Empirical Asset Correlations

In the last few years there has been tremendous growth in structured products, especially collateralized debt obligations. Investors in CDOs are essentially buying portfolio risk and therefore like to be appropriately compensated for the assumed level of risk. Pricing and valuation of CDOs require three key inputs: default probabilities, recovery rates and default correlations. Of the three, correlation is the most difficult to measure and to date there has not been consensus among market participants on which method to use, even though variations in correlation between underlying assets within a portfolio may have profound impacts on the tail of the portfolio loss distribution.

Correlation estimation methodologies use either ratings-based or market-based measures. In particular correlations are estimated based on:

* Historical agency rating and default information;

* credit spread information; and

* equity market information.

The advantages and disadvantages of each are discussed below.

Historical Agency Rating And Default Information

The advantage of this method is that ratings are accepted benchmarks and cover a reasonable period of time. Since defaults are rare events, making inferences is difficult across a wide range of industries and geographies. In addition, the majority of agency rated entities belong to North American institutions, thereby making it very difficult to extend inferences globally. Methodologies based on historical rating and default data also require some aggregation, either by rating class or general industries, and thus categorically do not permit estimation at more granular levels.

Credit Spreads Information

Alternatively, correlations can be measured using credit spreads based on bond market or credit-default swap market data. One advantage of using spread data is that it reflects market information. The main drawback of this approach, however, is historical and cross-sectional coverage. There are also liquidity and data quality concerns. For bonds, it is generally difficult to separate liquidity, tax, and other components from the default component. The CDS market provides a relatively cleaner signal for credit risk and therefore correlation calculation purposes. At present, however, the nascent CDS market has neither the historical, nor the cross-sectional coverage to allow for broad systematic inferences.

Equity Market Information

Correlations based on equity market information have a number of advantages in comparison to the alternatives discussed above. The main advantage is that they have wider coverage both across continents and across any given country. Furthermore, the information comes from liquid markets, and is of good quality. Thus, unlike the ratings-based approach, one can empirically observe nuances between firms on a global basis. Equity-based correlation methodologies also allow for firm-specific pair-wise correlations and more granular industry definitions than historical rating data methods. With this methodology, however, there is a concern that equity prices may reflect--in addition to credit related information--information that is unrelated to credit.

Comparing Models

The discussion above shows there are three feasible alternatives to pursue for the broad and systematic measurement of asset correlation: asset calculations based on default correlations, based on rating transitions, and based on equity market information. In this study, we estimate models in all three classes and compare the findings.

For default correlation-based asset correlations, historical agency ratings are used to calculate intra-industry and inter-industry default correlations which are then "translated" to asset correlations using a bivariate Gaussian copula. For rating transitions, the intra-industry and inter-industry asset correlations are measured directly using the co-movement of ratings. Finally for the equity case, we use the factor model embedded in the Vector Model (VECTOR) Version 2.0 to estimate inter- and intra-industry correlations.

These methods were compared by employing data that included U.S publicly rated companies from 1970 to 2004, which was comprised of 66,740 yearly observations containing 7,886 firms and 1,039 defaults. For default-based methods we use the following models: de Servigny and Renault (2002), Frey and McNeil (2003) adjusted, Robust Average Correlation Measure (RACM), which we devised based on the previous two measures, and an adjusted version of Gupton, Finger, Bhatia (1997). For more details see 'A Comparative Empirical Study of Asset Correlation,' Fitch QFR Special Report, June 6. The Directional Rating Transition Matrix (DRTM) was used as the rating transition model. The results are compared to Vector Model 2.0, which rests solely on equity market data.

The table below displays the average asset correlations for these models.

The intra-industry correlation estimates for all models, except rating transition model, are fairly close to each other. Similarly, inter-industry correlation estimates are also in the same range for all of the default correlation-based estimators, where purely equity-based correlations are somewhat higher. For both intra- as well as inter-industry correlations the rating transition-based correlations are significantly lower. For more than half of the industries, the rating transition model reports an intra-industry correlation of less than 6%, half of which are less than 2%. For inter-industry correlations, the rating transition model again produces the lowest correlations. The majority of the estimates centre around the 3­4% asset correlation range with the highest value being around 10.43%. For all models, the intra-industry average correlation is larger than the inter-industry asset correlation. Average intra-industry correlations ranges are 19-26%, excluding the rating transition model. Inter-industry range is about 14­20%.

We also tested a number of empirical hypotheses regarding the absolute and relative magnitudes of intra- and inter-industry correlations. The tests unanimously and conclusively concluded that inter-industry asset correlations are not zero. This observation is generally in line with expectations and market observables. To test the sensitivity of the results we conducted a bootstrap exercise. Within the bootstrap runs there was not a single occurrence for any industry where the inter-industry correlation was zero. We calculated that approximately a 5-sigma shock would be needed for any of the estimates to become zero, which in probability terms is an extremely small number.

We next examined if inter-industry asset correlations can be assumed to be constant across industries. Bootstrapped samples were used along with standard statistical tests such as the t-test, the Kolmogorov-Smirnov test, and the Wilcoxon test to conduct industry pair-wise comparisons. There are 25 separate Fitch industry groups, therefore 25*(25-1)/2 or 300 pairs were compared. Out of 300 possible combinations, a maximum of 10 could statistically have the same inter-industry correlations. Thus, one cannot assume that all industries can be assigned a single correlation figure. Similarly, for intra-industry correlations, out of the 300 possible pairs on average only nine could statistically have the same correlations.

Finally, the intra-industry correlations were compared with the inter-industry correlations: for every industry the intra-industry correlations are notably different (greater) than inter-industry correlations, thus verifying that models that yield similar intra- and inter-industry correlations in magnitude are possibly biased.

Conclusion

In this study we empirically estimated and compared asset correlations using default correlation-based, rating transition-based and equity-based methodologies. The empirical findings of the study show that: (a) inter-industry asset correlations are relatively smaller than intra-industry asset correlations, but they cannot be assumed to be zero, (b) intra-industry as well as inter-industry asset correlations vary across different industries, (c) there are notable empirical difference between intra-industry and inter-industry asset correlations, and (d) to the extent equity price movements tend to reflect systematic non-credit related information, correlations based on equity-based methods, especially those measuring inter-industry relationships are likely to be overestimated.

We note that ratings data typically reflect a very U.S.-centric view of the corporate universe. Therefore, methodologies that are solely based on ratings data pose problems, as findings based on ratings data cannot be easily generalized to regions outside of North America. Furthermore, rating transition based measures, yield notably lower correlations in comparison to all of the alternatives. Equity-based models are not bound by the constraints of the rated universe: their coverage is much larger cross-sectionally in any given country, as well as across different regions. In addition, methodologically equity-based asset correlations are more flexible, and lend to more granular analysis. Finally, changes in underlying economic fundamentals would be reflected in market data quickly, therefore minimizing the lag, if any, in capturing a potential structural change in correlation structure.

In the light of the empirical findings and the observations on methodological issues, we conclude that market-based methodologies are superior to solely ratings-driven methodologies in estimating asset correlations. Any possible systematic overestimation bias related to market based methods can be addressed with a calibration exercise.

This week's Learning Curve was written by Dr Ahmet Kocagil, managing director, Jalal Akhavein, director, and Matthias Neugebauer, director, at Fitch Ratings.