CAPITAL MANAGEMENT Credit Risk Measurement: Avoiding Unintended Results Part 4: Loan Loss Reserves and Expected Losses by Peter O. Davis and Darrin Williams his series emphasizes the nuances of credit risk measure- ment to avoid the consequences of applying methods T developed for one use to those for which they are not appropriate. Parts 2 and 3 looked at two specific credit risk metrics: probability of default and loss given default. This article examines the potential pitfalls in comparing loan loss reserves to measures of expected loss. These two concepts are similar, but perhaps not as directly comparable as is often assumed. or many bankers, the most II. Under the new Accord, qualify- definition of expected loss) found familiar credit risk metric is ing banks will be able to use their in banks’ internal credit models. Fthe loan and lease loss internal expected loss credit mod- The short answer? No. That does- reserve, often called simply the els to drive their minimum regula- n’t mean the two measures can’t loan loss reserve. The allowance for tory capital requirements.1 The be compared. It just requires an loan losses provides for credit growing use of internal credit mod- understanding of how they differ losses inherent in the bank’s port- els—an initiative accelerated by and where they should converge. folio. According to conventional Basel II’s capital requirements— wisdom, the loan loss reserve is has placed a more intense focus on Origins intended to absorb anticipated the consistency of these models The loan loss reserve was losses—not the worst or best case, with other internal bank metrics, established in 19472 as a financial but management’s view of the such as the loan loss reserve. reporting measure for investors; most likely case. At this juncture, the question expected loss was developed by The integration of bankwide is whether the anticipated, or financial engineers—often credit risk metrics, a process expected, loss reflected in the loan referred to as “quants”—for risk already under way, has been accel- loss reserve is the same as the management. Many of the differ- erated by the introduction of Basel expected loss (see Figure 1 for a ences between the two measures © 2004 by RMA. Peter Davis and Darrin Williams are members of Ernst & Young LLP’s Global Financial Services Advisory practice, where Davis is the director of Credit Risk Services. 68 The RMA Journal October 2004 Credit Risk Measurement: Avoiding Unintended Results Part 4 stem from their different origins. Figure 1 Loan loss reserves are based Credit Risk Measurement Terminology on empirical data and manage- ment’s judgment; complex mod- Probability of default (PD)—the risk that an obligor, or borrower, will fail to make els, when used, play a supporting full and timely payment on its financial obligations over a given time horizon. role. The past several years have Loss given default (LGD) —the risk that a loss will be incurred if there is a default witnessed unprecedented scrutiny event. of the loan loss reserve by regula- tory bodies. While concerns about Exposure at default (EAD)—the expected drawn exposure at the time of default; applies only to non-term exposures, such as lines of credit. earnings management and inade- quate disclosure drive the Expected loss (EL)—the average expected credit loss over a given time horizon: Securities and Exchange Expected Loss = PD x LGD x EAD Commission, bank regulators Unexpected loss (UL)—losses incurred under a high-stress scenario; typically identi- focus on capital adequacy and fied as a point in the tail of a credit loss distribution (e.g., at the 99th percentile). conservative reserve amounts. These differing viewpoints and es and capital covers unexpected Figure 2, for U.S. banks this is not heightened scrutiny have at times losses. But in the U.S., except at a the case. Across the banking sys- left the banking industry and very abstract level, expected loss tem, loan loss reserves currently public accountants feeling caught and the loan loss reserve are never are roughly double the annual in the middle.3 equivalent. Expected loss is charge-off rate. For banks with The quants, meanwhile, defined as the product of PD, low charge-off rates, the ratio of developed the quantitative con- LGD, and EAD (see Figure 1) or loan loss reserves to charge-offs is cept of expected loss (EL) versus the mean of a loss distribution, typically much higher. unexpected loss (UL) to distinguish measured over a one-year horizon. As a result, banks’ loan loss between “ordinary” credit losses Actual losses over a one-year hori- reserves are somewhere well and high-impact, low-frequency zon are approximated by the north of one-year expected losses, default events. The current annual net charge-off rate. functioning partly like capital in framework for measuring credit If expected losses and loan the idealized EL/UL credit risk risk—described in the first article loss reserves were the same, one measurement framework. in this series and embraced by would expect loan loss reserves to Recognizing that banks’ reserves bank regulators through Basel roughly equal a bank’s annual net may exceed one-year expected II—reflects an attempt to quanti- charge-off rate. As shown in losses, under Basel II banks will be tatively measure credit risk. Originated in academia, this Figure 2 framework migrated to large Net Charge-Offs and Loan Loss Reserves at FDIC-Insured banks and vendors as the models Commercial Banks 2.00% became more robust over the past 1.75% 10-15 years. So there are two “ver- 1.25% sions” of expected loss: one origi- 1.00% nated qualitatively by banks from 0.75% loan loss reserves, and the other 0.50% quantitatively based on an 0.25% EL/UL framework. As % of Loans and Leases 0.00% 1998 1999 2000 2001 2002 2003 ‘04:Q1 Comparing Loan Loss Reserves and Expected Loss Net Charge-offs Loan Loss Reserves Conventional wisdom holds that reserves cover expected loss- Source: FDIC Quarterly Banking Profile 69 Credit Risk Measurement: Avoiding Unintended Results Part 4 able to count a portion of their loan year time horizon for expected year EL and reserves, even if both loss reserves in excess of EL as eli- loss. However, for loan loss calculations relied on the same gible capital. Figure 3 shows that reserves, U.S. banks do not use a underlying default and loss given reserves at U.S. banks typically fall fixed time horizon. Some institu- default models. somewhere between EL and UL tions either explicitly or implicitly (with capital conceptually held to (through conservative assump- Look-back Period withstand losses at the 99.9 or tions) use a life-of-the-loan time The look-back period is the greater confidence interval). horizon. Reserves are held to number of years of history on cover all losses likely to be which the loss estimate is based. Differences Between Loan Loss incurred for the outstanding port- Banks that will use their internal Reserves and Expected Loss folio, or reserves to cover a multi- models under Basel II to get to EL One might easily look at the year period. Others have adopted are required to base their default difference between the loan loss a “loss confirmation period” con- probabilities (PDs) and losses reserve and expected loss and cept, where reserves are held to given default (LGDs) on at least conclude that banks aren’t being cover the time period from a cred- five to seven years of data, respec- consistent in how they report risk. it event (e.g., major customer, tively. No such requirement exists In fact, this isn’t necessarily so. leading to business failure) to for calculating loan loss reserves. A There are a number of reasons for charge-off. The time horizon may bank may adopt a short or long the two metrics to differ, even if vary by product. For example, look-back period as part of its over- the underlying risks of default retail products may have a one- all loan loss reserve methodology. and recovery are measured the year-or-less time horizon, while It may even choose to vary the same. Here are five: commercial products may have look-back period by product. 1. Time horizon. multiyear time horizons. Still When moving through the 2. Look-back period. other banks have not explicitly business cycle, differences in 3. Unfunded commitments. established a time horizon. look-back periods will produce 4. Expected versus incurred risks. Clearly, an EL measure that different results. Since a longer 5. Charge-off versus economic is based on a one-year horizon look-back period smoothes the loss. cannot be directly compared to economic cycle, if different look- loan loss reserves that are based on back periods are used for EL and Time Horizon a multiyear horizon. Differences in loan loss reserves, the impact will Thanks to Basel II, the indus- time horizon alone could result in be greatest around the try has standardized around a one- major differences between a one- trough/peak in the business cycle. Figure 3 Unfunded Commitments Expected Loss, Unexpected Loss, and the Loan Loss Reserve Expected loss typically Expected Unexpected includes unfunded commitments; loan loss reserves do not. Under Basel II exposure at default (EAD) assumptions, off-balance- sheet commitments are translated into loan equivalents and incorpo- rated into expected loss. Under U.S. accounting rules, losses on Probability of Loss unfunded commitments are Covered by Loan Loss Reserve included as an “other liability” on the balance sheet. To compare 0% Average Reserved Loss Unexpected expected loss with loan loss reserves, the “other liability” 70 The RMA Journal October 2004 Credit Risk Measurement: Avoiding Unintended Results Part 4 would need to be added to the loss resulting from a default event.