EBA欧洲银行-Professional-Workshop-Tomiyuki-Kitamura_14页_739kb

Summary of Macro Stress Testing at the Bank of Japan

Objectives

The Bank of Japan (BoJ) conducts macro stress testing with two primary objectives:

1. Risk Identification and System Resilience Evaluation: To identify potential risks facing Japan's financial institutions and assess the resilience of the financial system against these risk factors.
2. Stability Communication: To facilitate communication with domestic and foreign stakeholders to ensure the stability of the financial system.

Scope and Publication

• The framework covers 371 banks, including:
  • 10 major banks (including Global Systemically Important Banks, or G-SIBs)
  • 105 regional banks
  • 256 shinkin banks (regional cooperative financial institutions)
• Aggregate-level results of the macro stress test are published semiannually in the Financial System Report (FSR).
• Scenario design and model changes are reported in the FSR annex series.
• Paths of main variables in the stress scenarios are made available on the BOJ website.
• Published macroeconomic series include:
  • Domestic GDP
  • International GDP
  • Stock prices
  • Nominal interest rates
  • Exchange rates

Main Features of the Models

• The stress testing is of a top-down type, meaning it starts from macroeconomic conditions and assesses their impact on the financial sector.
• Two models are used:
  • Financial Macro Econometric Model (FMM): The main model used to simulate the financial system's response to macroeconomic shocks.
  • Interest rate model: A satellite model that evaluates the impact of changes in market interest rates.

FMM Overview

The FMM model captures feedback loops between the macroeconomic sector and the financial sector, including:

• Interest coverage ratio (ICR) of the business sector
• Credit costs of banks
• Capital adequacy ratio (CAR) of banks
• Loans outstanding of banks
• Nominal GDP (NGDP)

These variables interact in a dynamic way, with changes in one affecting the others.

Key FMM Equations

• Interest Coverage Ratio (ICR):
  $$
  I C R = f_{I C R}(N G D P, other\ variables)
  $$
• Credit costs of bank $b$:
  $$
  C C_{b} = f_{P D}(I C R, N G D P, other\ variables)
  $$
• Capital adequacy ratio (CAR) change:
  $$
  \Delta C A R_{b} = f_{C A R}(C C_{b}, other\ variables)
  $$
• Loans outstanding of bank $b$:
  $$
  L_{b} = f_{C A R}(C A R_{b}, other\ variables)
  $$
• Nominal GDP change:
  $$
  \Delta N G D P = f_{N G D P}(\Delta \sum_{b} L_{b}, other\ variables)
  $$

Illustration of Feedback Effects

• Nominal GDP is shown as a key variable in the feedback loop.
• Capital Adequacy Ratio (CAR) is presented with percentage deviations from the baseline for internationally active banks and domestic banks.
• Credit losses are calculated based on transitions between internal rating categories of banks, with different categories having varying loan-loss provisioning rates.

Estimation of Transition Probabilities

The transition probabilities from one rating category to another are estimated using the following equation:

$$
\ln\left(\frac{P T_{i,t}^{mn}}{1 - P T_{i,t}^{mn}}\right) = \overline{\alpha^{mn}} + \alpha_{i}^{mn} + \beta^{mn} \cdot \text{nominal GDP growth rate}{t} + \gamma^{mn} \cdot I C R{t} + \delta^{mn} \cdot \text{quick ratio}{t} + \eta^{mn} \cdot D E \text{ratio}{t}
$$

Where:

• $P T_{i,t}^{mn}$ is the transition probability of bank $i$ from category $m$ to $n$
• $\overline{\alpha}^{mn}$ is the mean of bank $i$'s fixed effects
• $\beta^{mn}$, $\gamma^{mn}$, $\delta^{mn}$, and $\eta^{mn}$ are coefficients representing the impact of macroeconomic variables on the transition probabilities

Notes:

• Category 1: normal
• Category 2: need attention (excluding special attention)
• Category 3: special attention
• Category 4: in danger of bankruptcy
• Category 5: de facto bankrupt or bankrupt
• Sample period: first half of fiscal 2005 to first half of fiscal 2013
• L: one-period lag; MA$n$: moving average of $n$ period lags
• O: parameter for major banks; R: parameter for regional banks
• In shaded areas, no statistically significant parameters are estimated, and transition probabilities are treated as exogenous variables

Interest Rate Model Overview

The interest rate model evaluates the effects of changes in the market yield curve on:

1. Net interest income (via loan interest rates, deposit rates, and bond interest income)
2. Market value of bonds

Estimating Loan Interest Rate Pass-Through

The model includes a detailed equation to estimate the pass-through of market interest rates to loan interest rates:

$$
\Delta i_{L,k,t} = \mu_{k} + \sum_{j=1}^{2} \kappa_{j} \Delta i_{L,k,t-j} + \sum_{j=0}^{\Lambda} \underbrace{(\beta_{j} + \sum_{m} \beta_{m j}^{*} X_{m,k,t-1})}{\text{short-run impact}} \Delta i{M,t-j}
$$
$$

• \underbrace{(\alpha + \sum_{m} \alpha_{m}^{*} X_{m,k,t-1})}{\text{adjustment towards}} (i{L,k,t-1} - i_{M,t-1}) + \text{long-run relationship}
  $$
  $$
• \sum_{m} \lambda_{m} X_{m,k,t-1} + \phi \bar{Z}{k,t} + \varepsilon{k,t}
  $$

Where:

• $i_{L,k,t}$: loan interest rate of bank $k$ at period $t$
• $i_{M,t}$: market interest rate at period $t$
• $X_{m,k,t}$: vector of pass-through explanatory variables

Scenario Design

The BoJ designs two types of stress scenarios:

Tail Event Scenario

• Characteristics: Severe adverse financial and economic conditions equivalent to the Lehman shock.
• Purpose: To assess the stability of the financial system through fixed-point observations.
• Cyclical Conditions:
  • Output gap troughs around minus 7 to minus 8 percent
  • Output gap worsens by at least 3 to 4 percentage points (i.e., the average in past economic recessions)

Tailored Event Scenario

• Flexibility: Designed to investigate the vulnerability of the financial system under different circumstances for each test.
• Purpose: To assess transmission mechanisms of salient risks by extending the model and source data as appropriate.

Conclusion

The Bank of Japan employs a top-down macro stress testing framework that includes both the Financial Macro Econometric Model (FMM) and an interest rate model. The FMM captures complex feedback loops between macroeconomic and financial variables, while the interest rate model evaluates the impact of market interest rate changes on net interest income and bond values. The Tail Event Scenario simulates severe economic shocks, and the Tailored Event Scenario allows for more flexible and targeted risk analysis. The results are published in the Financial System Report (FSR) and its annex series, with variable paths and transition probabilities made available for transparency.