Measuring & Pricing Credit Risk in Leasing Portfolios

by Robert F. Cunningham January/February 2008
For many years, bank regulators have been developing and refining the regulatory regime to ensure the safety of the global financial markets against shocks and event risk. Bank capital regulation and the consequent market reaction to the new regulatory measures are creating an environment with increasing motivation to adopt and apply sophisticated quantitative risk management tools.

Independent and captive finance companies are highly likely to be affected by this trend through their need for bank and capital markets funding as well as simply the competitive necessity of applying “best practices” to their operations.1 An overview of the basic concepts in quantitative credit risk analytics follows.

Measuring Credit Risk
Risk management requires knowing two things: the risk one “expects,” which may be priced and reserved for; and the risk of volatility — “unexpected risk” — that capital must cover. A best practice in measuring credit default risk relies on a dual risk approach: the risk that the obligor will default is measured separately from the risk of loss or inadequate recovery from the asset collateral value or other claims on the lessee due to the structure and terms of the transaction. These are quite distinct risks, and proper risk management requires that they be distinctly measured. The obligor risk is the Probability of Default (PD), and the transaction risk is the Loss Given Default (LGD).

The traditional approach to the credit function has been to evaluate creditworthiness using analysis of standard financial statements and other data such as payment history, reputation reports and credit ratings. The analysis, and judgment based on experience, combine for a “go/no go” decision and often a “risk rating” of a borrower. (i.e., categorizing the lessee into a numerical or alphabetic grading scheme from best to worst credits).

The key characteristic of this credit assessment process is the reliance on historical data. Of course, historical accounting-based information on a lessee’s financial condition and performance is essential for proper credit evaluation. But by their nature accounting statements and other historical data provide information about the past. The task of credit evaluation, on the other hand, is to estimate the future ability and willingness of a lessee to meet its obligations.

Modern credit risk management uses advances in financial theory, and the availability of data and data processing technology, to quantify credit default risk in a particularly useful way. Not only are historical accounting data used, but industry data and macroeconomic measures are included as well. In contrast to accounting measures, many of these are market measures and inherently forward-looking estimates that are highly correlated with the default rate — exactly the feature desired for measuring credit default risk. For example, the Standard & Poor’s Credit Risk Tracker™ North America model is based on financial and market data on 17,000 private companies, and with more than six million data points over nine years, has the best predictive record of any private firm credit default model.2

Default Probability
A firm’s PD is the likelihood that it will default within a given time horizon, typically one year. PD measures provide a continuous spectrum of default risk, which can be mapped to any internal risk rating system. Because the methodology for calculating PD precisely calibrates the calculated measure to the observed default behavior of firms in the CRT™ database, it is both highly reliable and an actual default probability, not simply a “ranking” system. Figure 1 displays the PD measure on a logarithmic scale calibrated to S&P’s public debt ratings, a color-coded “go/no go” ranking system and a typical internal risk rating system.

The PD measure provides a degree of precision not found in the conventional risk-rating approach. The “ordinal” rating systems order credits in terms of relative risk but the PD displays precisely how much difference in credit quality exists between two credits. It is apparent, for example, that a risk-rating 4 credit with a PD of approximately .8% is more than three times as risky as a risk-rating 3 at about .25% PD. In addition, market-based approaches for determining probability of default are objective, transparent and consistent across business lines and geographies.

Moreover, a major issue for most internal risk-rating systems is the “lumpiness” in risk discrimination that they exhibit. It is not uncommon for these systems to have as much as 75% of the portfolio graded into only two risk- rating categories, usually the middle of the “pass” range of risk grades, say, grades 3 and 4 as shown in Figure 1. Measuring the risk more precisely allows a much more granular structure of risk discrimination permitting more accurate risk-based provisioning and pricing, which accurately reflects the risk associated with each transaction.

Expected Loss
Risk-based pricing requires a measure of Expected Loss (EL), sometimes referred to as “provisioning,” because the loss is “expected” it is viewed as simply part of the cost of doing business with that credit and hence should be reflected in the pricing. The basic formula for EL is simply:

where: PD = Probability of Default
           EAD = 
Exposure at Default
(Unamortized Balance or UAB)
           LGD= Loss Given Default

For leases, unlike bank loans, the Loss Given Default is generally both better understood, since it is essentially the same as the UAB less the collateral value at the time of default, and is significantly lower than for all but the most senior secured bank loans.3 At any given point during the term of the loan or lease, the EL is determined by the PD at that point and the UAB. Since both can be taken as “givens” for a particular equipment type, the calculated EL will be driven by the equipment’s anticipated depreciation curve. LGD becomes just the difference between the unamortized balance and the expected FMV of the asset:

Combining equations (1) and (2) we determine the EL % as:

For example, a five year lease of equipment with an expected FMV at 30 months of 48% of original cost and an UAB of 62% made to a credit determined to have an PD of 0.75% (BB equivalent) would have an Expected Loss percent of:

This amount would be added to the lessor’s required spread as a “cost of risk” in determining risk-based pricing. Note that EL can also be used to determine the loan loss reserves on a portfolio or subportfolio basis because EL is additive. The sum of all the transaction ELs is the portfolio EL, the quantitative measure of Allowance for Lease and Loan Losses (ALLL), or Loss Reserves.

Unexpected Loss
In addition to the Expected Loss, we also need to know the variance around the EL, or the Unexpected Loss (UL). Since we can take the EAD and PD as givens, UL is also driven by the distribution of asset values. Figures 2a and b illustrate the asset value distribution: Figure 2a shows a typical value distribution at a point in time and Figure 2b illustrates the depreciation curve “distribution,” (i.e., the asset value distribution over time.) Once the asset value distribution is determined the UL can be calculated4 as follows:

where: LGD = Standard Deviation of the LGD

The volatility (Standard Deviation) of the LGD follows directly from, and is equal to, the standard deviation of the asset value distribution (See Figure 2a). From equation (4) the UL may be calculated given knowledge or assumptions about the asset value distribution. For example, at a point in the middle of the lease or loan term, with a 20% LGD (UAB = 50; E(FMV) = 40), an asset with a volatility (or SD) of 10%. For example, with a range of between 36 and 44 around the expected FMV of 40, would determine, for a lessee with a PD of .75%, a UL of .93% or 93 bps of original equipment Cost (OEC), or 186 bps relative to UAB.5

Economic Capital
The calculation of both EL and UL permits an approximation of Economic Capital. Economic Capital is the capital required to cover the “worst case” in the loss distribution at a desired level of confidence. It relates to a portfolio with its particular portfolio EL and UL. The difference between the portfolio EL and the “worst case” capital required, determined by the portfolio UL, is Economic Capital. It covers risk that is not “expected” and “provisioned by calculation of EL. The aim of risk-based pricing is to charge a return on this amount of capital so that pricing reflects the entire risk of an incremental lessee.

Economic Capital for a transaction can be approximated based on the portfolio’s required capital and the lessee’s correlation with the portfolio. With capital (net of EL) at 8% of portfolio and the lessee UL of 186 bps from the example above, an estimate of portfolio UL at 1% and of correlation at .4 gives:

For a required pre-tax return on capital of 30%, the return on Economic Capital (ROEC) would be:

Risk-Based Pricing Model
In risk-based pricing, both the EL and a return on Economic Capital are explicitly calculated as expenses in clearing the established hurdle rate.7 A pricing matrix can be constructed for each asset class or subportfolio in which Economic Capital Factors are calculated and applied to each transaction.

These analytics can also be used to determine the degree of any “mispricing,” (i.e., the extent to which the pricing structure does not, in fact, reflect risk.) Figure 3 shows the results of an analysis of actual pricing compared to calculated risk-based pricing.8 This type of analysis will reveal possible pricing opportunities both where better credits are “overpriced” and worse credits “underpriced” on a risk-adjusted basis. Syndication or securitization decisions can be made for assets that may be dragging down the portfolio risk/return dynamics and funding costs can thereby be optimized as well.

Conclusion
Advanced risk analytics developed in recent years and increasingly used by banks and other financial institutions are now both accessible and beneficial to leasing and finance companies as well. Risk-based pricing provides the link between credit risk and market pricing, leading to potentially superior performance. Lessors, which likely have superior asset knowledge and data, are especially well suited to introduce risk-based pricing. They may introduce the technology in stages and move toward quantitative portfolio management, replacing the traditional “originate and hold” model. The payoff is likely to be substantial: “Aggregate capital requirements are expected to drop for those firms that apply advanced measurement approaches … to credit risks … bringing increased profit margins … better priced products, and market share.”9

References & Notes
1 See The Basel II Accord: What Does It Mean for the North American Leasing Market?, Equipment Finance and Leasing Foundation white paper, 2003 for a comprehensive discussion of the impact of the Basel II Accords on bank and non-bank leasing companies.
2 Credit Risk Tracker™ North America Technical Documentation, Standard & Poor’s, September 2006, p. 5.
3 Mathias Schmit and Julien Stuyck, “Recovery Rates in the Leasing Industry”, Brussels: LeaseEurope, September 2002.
4 Stephen Kealhofer, “Managing Default Risk in Derivative Portfolios”, in Derivative Credit Risk: Advances in Measurement and Management. London: Renaissance Risk Publications, 1995, as referenced in Anthony Saunders, Credit Risk Management, New York: John Wiley & Sons, Inc., 1999, p.117.
5 This discussion is simplified and ignores possible correlation between defaults and LGD as well as asset value correlations for different types of assets in the portfolio. However, it is not unreasonable to assume that asset values are highly correlated for a given product line. Also it is well known that concentration limits on lessees can substantially diversify away much of the UL. Precisely how much depends on the correlations among the borrowers with the portfolio as a whole. However, it is possible that captives’ portfolios have a relatively high degree of correlation, at least within sub-portfolios for different asset classes.
6 Allocation of Economic Capital to the incremental exposure depends on its risk contribution, i.e., the transaction’s marginal contribution to total portfolio Unexpected Loss, and is referred to as “Exposure Capital” or the “Capital Attribution”. This allocation can be computed using a “capital multiple” which scales the individual attributions to the portfolio’s total capital. The formula for this approximation of Economic Capital is: (Cp–ELp)/ULp*Pip*ULi where Cp is required capital for the portfolio, ELp is the portfolio Expected Loss, ULp is the portfolio Unexpected Loss, Pip is the correlation of the exposure with the portfolio, and ULi is the transaction Unexpected Loss. See Charles Smithson and Greg Hayt, “A Guide for Capital Allocation”, Risk, June 2001.
7 “The Basel II Accord and Risk-Based Pricing”, Equipment Lease and Finance Foundation, February 23, 2004, p.21.
8 ibid., p. 22.
9 “Turning Basel II Compliance Into a Competitive Advantage”, Christopher McLaughlin, Bank Technology News, Vol. 17, No. 8 (August 2004), p. 48.

Robert F. Cunningham is senior vice president, client services at Inmatrix, Inc. He leads risk consulting for Inmatrix clients, applying the company’s analytical products to the development of superior risk metrics, primarily for community banks and the SME business segment. Most recently, he led Avalon Analytics, a consultancy he founded to assess risk and pricing issues in commercial finance companies.

Cunningham has more than 20 years experience in leasing and corporate finance at major financial institutions including PruCapital, Citicorp and Keybank for both small-ticket “program” and large-ticket structured transactions. His background includes roles in origination, structuring, and credit and risk analysis, with extensive experience in pricing and negotiation. He received a BA degree cum laude from Dartmouth College and an MBA degree from Harvard Business School.

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