RECOVERY ASSUMPTIONS

One major factor that is often glossed over in texts on modeling is where recovery assumptions come from. Recovery assumption can have a tremendous impact on the implied default rate that an analyst may get from the market. An analyst assuming a 60–70 percent recovery may believe that the default likelihood is many times larger than an analyst using a similar model but assuming no recovery.

As defaults and credit events generally end up in court, there is considerable uncertainty as to what an accurate recovery would be if a company defaults. Despite this, practitioners often look to historical defaults in order to get a feel for what an appropriate rate might be. One good source for historical data is provided by www.creditfixings.com, which posts historical CDS credit event auction results. However, due to the wide variance of recoveries (from over 96 percent to less than 1 percent), it is important to understand how similar the debt being modeled is to the debt of the companies that may be used as a comparison.

Generally, four major variables are commonly used in performing a recovery or “loss given default” (LGD) analysis: the seniority of the debt, the industry of the company, the ratio of assets to liabilities, and the state of the overall economy.

The seniority of the debt is generally the most important factor. Whether the bond is senior or subordinate, and how much senior and subordinate debt is outstanding, is crucial to a recovery assumption. Whether the loan is secured or not can be a major determinate as well. One assumption that is commonly used is that senior loans have recoveries of 40 percent while subordinates have recoveries of 15 or 20 percent. Extremely subordinated debt, such as debentures or trust preferred securities, often are assumed to have a recovery of zero. One method to get market opinions of relative recoveries is by looking at whether the company has both senior and subordinate debt, and assuming that they both have the same default probability (this isn't always the case but is often true). The gap in recovery that accounts for the pricing differential can be obtained by using solver or simple algebra. This will only give information on the relative recovery of the two securities and not the absolute recovery rate.

The industry of the company is also important. Generally, banks and other financial companies are assumed to have lower recoveries, since they often are taken over by governments that insure depositors or policy holders to the detriment of the creditors. Large industrial or consumer goods companies with lots of hard assets to support the debt often have higher recoveries.

Knowing a company's industry also gives guidance about a company's ratio of assets to liabilities. Generally, companies in the same industry have similar capital structures, which can give guidance on what recoveries can be expected. Additionally, information from our work with structural models can come in handy here. The general assumption is that the knock-out barrier is hit when the value of the assets reaches the sum of the short-term liabilities and one-half of the long-term liabilities. Setting this (minus some workout expenses) as the total recovery amount is consistent with a structural analysis.

Finally, the state of the economy is recognized as being a very important contributor to the recovery rates. Bonds that default during economic downturns as a whole can be expected to produce lower recoveries than defaults while the economy is performing well. As a result, some modelers include “state variables,” which account for the state of the economy and alter the recoveries that can be expected in different economic climates. These state variables can be constructed either as a continuous process or as a discrete “regime-change” variable (i.e., economic expansion/contraction).

Simulation Setup

While in many cases the market's default probability is all that is needed for an analysis, there are still situations when a full model is necessary. Where the decision has been made to use a reduced form model, implementation of the default probability into a model is relatively straightforward and differs mostly based on how recovery rate is modeled and what output is required. The most common reason for creating a simulation is the desire to understand how a portfolio of credits would be expected to perform. Simulation allows us to consider not only the riskiness of the assets in a pool, but also the impact of the correlation between these assets.

Another reason to simulate asset performance is that simulations allow us to relax some assumptions that go into building default probabilities. For example, in a structural model, the assumption that returns on assets follow a normal distribution can be relaxed (e.g., other distributions that match historical price movements or ones with fat tails could be used). While it is not internally consistent, it does allow the analyst some ability to respond to requests for fat-tailed distribution analysis or other types of analysis that are less dependent on normal distribution assumptions.

Accounting for Liquidity

While so far we have assumed that the entirety of the spread over the risk-free bond is due to the risk of loss due to a default, there is ample evidence that bond prices include other factors as well. Markets are not truly efficient, and transaction costs, regulatory requirements, and restrictions on capital movements across borders all impact the relative pricing of bonds, as do a number of other factors. The most important of these factors is liquidity, and as a result researchers into quantitative finance often group all the non-credit-related factors in a bond's pricing under the label of liquidity.

Empirically, spreads have proven to be wide of where the risk-neutral default probability would indicate. To say this in another way, bonds default less often than they should, given where they price. This persistent discrepancy has generally been ascribed to liquidity in the research, specifically to the worry that liquidity for securities may disappear at a time when cash is desperately needed. Such a liquidity crunch has been observed in the market on a number of occasions, in particular during late 2008, when even debt securities issued by high-quality nonfinancial companies such as Pfizer saw precipitous drops in value despite little exposure to the credit events that were occurring.

Since the relationship between price and default rate is different in the two types of models that we have discussed in this chapter, liquidity adjustments will have opposite impacts. In structural models, we use accounting information and historical equity volatility to estimate a default probability (and hence, a price). However, since prices reflect risks above and beyond credit risk, structural models tend to underestimate price, so typically a liquidity adjustment needs to be added to the spread that the model predicts. Reduced form models, on the other hand, start with market pricing and are used to compute default probability from there. Since market spreads are wide of the observed loss rates, our default probabilities will be too high unless we subtract out a liquidity component.