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One of the critical elements of the new Current Expected Credit Loss (CECL) accounting standard is the requirement that holders of credit-sensitive assets estimate losses over the remaining life of each asset in their portfolios. Given that many lenders and investors in credit assets hold loans or bonds that have remaining lives of more than one year, this estimation process then becomes the forecasting of multi-year loss rates.
Turns out, this is not an easy thing to do.
In this blog post, I examine the pattern of default on commercial debt from the perspective of a small or regional financial institution seeking to implement CECL. This post, first of two and possibly several, will focus on how that smaller institution estimates default over the remaining life of a debt instrument extended to a commercial counterparty. This blog addresses only commercial counterparties, as retail borrowers exhibit their own pattern of default; I will address retail defaults in a subsequent post.
Let’s suppose Sarah is the person responsible for implementing CECL at her employer, the XYZ Bank, a well-regarded and successful regional bank in the central United States. Over the course of many months of analysis and reflection, she has chosen to estimate CECL by the probability of default / loss given default method in which
Expected Loss (EL) = Probability of Default (PD) times Loss Given Default (LGD)
Sarah has chosen this approach because the XYZ Bank has risk ratings for commercial borrowers that are calibrated one-year default rates based upon her bank’s experience and the U.S. corporate bond market. In fact, the bank has established its “obligor risk ratings” so that the PD for each rating aligns with historical default rates from the bond market. The bank’s “facility risk ratings” are calibrated to EL, itself derived from the mathematical product of PD and LGD, with the LGD derived from defaulted loans in the bank’s historical loan portfolios. EL is integrated into a number of other bank processes, including loan loss provisioning, loan and relationship pricing and, through its cousin Unexpected Loss, the bank’s system of economic capital.
Why not take advantage of this existing PD LGD system for the XYZ Bank’s compliance with CECL, something that everyone says makes sense?
So, Sarah proceeds, and one of her first decisions for CECL is to capture the “remaining life” element of CECL in cumulative default rate for the time to maturity of each credit asset:
CECL = remaining cumulative PD times LGD.
Put differently, estimation of lifetime credit losses requires firm understanding of the expected future pattern of an obligor’s credit risk as observed through movement of credit ratings, otherwise known as credit migrations.
But the PDs that underlie the bank’s obligor ratings and all other applications of EL are one-year PDs; that is, PDs estimated for the next 12 months. How are you going to get multi-year PDs from one-year PDs?
Well, one way is to try to build statistical models of multi-year cumulative default rates based on predictor variables that are within the range of data elements available to the bank in the everyday forecasting of PDs that would be required for estimate CECL on individual loans.
Unfortunately for Sarah, but good for the bank’s shareholders, the XYZ Bank does not have enough historical data to build models of multi-year default probabilities. Like many well-run banks, the XYZ Bank has few historical defaults, consistent with its low long-run rate of loan charge-offs. In fact, the only PD models that XYZ has successfully developed, validated and implemented are one-year PD models for its commercial loan portfolios.
Even if she had sufficient data, building such models would be very difficult for several reasons:
One-year rates of default are easily modeled from financial ratios of borrowers if the bank has such data on both defaulted and non-defaulted borrowers.In my experience, banks often don’t retain such financial information and, for smaller private borrowers, financial statement information can sometimes be unreliable or incomplete.
The borrower’s future financial condition—that cannot necessarily be read from today’s financial statements—will determine default probabilities in the future and especially the distant future.
Another approach is to develop multi-year default rates based on the one-year default rates from the bond market to which the XYZ Bank has calibrated its risk ratings for commercial obligors. This, of course, is an exercise in the term structure of default rates and it is a critical element of CECL for all investors in credit, not just the XYZ Bank.
Sarah decided to take this latter route, but how to build these term structures properly?
Well, in Sarah’s case, she has reliable one-year default rates from the bond market, as well as the bank’s historical loan portfolios. And, as we noted previously, the bank’s system of obligor ratings is tied to these one-year default rates. Can she use these one-year default rates to derive the default rates for each rating over the remaining lives of her portfolio?
Fortunately for her, Moody’s publishes cumulative default rates over 20 years based upon the actual pattern of defaults in the bond market. She starts with the idea that she can solve for the marginal default rates for each year by estimating the marginal rates of survival (one minus the default rate) in that year. She further assumes, as her null hypothesis, that the average one-year default rates published by Moody’s hold true for years two through 20—that is, the survival rates are constant one year to the next.
The forecasted cumulative default rates for non-investment grade bonds based on this constant one-year default rate are shown in the figure below, along with the actual cumulative default rates published by Moody’s. The assumption of constant survival rates produces cumulative default rates for non-investment grade bonds quite close to the actual cumulative default rates through year five. However, the assumption of constant survival rates over-estimated actual cumulative default rates thereafter, implying that actual survival rates in years six and beyond are higher than the average one-year survival rate.
In the case of investment-grade bonds, the opposite condition holds (see figure below). The one-year survival rate leads to forecasted cumulative default rates that consistently underestimate the actual default rates. In fact, the estimated default rates are more than twice the actual default rates by year 10, and the difference widens thereafter.
These patterns have been understood for some time, though not widely publicized. Sub-investment grade bonds that do not default in the first five years tend to improve in credit quality, and their default probabilities drop. In contrast, investment grade issuers that do not default in their first year tend to decline in credit quality, and their default probabilities increase.
Sarah understands that the actual term structure of default rates in the bond market is more complex than the simple assumption of constant survival rates. In fact, a quick review of the literature on term structures of default rates reveals that the topic gets complex quickly. She discovers that:
The most common model of the term structure of default rates is something called a “Markov chain,” of which there are several types.
A is a stochastic model used to represent randomly changing systems.A Markov chain is a type of Markov model that represents the state of a system in which one or more random variables change through time.
In her initial investigation of Markov chains, Sarah learned:
Markov chains are used frequently by European banks as the analytical frameworks necessary to comply with IFRS 9, a regulatory requirement that is similar to CECL. Regulatory requirements for IFRS 9 are significant, including the expectation that firms use forward-looking information, including forecasts of macroeconomic conditions, in the techniques they use to extrapolate PDs.
It matters whether your bank’s system of obligor ratings is “point in time” (PIT) or “through the cycle” (TTC). IFRS 9 requires PIT ratings to allow for current macroeconomic conditions to influence the risk rating that is the starting point for the Markov chain.
This is pretty heady stuff, thinks Sarah. So, she takes a deep breath, because her CECL journey has taken a new turn and she realizes that this journey will take time, energy and lots of study.
I will relate that journey in an upcoming post to this blog.
1. Gerhold, P., A. Kleppe, M. Seifert and D. Thakkar. 2017. Constructing the PD term structure. Available at SSRN: https://ssrn.com/abstract=2998824 or http://dx.doi.org/10.2139/ssrn.2998824
2. Bogren, F. 2015. Estimating the term structure of default probabilities for heterogeneous credit portfolios. Master’s Thesis, Royal Institute of Technology, Stockholm.