Calibration Issues for Credit Risk Drivers

Part 6: Measuring Correlation across Risk Drivers- Calibration Issues

Most of the literature available considers only the default correlation (correlation among the default of obligors). This may be sufficient as long as PD represents other risk drivers. However, in this article we are espousing the cause of considering at least four risk drivers and considering correlation as a separate risk driver. The following table indicates the correlation among the risk drivers.

As seen from the table, practically every type correlations is not measured.

Take Note Transformation Process: Empirical findings on correlation: asset correlation is lower for smaller firms than larger ones but on an average, PD levels are generally higher for SMEs than for larger corporate firms, average asset correlation is lower for SMEs at a given PD level. Basically, this is because SMEs tend to be less correlated with the market due to a higher ratio of idiosyncratic risks, relative to systematic (general market) risk, than larger firms. In other words, compared to larger corporate firms, SMEs are less likely to react in a parallel manner to developments in the general economy because their fortunes are more tied to factors unique to them.

Correlation of Exposure with Other Risk Drivers

Exposure vs Exposure and Granularity adjustments: Granularity level adjustments are required only because the exposures are not uniform, since the Accord has developed estimates for various risk drivers – the basis of average of exposure in the portfolio. However, it is very difficult to develop this adjustment. One of the dimensions of exposure vs exposure is also called the concentration risk. Concentration can be within the same obligor, group of obligor or obligors whose cash inflow (idiosyncratic factors) are related with each other directly or through macroeconomic factors

Exposure vs. LGD – Concentration Risk

Relationship of Exposure with LGD

It can be said that LGD is an average measurement of credit risk as exposure is increased. The Basel Committee recognizes that the Accord has not provided a full treatment to concentration risk and encourages banks to use improved risk measurement methods for concentration risks.

Suppose a lender is comfortable with LGD L1. He has collateral of USD X. He can go up to the Xmax till the loss given default touches LGD L1. If you look at this graph, every marginal dollar does not have the same risk. If he can stop short of Xmax, he has actually reduced his risk.

According to the Accord:

“A risk concentration is any single exposure or group of exposures with the potential to produce losses large enough (relative to a bank’s capital, total assets, or overall risk level) to threaten a bank’s health or ability to maintain its core operations. Risk concentrations are arguably the single most important cause of major problems in banks.”

Linkages of Exposure with PD and LGD is also called Concentration Risk. Concentration does not imply concentration only at the obligor level. Concentration can be across the exposures due to the common impact of the macro economic factors. Under this section, we are considering concentration for the same obligor. We have also considered concentration within the portfolio elsewhere. Ideally, it should be across the portfolio.

Take Note: The best practice is an active examination of all portfolios to discover concentration within and across the portfolio by identifying common or correlated risk factors likely to impair credit risk of each of the obligors. Banks need to conduct such examination periodically. Portfolios should be evaluated for following factors:

• Large exposure limits
• Same economic sector or geographic regions
• Obligors having common links for financial performance
• Indirect credit exposure due to risk mitigation techniques.

Correlation of PD vs PD

Various formulae in Basel have only considered the impact of correlation of PD into their calculations. Other correlations are not considered explicitly. Regulators themselves may develop models for certain types of exposures. The Federal Reserve has developed one such model for single-family mortgage residence. This model helps banks to either use the model directly (and therefore may also be able to share the data and further refinement into measurements and best practices) or benchmark their models against the regulatory models. There should be no surprises if a middle-market model is developed in Germany.

Credit card PD and correlation

Correlation of PD in single family mortgage in US

Correlations between PD and LGD

As the correlation between these two variables increases, so does the level of credit risk. Generally, credit risk models treat PD and LGD as independent variables. The Basel Committee makes the same assumption. In contrast, there is considerable empirical research showing a reasonably strong positive correlation between these two variables. The correlation can be explained due to the following two reasons

• Impact of economic downturn on PD and assets value – aggregate default rates are usually higher than average economic downturns. Such periods also tend to be associated with a depressed asset values and thus higher than average losses when loans default.
• Supply and demand of defaulted securities – Increase in default leads to an increase in the supply of defaulted securities and correspondingly to a reduction in their prices and therefore increase in LGD.

PD and LGD are correlated due to their correlation with economic factors. However, this should be understood with caution. Ratings transition matrices, asset correlations and LGDs can all be made a function of macroeconomic variables, and there is reasonable evidence to support doing so. But there are risks in proceeding in this direction. In particular, there is the potential for larger increases in measured risk in downturns, and declines in booms.

Significant empirical and theoretical research has been done to estimate PD and much lesser attention has been dedicated to the estimation of Recovery Rates (RR) and to the relationship between PD and RR. This is due to:

1. Credit pricing models and risk management applications tending to focus on the systematic risk components of credit risk, as these are the only ones that attract risk premia.
2. Credit risk models traditionally assumed RR to be dependent on individual features (e.g. collateral or seniority) that do not respond to systematic factors, and to be independent of PD.

Empirical evidence from many countries shows that the collateral values and recovery rates are volatile and have negative correlation with PD during economic downturns.

This link between recovery rates and default rates has traditionally been neglected by credit risk models, as most of them focused on default risk and adopted static loss assumptions, treating the recovery rate either as a constant parameter or as a stochastic variable independent from the probability of default ( as we will see both these assumptions are not correct).

Correlations between PD and RR-Modelling

Recognition of PD and LGD correlation by Basel Accord: The Basel Committee has indirectly attempted to address the correlation issue by requiring banks to use default-weighted average LGD rather than using simple average LGD. Since most defaults occur when economic conditions are weak, the default-weighted estimate is likely to be close to the estimate that applies when PDs are high. Thus it could be viewed as a conservative approach, in that it does not recognize a fall in the LGD when the PD declines.

Ratings of individual assets only give an indication of the expected default rate or loss attached to these exposures. Greater accuracy in risk measurement can be attained by measuring the correlations among the risk loss (ideally correlation among all three dimensions – exposure, PD and LGD)

Correlation of Maturity with Other Three Risk Drivers

Credit spread is a measure of credit loss/credit risk which can be calibrated to maturity and other credit risk drivers. Credit spread of bonds of different PD represent differences in PD. Credit spreads are also called risk-neutral PD.

However, in general, corporate spreads are many times wider than what expected default losses would imply. What can be the reason for this? Various empirical researches have found out the following reasons:

• Liquidity premia is in-built into the credit spread. Empirical studies have found that many a times Liquidity premia exceeds the expected losses.
• Tax treatment of loss and interest.
• Correlation elements: The other explanation is that the PD does not take into account the correlations while credit spreads also consider the correlation aspect. For a bond of company A with PD of say BBB there is no diversification, while PD calculated for BBB companies is the average PD of such grade of companies over a period of time.
• Ex-post measurement: Market has better information. PD estimates are the estimate of the past (ex-ante) while credit spreads are the estimates of the future( ex-post). However, empirical structural models have not been able to explain the credit spread. It could even be the case that structural models account very well for the credit risk component of bond prices and returns while, at the same time, credit risk is actually responsible for only a part, perhaps not even a very large part, of spreads and returns. Still not much of the support is available to separate the other factors from credit spread to enable us to measure the credit risk or PD.

Term structure and credit spread: It is a graph of credit spread as a function of time to maturity of the risky bond.

Research has yet to find out whether the hump is due to changes in the perception about the credit risk or due to other factors.

Very limited empirical and theoretical explanations are available for the difference between steepness between the differences in yield curves.

Importance of firm-specific factors in credit spread: Recent studies suggest that the fundamental factors of the firm help to explain more then 50% of credit spread. This may be for two reasons:

• Structural models of default, introduced by Merton (1974), posit that default occurs when the firm-value process reaches some default threshold, suggesting that firm fundamentals should be the driving force behind changes in the bond’s probability of default.

• Firm-fundamentals may also play a role in explaining the time-series variation in credit spread changes.

Take Note: Next-level Risk Practices – Integration of credit risk and market risk

The main sources of risk affecting fixed income assets are interest rates and credit risk. As is explained in the credit-spread section, it is very difficult to segregate these two components. Further, losses due to interest rate changes do not necessarily happen simultaneously with losses due to changes in the credit quality of the counterparties. Therefore, it makes sense to measure and manage these sources of risk in a common framework in order to take the dependencies between them into account. Existing tools and the regulatory environment consider market and credit risk separately. With the publication of the Interest Rate Risk Management paper and a requirement to provide for the capital for the same, an integrated approach to market risk and credit risk management and measurement may emerge starting from fixed income assets.