The deviations from potential provide signals for policy makers when to tighten or loosen macroprudential policies.

Default Risk Dynamics

41. Figures 2 and 3 show the demeaned probability of default of the firm and of the banking sector (the black line). Default risk spiked during the 2009 Global Financial Crisis and during the 2012 European Sovereign Debt Crisis. According to the model, default risk is currently low, as credit spreads are low.

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France: Corporate Probability of Default

(quarterly; demeaned)

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Note: The figure shows the demeaned probability of default of the corporate sector. The x-axis denotes the year. The y-axis denotes percentages (0.01 equals to 1 percent).Source: IMF staff calculations.

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France: Banking Sector Probability of Default

(quarterly; demeaned)

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Note: The figure shows the demeaned probability of default of the banking sector. The x-axis denotes the year. The y-axis denotes percentages (0.01 equals to 1 percent).Source: IMF staff calculations.

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42. The shock decomposition reveals what shocks are driving default probabilities. The three most important shocks are cross-sectional, idiosyncratic risk shocks (represented by the yellow bars ‘eF’), aggregate risk shocks (light blue bars ‘eB’), and productivity shocks (blue bars ‘ey’). Corporate default risk is driven to a significant extent by cross-sectional, idiosyncratic risk. Banking default risk is mostly driven by aggregate risk.

Risk Gaps

43. Figures 4 and 5 show the deviations of the probability of default from the welfare-maximizing optimum. Risk fluctuates during time between being too high and too low. Risk is too high (when the risk gap reaches positive territory) during four episodes: prior to the Technology Crisis, prior to the Global Financial Crisis, prior to the Sovereign Debt Crisis, and now. Default risk in the corporate sector was particularly elevated during the 2002 Technology Crisis, and now, although it is now low in absolute terms. Default risk of the banking sector was particularly elevated during the Global Financial Crisis and appears now adequate.

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France: Corporate Risk Gap

(Corporate PD–Optimal PD)

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Note: The figure shows the gap of default risk of the nonfinancial corporate sector. The x-axis denotes the year. The y-axis denotes percentages (0.005 equals to 0.5 percent excessive default risk in absolute terms).Source: IMF staff calculations.

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France: Banking Risk Gap

(Bank PD–Optimal PD)

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Note: The figure shows the gap of default risk of the banking sector. The x-axis denotes the year. The y-axis denotes percentages (0.005 equals to 0.5 percent excessive default risk in absolute terms).Source: IMF staff calculations.

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Capital Gaps

44. Figures 6 and 7 show the deviations of firm capital and banking capital from the welfare maximizing optimum in percentage deviations. Again, four episodes stand out where more corporate capital is needed marked by a positive gap: prior to the Technology Crisis, prior to the Global Financial Crisis, prior to the Sovereign Debt Crisis, and now. Bank capital was too low during the Global Financial Crisis and the Sovereign Debt Crisis and appears now to be adequate.

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France: Corporate Capital Gap

((Optimal Capital–Corporate Capital)/Corporate Capital)

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Note: The figure shows the gap of aggregate capital of the nonfinancial corporate sector. The x-axis denotes the year. The y-axis denotes percentages (0.05 equals to a 5 percent gap relative to the total market cap).Source: IMF staff calculations.

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France: Banking Capital Gap

((Optimal Cap–Bank Cap)/Bank Cap)

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Note: The figure shows the gap of aggregate capital of the banking sector. The x-axis denotes the year. The y-axis denotes percentages (0.2 equals to a 20 percent gap relative to the nominal amount of aggregate capital).Source: IMF staff calculations.

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Scenario Generation

45. During the historical period, the worst downturn was during the Global Financial Crisis. Consequently, the stress test asks what the effect of the Global Financial Crisis on the French economy would be today. For this, the structural shocks were reconstructed from the historical time series. The shocks of the Global Financial Crisis during 2008–2011 were applied now to simulate the macro stress test between 2018–2021.

Stress Test Results

46. The stress tests show that bank capital is about adequate, while more corporate capital is needed under adverse conditions. Firms a more vulnerable than banks at the current juncture. Nevertheless, corporate and banking risk gaps are elevated under adverse conditions. The corporate risk gap reaches unprecedented highs, while the bank risk gap is considerably lower than during the Global Financial Crisis, if stress intensifies. Figure 8 shows the results of the macro stress test.

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France: Gap Analysis of Default Risk and Capital of Nonfinancial Corporates and Banks, and Macro Stress Test

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Note: The figure shows gaps of default risk and aggregate capital of the nonfinancial corporate sector and the banking sector. The x-axis denotes the year. The y-axis denotes percentages (in the case of risk 0.005 equals to 0.5 percent excessive default risk in absolute terms; in the case of capital 0.2 equals to a 20 percent gap relative to the nominal amount of aggregate capital). The grey bars highlight recession periods of France’s economy. The dotted red line simulates a crisis period that is in magnitude like the Global Financial Crisis.Source: IMF staff calculations.

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Coverage

61. The interconnectedness analysis uses data compiled for the HCSF on contagion. The HCSF has initiated a long-term work agenda on cross-sector contagion. The first step of this effort has been the creation of a dataset on bilateral exposures in marketable securities across sectors, compiled originally in Benhami et al. (2018). The data collection remains a work in progress; exposures between banks and insurance companies are missing, as are exposures beyond marketable securities. The authorities plan to expand⁹ and exploit this data in a model to assess shock propagation through interconnectedness.¹⁰ The data cover exposures in marketable securities held by French-domiciled banks, insurance companies, and funds. Marketable securities include debt, equity, and fund shares.

62. The data used in the cross-border assessment are collected unilaterally and reflect the complete exposures in marketable securities for banks, insurance companies, and funds. For banks, holdings data are collected from the Production de statistiques de titres en détention (PROTIDE), listing securities held by individual entities. For insurance companies, holdings data are collected from the Tableau complémentaire aux éléments de placements (TCEP) in Solvency I and Solvency II reporting, listing securities holdings for individual entities; a structural break with the implementation of Solvency II in January 2016 creates qualifiers for interpreting the data. Finally, for funds, data on the investment portfolios of French collective investment undertakings (CIU) are collected by the BdF at a security level. These data thus represent both domestic and cross-border positions in marketable securities for the French financial system. Data are provided annually for banks (2008–2017) and insurance companies (2011–2017) and quarterly for funds (2008–2017).

63. The data used in the domestic assessment represent bilateral exposures in marketable securities to and from French-domiciled funds. The data used in the cross-sector interconnectedness assessment constitute a subset of the data used in the cross-border assessment. The distinction arises from the effort to create a dataset of bilateral exposures in marketable securities between French-domiciled financial institutions using data from reported asset holdings. On the asset side, the data provide funds’ domestic holdings with respect to banks and insurance companies. On the liabilities side, the data show all financial domestic holders of French-domiciled funds’ shares, which are compiled from banks’ and insurance companies’ reported holdings. Data are provided annually between 2010–2016.

64. While the unilateral dataset captures a larger share of exposures, the bilateral dataset provides deeper granularity for domestic exposures. The unilateral dataset coverage relative to total assets is 10.5 percent for banks, 92.7 percent for insurers, and 96.3 percent for funds. The coverage of the bilateral dataset is much smaller at 2.2 percent for banks, 29.8 percent for insurers, and 25.7 percent for funds,¹¹ but has the benefit of showing party-to-party exposures. Overall, the unilateral dataset covers EUR 4.8 trillion in assets (of which EUR 1.1 trillion to French financial entities), while the bilateral dataset covers EUR 835 billion in assets between French financial entities.

Gaps

65. In the bilateral dataset, exposures in marketable securities between banks and insurers are not readily accessible. Also missing are exposures in instruments other than marketable securities for all types of financial entities in the unilateral and bilateral datasets. The partial completeness of the data means that interconnectedness may be understated, primarily along two dimensions. First, domestic interbank exposures across all instruments are missing; marketable securities of other French banks constitute 1.6 percent of total assets, but exposure through interbank loans is much higher at 31 percent of total assets.¹² Second, bilateral exposures between banks and insurance companies are missing; insurers hold 11 percent of their balance sheet in securities issued by French banks.

66. While the first omission is related to third-party access, the second omission relates to the stage of completion of the HCSF’s work agenda.¹³ The cross-border interbank contagion analysis uses loans to capture a missing dimension of interconnectedness for banks. Also, a closer examination of trends within and across financial groups would have necessitated information on which entity-level banks, insurers, and funds (or asset managers) form part of a specific financial group. This remains work in progress, so information on financial group membership was not available for this analysis.

Direct Exposures in Cross-border Marketable Securities

67. Total exposures in marketable securities across banks, insurance companies, and funds stand at EUR 4.8 trillion, an increase of 27 percent since 2011. Insurance companies and funds have dramatically increased their total exposures since the Euro Area crisis, while banks’ total exposures have declined slightly. In 2017, total exposures for insurance companies have increased to EUR 2.4 trillion (+36 percent since 2011), decreased to EUR 896 billion (-12 percent since 2011) for banks, and increased to EUR 1.5 trillion (+30 percent since 2011) for funds.

68. Cross-border exposures in marketable securities have increased in aggregate since the last FSAP but not proportionally to domestic exposures overall due to sector trends. Insurers and funds have increased cross-border exposures to EUR 1.15 trillion and EUR 784 billion in 2017 (+25 percent and +47 percent since 2011). As a share of total exposures in marketable securities, however, cross-border exposures for insurers and funds account for 49 percent and 52 percent in 2017 (-2 percent and +8 percent since 2011).¹⁴ Banks drastically reduced their cross-border marketable securities holdings in the aftermath of successive crises in 2008 and 2010 in favor of domestic alternatives. While cross-border exposures for banks have been reduced to EUR 375 million in 2017 (-39 percent since 2011), this has been offset by a proportional increase in domestic exposures; since 2011, cross-border exposures continue to comprise a steady share of 42 percent of all marketable securities holdings.¹⁵

69. French financial entities maintain a global presence but are most heavily invested in the Euro Area, the United States, and the United Kingdom. Banks, insurers, and funds have a comparable geographic footprint, maintaining diversified exposures around the globe but focused in a few markets (see Figure 10). Since 2012, changes have largely been proportional at the country level.

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France: Composition of Exposures in the Unilateral Dataset

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Source: Haut Conseil de Stabilité Financière (HCSF).

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France: Direct Cross-border Exposures of French Financial Entities

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Note: Units are in EUR billion.Source: Haut Conseil de Stabilité Financière (HCSF).

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France: Direct Cross-border Exposure Network Properties in Unilateral Dataset

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Source: Haut Conseil de Stabilité Financière (HCSF).

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France: Significant Trends in Cross-border Common Exposure

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff calculations.

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France: Composition of Domestic Exposures in the Bilateral Dataset

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Source: Haut Conseil de Stabilité Financière (HCSF).

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France: Network Visualization of Cross-sector Exposures

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Note: Only exposures over 1 billion EUR shown.Source: Haut Conseil de Stabilité Financière (HCSF).

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France: Direct Exposure Network Properties in Bilateral Dataset

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Source: Haut Conseil de Stabilité Financière (HCSF).

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France: Significant Trends in Domestic Common Exposures

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

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France: Common Exposures in Assets Relative to the Average Domestic Portfolio

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

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70. At the country-sector level, trends in domestic and cross-border exposures for banks, insurers, and funds imply a shifting composition (see Figure 9). Changes in the composition of French financial institutions’ holdings are evident from Figure 17. Broadly, there has been a significant shift toward domestic and foreign NFCs across banks, insurers, and funds. Banks’ domestic exposures to the French government form the most substantial individual exposure, while exposure to domestic nonbank financials has been steadily increasing. Insurance companies have significantly increased exposures to the French government but also to nonbank financials. Insurers’ cross-border exposures are concentrated in monetary financial institutions (MFIs) and NFCs. Funds’ overall declining exposures to domestic MFIs since 2011 has been offset by increased exposure to NFCs and other French funds. The fastest-growing exposures for funds, however, have been to foreign non-MFIs and NFCs.

71. Exposures are predominantly comprised of debt securities. Banks hold most of their domestic and cross-border exposures in debt securities; 80 percent for domestic positions and 69 percent for cross-border positions. Similarly, insurance companies’ exposures are primarily in debt securities (76 percent for domestic and 72 percent for cross-border securities), but domestic exposures in equity have increased since 2015.¹⁶ Finally, funds hold mostly debt securities domestically and abroad. Since 2012, funds have invested increasingly in domestic equities and other domestic funds, so that the domestic positions are evenly split between debt (33 percent), equity (33 percent), and fund shares (34 percent). Abroad, French funds are primarily invested in debt securities (55 percent), followed by equity (33 percent) and foreign fund shares (12 percent).

72. The direct exposure network properties further reflect the evolving composition of cross-border exposures at the country-sector level. Examining the network of exposures of French financial entities to country-sector counterparties lends further support to the narrative of changing composition. The number of counterparties (vertices) for banks has remained relatively constant, while the number of connections (edges) has declined (Figure 11). This indicates that fewer banks are invested in cross-border counterparties in 2017, coinciding with the reduced aggregate cross-border positions. With fewer connections and a similar number of country-sector counterparties, heterogeneity in cross-border exposures for banks, prima facie, is relatively higher; international banks have drawn down cross-border positions while maintaining counterparties, while smaller banks have withdrawn from exposures to cross-border counterparties. For insurance companies and funds, increased aggregate cross-border positions have coincided with a larger number of counterparties and connections, suggesting increased individual diversification. To the extent that a greater number of insurers and fund sectors are holding similar exposures that diversify away idiosyncratic risk, however, it is not immediately clear whether aggregate risk is increasing as a result. Common exposures are subsequently examined in greater detail to ascertain whether French financial entities are subject to similar risks from their holdings of marketable securities.

Common Exposures in Cross-border Marketable Securities

73. An assessment of risks stemming from common exposures in assets requires a more careful examination of direct exposures. The previous section summarized the properties of the unilateral datasets and the resulting direct networks for banks, insurers, and funds. Common exposure networks are helpful to determine whether a subset of financial entities is susceptible to similar market risks stemming from their cross-border holdings of marketable securities. Whereas direct exposure networks represent exposures in physical assets and liabilities, common exposure networks represent exposures in terms of composition similarity in portfolios of assets and liabilities.¹⁷

74. The common exposure analysis examines the similarity in the composition of French financial entities’ portfolios. The methodology in Giudici , Sarlin and Spelta (2017) uses a linear transformation of distance to define the similarity between portfolio vectors, which the authors call out-flow common exposure for assets and in-flow common exposure for liabilities.¹⁸ There is a one-to-one correspondence between the correlation of two vectors and distance; we favor the use of distance because the objective is to identify clusters that are most similar.¹⁹ If two entities have a greater proportion of their asset portfolio invested in similar counterparties, the out-flow common exposure will be higher; equivalently, correlation will be higher, and distance will be lower. Larger exposures to similar counterparties relative to the rest of the portfolios will mean that entities are exposed to greater common risk. Given the unilateral nature of the datasets under consideration in this section, similarities only on the asset side are examined. The analysis is carried out for banks, insurers, and types of funds, where counterparties consist of cross-border exposures at the country-sector level. Significance can be assessed based on a t-test of the correlation coefficient.²⁰ For out-flow cross-border assets, significance is achieved at all conventional levels for every out-flow common exposure measure reported.

75. Common exposure risk for cross-border asset holdings is relatively high within the fund sector, as well as between banks and insurers. Table 1 characterizes common exposure risk using the methodology of Giudici, Sarlin and Spelta (2017). The out-flow common exposure between pairs of entities is shown below the diagonal, while a percent change since 2012 is shown above the diagonal. The out-flow common exposure is high between equity and mixed funds (1.32), bond and mixed funds (1.24), mixed and other funds (1.40), and equity and other funds (1.17), suggesting the presence of a cluster. Elsewhere, common exposures between insurers and banks and between insurers and mixed funds are relatively high (1.20 and 1.19), suggesting the presence of a second cluster. A final comment is that bond funds have highly significant overlap with every other sector. Common exposure indicates the extent to which portfolios overlap proportionally, so that if a shock affects one, it is likely to affect all.

Table 1.

France: Common Exposures in Cross-Border Assets

Note: The lower triangle shows out-flow (asset) common exposure between two sectors for 2017; this is scaled between 0 and 2. A higher value indicates higher similarity in exposures. The upper triangle shows the percent change since 2012. See Appendix III for further details. Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

Table 1.

France: Common Exposures in Cross-Border Assets

Note: The lower triangle shows out-flow (asset) common exposure between two sectors for 2017; this is scaled between 0 and 2. A higher value indicates higher similarity in exposures. The upper triangle shows the percent change since 2012. See Appendix III for further details. Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

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Table 1.

France: Common Exposures in Cross-Border Assets

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Note: The lower triangle shows out-flow (asset) common exposure between two sectors for 2017; this is scaled between 0 and 2. A higher value indicates higher similarity in exposures. The upper triangle shows the percent change since 2012. See Appendix III for further details. Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

76. Fund sectors may have individually diversified direct exposures, but the funds industry overall is susceptible to elevated aggregate risk through common cross-border exposures. While examining direct exposures, we found that funds had increased cross-border exposures overall, resulting in a network with more vertices and edges; this suggested that perhaps individually, fund sectors were diversifying idiosyncratic counterparty risk. By assessing the similarity in portfolio composition, however, we find that any potential individual diversification by fund sector has also led to increased aggregate risk for the funds industry; increasingly, fund sectors are investing in the same country-sector counterparties, forming a cluster of common exposure.

77. Despite declining cross-border exposures for banks and increasing cross-border exposures for insurers, common exposure is also elevated. Banks and insurers have displayed opposite tendencies in direct cross-border exposures. Nonetheless, there is significant portfolio overlap at the country-sector level, so that both are susceptible to similar shocks. If domestic exposures from the unilateral dataset are also considered, common exposure for banks and insurers rises to 1.46, driven by the shift in portfolio composition of insurers toward French government bonds.

78. Some recent trends in cross-border common exposures must be monitored. Figure 12 shows the evolution between pairs of entities with significant common exposures trending upward in recent years. While generally not higher than in 2012 (as indicated above the diagonal in Table 1), common exposure in all pairs has been increasing since 2015. Particularly, a cluster of common exposure is being formed between equity, bond, mixed, and other funds. Insurers are on the periphery of this cluster through their common exposure with mixed funds, while banks are connected through common exposure with insurers. Since 2015, the strength of these relationships has been increasing, suggesting that shocks affecting the cited fund sectors will also impact insurers. Banks are more likely to be affected by shocks that are common only to insurers.

Direct Exposures in Domestic Marketable Securities

79. The bilateral dataset provides unique insight into direct exposures across sectors, but careful interpretation is necessary. Total domestic exposures in marketable securities held by domestic financial entities stand at EUR 1.1 trillion. The bilateral reporting dataset covers EUR 835 billion of assets at a greater granularity, for instance by showing party-to-party holdings even for funds. The lower coverage of total assets is primarily due to the omission of insurance companies’ exposure to marketable securities issued by banks.

80. Funds are connected to insurance companies through liabilities and to banks through assets. Domestic exposures in the bilateral dataset are dominated by insurance companies holding fund shares issued primarily by mixed and money market funds (Figures 13 and 14). Banks’ relatively low positions reflect the nature of the data, in the sense that marketable securities comprise a much smaller proportion of banks’ balance sheets relative to insurance companies and funds. However, a significant portion of funds’ domestic holdings in marketable securities is comprised of debt issued by banks.

81. While aggregate exposures are increasing, there is greater consolidation among counterparties. The first panel in Figure 15 shows the number of vertices and edges, representing the total number of counterparties and direct exposures, respectively. The number of vertices has been steadily declining throughout the entire sample, indicating a lower number of counterparties with exposures in assets and liabilities. The number of edges has also been steadily declining. Taken jointly with increased domestic exposures, this suggests consolidation and increased interconnectedness between funds and the rest of the financial system.

82. The domestic network has become slightly less sparse, and therefore more interconnected. The second panel in Figure 15 shows the density of the network and the average distance. The density of a network is the ratio of edges relative to the total number of possible edges that would arise if the graph were fully connected,²¹ while average distance measures the average number of edges along the shortest path between two vertices in a graph. The domestic network in 2017 is comprised of 9,670 funds, 132 banks, and 130 insurance companies, amounting to 9,932 vertices in total. From these vertices, there are a total of 61,348 edges representing an exposure from a bank or insurance company to a fund. With a density of 0.06 percent, the network is relatively sparse, although in line with the literature on financial networks. Additionally, the average distance is 3.24 and varies between 1 and 14, so that any two vertices are, on average, connected through 2 or 3 other vertices. The low density and average distance suggest that some financial entities are acting as hubs; that is, many financial entities form clusters through 2 or 3 other well-connected financial entities.

83. The network is clustered around a few well-connected banks and insurance companies and many sparsely-connected funds. The third panel of Figure 15 shows the cumulative degree density distribution for the network in 2008 and in 2017. The degree represents the number of inward- and outward-oriented edges connected to a vertex. The cumulative distribution shows that 75 percent of the probability mass is concentrated below 10 in 2017, indicating that 75 percent of all financial entities in the sample are connected to at most 10 other entities. Nonetheless, there exists a very small number of entities with more than 1000 links; these include three banks and six insurance companies. Over time, the distribution has shifted left so that the highly-connected entities are progressively less connected; alternatively, there are fewer highly-connected entities.

Common Exposures in Domestic Marketable Securities

84. A nuanced assessment of risks resulting from direct exposures requires an examination of common exposure. The results of the previous section indicated the presence of clusters around insurers (liabilities) and banks (assets) in the domestic network. Shifting focus from direct to common exposure, we can assess the extent to which overlapping portfolios may present an indirect risk. Interpretation of results are tempered by the low coverage of the bilateral dataset that includes 2.2 percent of banks’ total assets, 29.8 percent of insurers’ assets, and 25.7 percent of funds’ assets. The analysis is carried out for banks, insurers, and types of funds, where counterparties consist of domestic financial institutions. Significance can be assessed based on a t-test of the correlation coefficient, and a common exposure of 1.07 is significant at the 1 percent level.²²

85. On average, diversification of idiosyncratic risk does not lead to increased aggregate risk through common exposure. Figure 17 shows the out-flow common exposure relative to the average portfolio in the sample (red) and total direct exposure (blue). The average out-flow common exposure reaches low levels of significance for a subset of entities considered.

86. Common exposure in assets is high, however, between bond, other, and money market funds, as well as between banks, insurers, and mixed funds. Table 2 characterizes common exposure risk using the methodology of Giudici, Sarlin and Spelta (2017). The out-flow common exposure between pairs of entities is shown below the diagonal, while a percent change since 2012 is shown above the diagonal. Two clusters seem to exist. First, bond funds have significant common exposure with other funds (1.40) and with MMFs (1.40). Second, banks and insurers²³ have significant domestic common exposure (1.30), as well as with mixed funds (1.20 and 1.52). Thus, domestic portfolios within the fund industry display some overlap, though slightly different to the overlap observed for cross-border exposures, while banks and insurers display overlap in portfolios of both domestic and cross-border exposures.

Table 2.

France: Common Exposures in Domestic Assets

Notes: The lower triangle shows out-flow (asset) common exposure between two sectors for 2016; this is scaled between 0 and 2. A higher value indicates higher similarity in exposures. The upper triangle shows the percent change since 2011. See Appendix III for further details. Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

Table 2.

France: Common Exposures in Domestic Assets

Notes: The lower triangle shows out-flow (asset) common exposure between two sectors for 2016; this is scaled between 0 and 2. A higher value indicates higher similarity in exposures. The upper triangle shows the percent change since 2011. See Appendix III for further details. Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

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Table 2.

France: Common Exposures in Domestic Assets

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Notes: The lower triangle shows out-flow (asset) common exposure between two sectors for 2016; this is scaled between 0 and 2. A higher value indicates higher similarity in exposures. The upper triangle shows the percent change since 2011. See Appendix III for further details. Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

87. On the liabilities side, funds display significant common exposure. Figure 18 shows the in-flow common exposure with respect to the average portfolio in the sample (red) and total direct exposure (blue). For all funds except MMFs, common exposures have increased concurrently with direct exposures; not only are funds exposed to their counterparty, but they are also exposed to each other indirectly through common funding shocks. Table 3 shows the in-flow common exposure between pairs of entities below the diagonal, while a percent change since 2012 is shown above the diagonal. Here we see a cluster of common exposure forming for the entire fund industry, centered around mixed funds; that is, the funding composition of mixed funds overlaps most strongly with equity (1.77), bond (1.80), hedge (1.82), and other funds (1.76); MMFs exist on the periphery of this cluster, though significant funding overlap (1.40) is still evident. The difference is stark for banks and insurance companies that show no funding overlap with the rest of the financial system. The results here are likely dominated by the structure of the domestic dataset, where funds are connected through a few insurers on the liabilities side.

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France: Common Exposures in Liabilities Relative to the Average Domestic Portfolio

Citation: IMF Staff Country Reports 2019, 324; 10.5089/9781513517797.002.A001

Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

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Table 3.

France: Common Exposures in Domestic Liabilities

Notes: The lower triangle shows out-flow (asset) common exposure between two sectors for 2016; this is scaled between 0 and 2. A higher value indicates higher similarity in exposures. The upper triangle shows the percent change since 2011. See Appendix III for further details. Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

Table 3.

France: Common Exposures in Domestic Liabilities

Notes: The lower triangle shows out-flow (asset) common exposure between two sectors for 2016; this is scaled between 0 and 2. A higher value indicates higher similarity in exposures. The upper triangle shows the percent change since 2011. See Appendix III for further details. Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

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Table 3.

France: Common Exposures in Domestic Liabilities

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Notes: The lower triangle shows out-flow (asset) common exposure between two sectors for 2016; this is scaled between 0 and 2. A higher value indicates higher similarity in exposures. The upper triangle shows the percent change since 2011. See Appendix III for further details. Source: Haut Conseil de Stabilité Financière (HCSF) and IMF staff.

88. Some recent trends of out- and in-flow common exposure should be monitored. Figure 16 shows the evolution between pairs of entities with significant common exposures. Since 2013, both clusters identified previously by significant out-flow common exposure have shown an upward tendency, indicating that despite any potential diversification of idiosyncratic counterparty risk individually, the portfolios are increasingly overlapping. As well, the cluster identified by significant in-flow common exposure has been increasing in proximity of funding composition over the entire sample.

89. Results on domestic common exposures should be interpreted cautiously. The data do not cover significant balance sheet exposures for banks, so that the impact of high common exposure may not be very consequential. Additionally, the disaggregated nature of the data means that some of the results may be driven by the group ownership structure. Information on groups was not made available to the mission, but this is something that could be explored by the authorities.²⁴