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Fixed income risk modeling is establishing a more nuanced and separate identity for best practices and leaving behind its equity-like roots. There is the recognition that the fixed income factors are the same as used by any good bond manager. There is yield curve risk, with its associated sensitivity of key rate durations, and there is spread risk and its associated sensitivity of spread duration. It is here, in spread risk, where the nuances are being enhanced. Here, I will cover the current practice of the bucket approach for corporate spread risk, and, based on our research at FactSet, offer an alternative approach using a relative valuation model.

The mainstream approach to modeling spread risk is the bucket approach, and for corporates it has a certain intuitive appeal. It assumes that spreads move according to some common attribute, usually based on membership in a cross section of sector and rating. The common attribute, usually termed "beta," must dominate across the members of the bucket relative to the idiosyncratic term. This is critical— otherwise, one might as well just go ahead and model the bond's spread by itself. For the moment, we're going to set the idiosyncratic term aside.

Unfortunately, this assumption tends not to hold up in practice. I arbitrarily picked U.S. BBB Finance and measured the explanatory power of the common attribute for each bond in this index. Over 2013, the median R squared of the regressions is 0.08. Please note, by using the median means, half of the regressions are less than that.

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Instead, let's consider an alternative way of deriving corporate spread risk. A Merton model is a relative value model that relates equity risk to corporate spread risk. By one perspective, it assumes that the bond holders are selling a put on the value of the company's assets to the equity holders. This model takes, as inputs are the current equity price, the debt to equity ratio of the company, the equity volatility, and the time to maturity of the debt. However, the key value it produces is a probability of default. From that, we can derive the credit spread of the bond. This approach confers several advantages.

First, corporate spreads don't always reflect true executable levels. However, equity prices do tend to reflect real transactions and thus have the potential for higher information value. For this reason, research shows that equity prices are better predictors of default than ratings. The implication is that a corporate spread risk model based on equity prices will be a better predictor of future dispersion and distress than a bucket approach based on ratings.

The second advantage is more subtle. The name of the game in risk is in understanding correlations. The real value in risk measurement is in quantifying the correlation of multiple events across multiple securities. Using equity prices means using properly correlated inputs. Again, this is in contrast to the bucket approach, where all securities have the same perfect correlation.

However, there are practical advantages to using a Merton framework for corporates as well. First, this approach is equivalent to creating an issuer-specific spread curve, without all of the messy data details that such an approach would entail. Second, corporate spread risk comes in a variety of flavors across the capital structure, from bank loans to private placements to preferreds to convertible bonds and credit default swaps. And all the time the Merton framework maintains the proper correlations.

But there is an unstated assumption that I've been glossing over: namely that every corporate has a parent with publicly traded equity. However, if we relax the assumptions a bit, we can still proceed. Every night at FactSet we compute average equity risk attributes and factors across countries, sectors, and ratings. These private entity proxy risk factors are used to derive equity returns and, thus, spreads.

The bucket model also has problems with idiosyncratic risk, or the error term of the model. In equities, this is well-defined and measurable for a given universe. However, I contend that in fixed income, idiosyncratic risk exists but is unobservable.

This comes from the natural illiquidity of the bond market. TRACE reports that 80% of the U.S. Investment Grade corporate market does not trade each day, and similar statistics are available in other trading venues. Thus, instead of actual transactions, measuring idiosyncratic risk is really measuring the pricing service. And even then, the pricing services don't agree.

Let's return to my favorite scapegoat, U.S. BBB Finance, and look at the month-end prices over 2013 for the largest bonds across comparable index providers. One would expect the largest bonds to be the most visible and therefore have the greatest unanimity of valuation opinion. However, the average price dispersion of the 10 largest bonds is $0.46. For the next 10, the average price dispersion is $0.68. The differences in prices are significant, variable from month to month, and rapidly get worse as the issues get smaller.

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Now, I've been hammering on the shortcomings of bucket models pretty hard. However, they do have their purposes.If you're using a fixed income-only system, and all you know about is bonds, you can't take advantage of the information content in equities. But the solution there is to move to a multi-asset class system. Another reason could be the risk statistics you're looking at. If all your risk model produces is tracking error, which is a linear equation, then simpler assumptions and lower accuracy are required to compute the central tendency of the distribution versus the tails. However, if you use a Monte Carlo-based risk model, you can use more complex valuations and nonlinear repricings. In short, the bucket approach to spread risk modeling is based on unjustified assumptions and lacks the explanatory power and accuracy of relative valuation models.

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Vice President, Senior Director, Analytics Strategy
Bill has written and spoken extensively on fixed income hedging and return attribution, he has a Master's degree in Operations Research from the University of North Carolina and is a Chartered Financial Analyst and Professional Risk Manager.

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