Understanding capital requirements

A new methodology provides route to a more honest dialogue between regulators and banks

By Alexandre Petrov, Ph.D., Executive Advisor for Credit Risk Models, Nordea, Stockholm

Credit risk classification systems have been in use for a long time in the financial industry. With the advent of Basel II, those systems became the basis for banks’ capital adequacy calculations. The Basel II risk-weighted asset (RWA) formula is intended to calculate the capital necessary to cover the unexpected loss (UL), based on probability of default (PD), loss given default (LGD) and exposure at default (EAD). What is needed going forward is an efficient and honest dialogue between regulators and investors on capitalization.

This dialogue must be built on the bank management’s view of risk in the portfolio. It is a definite advantage to have a framework that enables structured integration of management’s judgment into the model rather than adding it outside the model. Such a framework facilitates clear credit steering. Furthermore, using the same models for different purposes in the credit process makes the fulfillment of the Basel II use test obvious.

For PD, the regulation requires “long-run average of one-year default rates.” From a purely mathematical point of view, checking the assumptions used for deriving the Basel II RWA formulas, the arithmetic average of point-in-time (PIT) PDs should be used in RWA formulas, supporting our view that through-the-cycle (TTC) PDs should be used for capital requirement calculations. If the PD used is not TTC, it will vary with the cycle, and the capital requirement will also vary. This is the background to the discussion on procyclicality: In adverse times, capital requirements for banks may increase, forcing them to cut lending. Hence the cycle will be strengthened, which is clearly an undesired effect.

Methodology pros/cons in capital requirements calculations

TTC and PIT PDs each have their advantages and disadvantages, and a good steering system ideally should have both. In real life, most rating models are so-called hybrid models (models that vary with the cycle to a certain extent, but not fully). I describe a way of adjusting PDs from a hybrid model to TTC and PIT PDs. The idea is to use data and expert opinions regarding where the bank is in the cycle (taking into account the degree of PIT of the rating model) for adjusting the rating of counter parties to both TTC PD and PIT PD.

This methodology has a number of advantages:

Uses the same assumptions and is developed within the same framework as the Basel II RWA formulas, which makes for easier regulatory approval, and increases business unit and management “buy-in.”
Results in simple analytical expressions for calculation of PIT PD and TTC PD from any PD of a hybrid rating model allowing easy implementation of the method in IT systems.
Makes a convenient and natural quantitative definition of the degree of PIT of each rating model and suggests a method for estimating it. (The estimation of stability of the rating model with respect to the economic cycle is required by regulators as part of validation in Basel IRB regime.)
Estimates external data-driven economic cycle for TTC PD calculation, supported by regulators, and consistently incorporates expert judgment for PIT PDs and pricing.
Delivers a consistent definition of states of economy, as well as statistical and macroeconomic models for predicting future states of economy. In the journal article* that I co-wrote with Magnus Carlehed, we discuss the distribution assumptions of the economic cycle variable Z, starting from a “static” standard normal distribution assumption for Z and then comparing this with an assumption of a time dynamic for Z, where some level of autocorrelation between Z values is introduced.
Gives information to help determine portfolio deterioration resulting from the fall of obligors’ internal quality from the economic cycle effect. The corresponding portfolio monitoring procedures are proposed.
Provides a clear link between Pillar 1 individual obligor assessment by rating models and Pillar 2 collective (portfolio) credit risk models.
Enables the users to make predictions for the development of PD of obligors/portfolios in the scenarios – given a view into the dynamics of the economic cycle or an economic stress scenario.
Provides a validation framework for regulatory approval as well as a methodology for estimating method parameterization, such as degree of PITness of rating model and volatility of PDs.

The dual PD framework is becoming more and more necessary for an efficient steering of banks (algorithmic run of the methodology is proposed for bank implementation) as capital becomes a more and more scarce resource. Risk-based pricing and steering is becoming the industry standard, and its importance will continue to grow.

When and where

The proposed methodology of decomposing PIT PD and TTC PD has important implications on credit steering based on risk-adjusted profitability (RAROC). To avoid short-sighted and risky decisions, it is natural to ask for a RAROC for the lifetime of a loan, which is typically several years. For the allocated capital, we could use some multiplier times the Basel capital requirement, where TTC PD is used. However, for calculating Expected Loss (EL), I suggest using TTC PD or PIT PD or a combination depending on the maturity of the loan. For loans shorter than one year, I suggest PIT PD be used for EL calculation. For loans with longer maturity we may still use PIT PD for the first year, but predictions of PIT PD for the following years.

This method for calculating EL, and hence RAROC, allows countercyclical credit steering. Suppose that we are at the bottom of an economic downturn. Then PIT PD will be high and short term loans will be discouraged. However, profitability of long-term loans will be calculated using the lower TTC PDs (or a mix), so selective lending to good customers will still be possible. Conversely, in the highest point of upturn, the framework implies prudence in lending in a moment when PIT PDs are low, and EL based on such PDs would be too optimistic.

The methodology also allows a more precise risk differentiation between various portfolios in Pillar 2; not only the classical view from the PD perspective in absolute terms, but also the volatility of PD. As a result, portfolios that require less capital based just on the PD level may require more capital if PD volatility is taken into consideration, and vice versa.

Integrating management’s judgment into a model, rather than from the outside, facilitates clear credit steering and supports a more meaningful dialogue on capitalization with regulators and investors.

Result: stability

Increasing capital requirements during a crisis will result in a worse situation, adding to realized losses and increased capital requirements. In times of growth, without the method described in this article, banks will allocate less capital, as their hybrid PD values will be less than the TTC PDs. This is why this method is important for regulators; it creates capital during times of economic expansion that can then be utilized during economic downturns.

The method described has been implemented and approved in Sweden where the quarterly bankruptcy statistic is used for the estimation of the state of the economy. As bankruptcies are increasing in Sweden and other EU countries – they are offsetting higher “hybrid” PD estimates of rating models creating a more stable PD TTC to be used in RWA and capital requirement. This results in stable capital requirements in bad times. Of course banks can be less interested in this approach in good times as this method will force them to put aside capital; however this is exactly what regulators are looking for to build a more robust financial system.

Details of this methodology are published in the Journal of Risk Model Validation Volume 6/Number 3, Fall 2012 (1–23), “A methodology for point-in-time–through-the-cycle probability of default decomposition in risk classification systems”, by Magnus Carlehed and Alexander Petrov.