Retail and wholesale credit decisions are made in a specific macro condition of the economy. Capital however is calibrated to a long-run average. Today, these two views live in separate Probability of Default (PD) models with separate use cases. However, separate governance, separate validation cycles, additional administration for maintenance and additional costs are creating frictions when maintaining distintinct models. What if one underlying model could serve both purposes, with the model's PIT macroeconomic alignment driving credit decisions and the model's TTC view driving capital?
At Auriscon Ltd, we propose a hazard PD model design for eleveting both, the precision in PIT accuracy and the economic benefit from re-using of existing models, with PD generation adaptable to the different use cases in application scoring and capital calculations:
• For application scoring, the PD model runs on the current macro state; delivering a genuine point-in-time (PIT) PD that reflects today’s macroeconomic impact on credit drivers.
• For use in regulatory capital calculations, the same model is transformed to a through-the-cycle (TTC) output delivering a long-run average PD view.
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Why this matters: The regulatory landscape and the dual-use-PD
Stress Testing is well established as a risk management tool across financial institutions. This holds particularly true in in relation to Bank Capital, where regulatory requirements demand that banks adhere to regular internal and external stress testing exercises. A common question of interest to Portfolio and Risk Managers when evaluating the uncertainty of extreme market events is the following:
“How sensitive is my portfolio to losses as a result of macro and financial shocks?”
Macro Stress Testing aids in exploring exactly this. i.e. how hypothetical future economic or environment shocks transmit to portfolio losses and income conditions. In a portfolio-driven approach the drivers of a portfolio are identified and plausible scenarios are devised to facilitate the stressing of these drivers. For example, if unemployment rate would be identified as the key driver of losses in a retail portfolio, the stress test had to reflect changes in the unemployment rate and further, to explain how change in unemployment rate transmit to credit factors and to credit losses. However, other requirements may be imposed on the design of scenarios, for example by incorporating suitable liquidity and funding shocks into the scenarios.
To begin a scenario design one has therefore to identify the risks that matter most first, that is the identification of financial risks that can impact negatively on the financial or solvency position of the financial institution. However, the stress scenario is not meant to forecast of economic conditions in the near or distant future.
Scenario Design
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Given the abundance of possible scenarios, a viable approach for consistent scenario generation is to produce a base scenario based on the dynamics and the dependencies observed in the past. The Vector Autoregressive Regression (VAR) model serves this purpose well. For exemplification consider lag choice \(p=1\), a vector of \(k\) macro variables \(\boldsymbol{y}_t \in R^k\), a constant vector \(\boldsymbol{c} \in R^k\), a coefficient matrix \(\boldsymbol{A}\) of dimension \((k \:\text{x} \: k)\). The error terms associated to each ADL equation in the VAR model have zero mean and a stationary covariance matrix with zero off-diagonal elements in the covariance matrix.
\[\text{E}[\boldsymbol{\epsilon}_{t}]=\boldsymbol{0} \:\: \forall{t} \:\: \text{and} \:\: \text{E}[\boldsymbol{\epsilon}_s \cdot \boldsymbol{\epsilon}_t] = \boldsymbol{\Omega}\]
A VAR model with lag 1 is specified by
\[\boldsymbol{y}_t=\boldsymbol{c}+\boldsymbol{A}\cdot\boldsymbol{y}_{t-1} + \boldsymbol{\epsilon}_{t}\]
A fitted VAR model, e.g. written below for VAR(1), provides the means for multi-period forecasting.
\[\boldsymbol{\hat{y}}_t=\boldsymbol{\hat{c}}+\boldsymbol{\hat{A}}\cdot\boldsymbol{\hat{y}}_{t-1}\]
TIP: The Vector Autorregression (VAR) method is suitable for analysing macroeconomic and financial data with the aim to project the trend of each variable. Similar to historical scenarios, the VAR approach is implicitly accounting for relationships among variables. Precisely, any VAR model is consistent with the historical time series patterns underlying the data. For instance, the historical evolution of bond returns may have an impact on the historical evolution of stock returns and vice versa, and this interelationship is incorporated by specifying a VAR model. → READ MORE ...
To ensure devised scenarios are credible an alignment with economic theory, historical correlation pattern, and multi-variable severity is paramount. From the scenario narrative co-movements of variables have to be plausibly coherent. A demand recession scenario produces different co-movements than a supply shock or a financial crisis scenario. Guidance should be sought in regulatory templates (e.g., the Bank of England's annual cyclical scenario), and augmentation can be found in the institution's internal risk appetite.
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