TUNING THE MODEL—DATA SETS AND DRIFT
While the traditional Merton Model is fairly robust, certain assumptions in its application have major implications for the results. One key factor is μ, the expected return or “drift” of assets over time. Some practitioners set the drift term to equal zero on the theory that most assets used by an operating company need to be financed, so riskless returns associated with these assets go to note holders and do not impact the optionality of the equity. Other practitioners use the risk-free rate or the inflation rate. To our knowledge, as of 2010 there has not been a comprehensive study or analysis published on the role of drift in credit modeling. However, for longer-term analysis, the drift term can have a major impact on the results.
FIGURE 5.5 The completed Model Builder 5.5, with potential options for drift laid out in H9:I12. Note that the applied drift rate in L8 is 0.00 percent.
Perhaps more important to the results is how volatility is calculated. There is no widely accepted rule as to how equity volatility should be calculated. Different methods of gathering volatility data can result in substantially different estimations of default risk.
Volatility
In general, volatility will be the most important variable for determining the risk of a company, and as a result most of the work in tuning the model will be done with this variable. Admittedly, to calibrate the model is much more of an art than a science, and different financial engineers will have different opinions on how to best calibrate their model to best determine default probability in the future.
One key factor to consider is that the observed volatility of equity, and therefore the volatility of a company's assets, is correlated with the market as a whole and will move up and down for reasons that are likely not related to the particular company that is being analyzed. Whether to correct for these global changes is a difficult question to answer. On one hand, it hardly seems accurate to incorporate marketwide volatility when looking at a company that does not hold a large number of financial instruments among its assets (an airline, for example). On the other hand, economic downturns do increase the propensity of all companies to default; default rates during recessions can be many multiples of the rates observed during expansion. In general, most modelers do not make distinctions between the volatility associated with the company (idiosyncratic volatility) and volatility experienced by the market as a whole.
Strengths and Weaknesses of Structural Models
The Merton model was the first in a class of models that are called “structural models” because they take into account the structure of a company's balance sheet. Later in this chapter we will consider “reduced form models,” which calculate default probability from debt or credit default swap prices.
Structural models are premised on the fact that publicly traded equity is the market that offers the most accurate information about a company's health and riskiness. By accounting for the structure of a company's balance sheet, these models offer a framework for using the information-rich equity markets to measure risk in the debt markets. There is some evidence that structural models pick up on signs of corporate distress substantially before other measures, primarily rating agencies, are able to see them.
Many times, structural models will offer some guidance for debt instruments where the documentation is not easily obtainable and there is minimal trading history available. Structural models can also be expanded to nonpublic companies by creating indexes of similar companies and using their returns as proxy for the firm in question. Some methods for accounting for incomplete data sets are covered in Chapter 7. And importantly, estimating recovery in the case of default is fairly straightforward as there is already a projection of asset values at default that is plugged in.
However, there are a number of weaknesses inherent in structural models, both theoretically and from a practitioner's point of view. In general, all models that are built on the Black-Scholes methodology are explicitly assuming a lognormal distribution of future price movements, an assumption that has been widely (and rightly) criticized for ignoring the importance and frequency of large swings in value. A more in-depth discussion of this issue is available in Chapter 8.
Additional theoretical issues include the oversimplification of company structure and the inability of structural models to account for specific debt covenants or actions that may increase the value of equity but decrease the value of debt (such as dividend recapitalizations or mergers). But the most glaring theoretical deficiency is the fact that Merton's model does not account for cash flow or liquidity. Measures of a company's ability to make payments in the short term are mainstays of traditional credit analysis and can be important guides to whether companies will run into trouble. Many companies that look relatively stable can run into trouble quickly if liquidity is threatened; witness Bear Stearns and AIG during the credit crunch of 2008. While the equity prices were late to reflect the vulnerability of these companies, classic debt analysis highlighted the weaknesses, and as a result debt valuations led equity as the companies collapsed.
From an academic's perspective, a number of key assumptions are required for the structural model to be an accurate representation of the market. Lack of transaction costs, the applicability of stochastic processes under a known distribution, and stationary asset volatility are three primary assumptions with which concerns have been voiced. While all modelers need to be aware of these basic assumptions, we will not cover these issues here.
From a practitioner's perspective, the main barriers to using structural models are their computational complexity and their consistent overpricing of debt, as well as the amount of data that they require. In order to properly calibrate the calculation of a firm's asset value and the volatility associated with it, there needs to be a historical record of not only equity prices, but also of historical liability levels. This data, while possible to obtain, can be difficult to gather and employ. Moody's-KMV has distinguished itself as having a large database, which allows users to quickly employ their structural model effectively.
However, even if an analyst is faithfully recreating a company's historical financial situation, structural models consistently price debt to a higher level than the market does. This either means that the market is accounting for some of the risks that structural models are not accounting for, or there is a liquidity premium built into the market pricing that structural models are not catching. In general, premiums for factors other than credit risk (such as liquidity or regulatory risk) make projecting credit risk from market pricing very difficult.