ECONOMIC CAPITAL, LOAN PRICING AND RATINGS ARBITRAGE

Transcription

1 ECONOMIC CAPITAL, LOAN PRICING AND RATINGS ARBITRAGE Maike Sundmacher = University of Western Sydney School of Economics & Finance Locked Bag 1797 Penrith South DC NSW 1797 Australia. Phone: m.sundmacher@uws.edu.au Craig Ellis University of Western Sydney School of Economics & Finance Locked Bag 1797 Penrith South DC NSW 1797 Australia. Phone: c.ellis@uws.edu.au Keywords: economic capital, loan pricing JEL codes: G210, G280, G320 =Contact author - 1 -

2 ECONOMIC CAPITAL, LOAN PRICING AND RATINGS ARBITRAGE Abstract The role of economic capital has grown significantly in recent years. Although not a regulatory requirement, an increasing number of financial institutions use economic capital for such purposes as measuring and managing the performance of people, products, risk exposures, and to manage and optimise capital levels. From a risk management perspective, pricing loans based on economic capital is preferred to regulatory capital for its ability to better capture the unique risks and cash flows associated with an exposure. This paper examines the issue of economic capital and its use in loan pricing. Using a loan pricing model based on economic capital we examine the impact of ratings on loan price and show how financial institutions can engage in ratings arbitrage to target higher external credit ratings without having to increase capital levels. The potential implications for regulatory authorities of such arbitrage are also discussed

3 ECONOMIC CAPITAL, LOAN PRICING AND RATINGS ARBITRAGE 1. Introduction The Basel II capital framework published by the Basel Committee on Banking Supervision (BCBS) in June 2006 requires financial institutions to hold minimum capital levels against their market, credit and operational risk exposures. For credit risk the BCBS provides financial institutions with a choice of three increasingly sophisticated approaches: Standardised, Foundations Internal Ratings-Based, and Internal Ratings-Based. By providing a spectrum of approaches the BCBS addresses one of the major criticisms associated with the existing capital guidelines, namely that capital calculations are the same for all institutions, independent of their size, the complexity of their activities, and their sophistication in risk management and measurement. While the calculation for credit risk capital is pre-determined by the BCBS under the Standardised approach, the Internal Ratings-Based approaches allow financial institutions to use internally generated data in their capital calculations. To be eligible to use the Internal Ratings-Based approaches a financial institution needs to satisfy certain qualifying quantitative and qualitative criteria 1. Compliance with the criteria may require significant investment by the institution. The incentive however is that the use of an Internal Ratings-Based approach is likely to result in a better alignment of risk and capital. This is important as excess capital is expensive for institutions, in both monetary terms and with regards to performance measurement, while too low capital levels might threaten the survival probability of an institution in case of financial distress. 1 The minimum requirements for the Internal Ratings-Based approaches are outlined in Basel Committee on Banking Supervision (2006: )

4 In addition to mandatory regulatory capital calculations, institutions may also use internally derived data to estimate their capital requirements. These internal estimates are typically based on the concept of economic capital, which is generally considered to be a better indicator of the riskiness of assets as it considers the unique risks and cash flows associated with the institution s exposures. PWC (2005: 3) find that an increasing number of financial institutions use economic capital to measure and manage the performance of people, products, risk exposures and to optimise capital levels. This combined with the imminent implementation of the Basel II framework, suggests that economic capital is gaining greater importance in financial institutions risk measurement and management activities. This paper examines the issue of economic capital and its use in loan pricing. We adopt the approach outlined by Ford and Sundmacher (2007) and assume that financial institutions price their loans with the aim to generate a target return on employed capital by applying a bottom-up approach, in which the specific risks, costs and revenues associated with the loan are each considered. The advantage of the approach is that financial institutions hold neither excess nor insufficient capital against their exposure and thus avoid mis-pricing their risks and costs. While overpricing loans might render financial institutions uncompetitive, underpricing increases the financial institution s risk exposure as risks and costs are not adequately captured in the price of the loan and thus the institution will be more susceptible to financial distress. Taking this into consideration, economic capital can be regarded as a form of risk currency in financial institutions (Hull, 2007: 365) as it directly reflects the risk levels taken by a bank. The paper is structured as follows. In the next section we define economic capital and identify its different components to isolate the variables that ultimately drive capital levels. Next we discuss the choice of the beta distribution in determining economic capital levels. The third section introduces a loan pricing approach based on - 4 -

5 economic capital. In the fourth we demonstrate the potential for ratings arbitrage through model adjustments in economic capital calculations using the beta distribution. The final section concludes and highlights potential implications for regulatory authorities and other bank stakeholders, such as credit rating agencies. 2. The Nature of Economic Capital Economic capital is commonly described as the amount of capital required to capture potentially large losses in a financial institution (Ong, 1999: 57; Berg-Yuen and Medova, 2004: 7), where the level of capital is dependent on the institution s chosen confidence level and time horizon (Jokivuolle, 2006: 7; PWC, 2005: 3) 2. The confidence level can be linked to the target credit rating of the institution. Institutions with high levels of capitalisation are perceived to have a low default probability. Thus, a higher capital level usually attracts a higher credit rating. Alternatively, an institution that targets a particular external credit rating such as AA, will be required to hold a certain level of capital. Hence, Jokivuolle s (2006: 7) definition of economic capital as the amount of capital required for a given credit rating is practical, particularly given that external credit ratings are publicly observable. In order to better understand the nature of economic capital it is beneficial to decompose it into its different components. The concepts of expected and unexpected losses form the basis of the measure of economic capital. The expected losses (EL) of a loan or loan portfolio are seen as a normal cost of doing business (Smithson 2003: 8) and as such should not attract capital. Rather financial institutions should consider the EL in the pricing of a loan transaction. 2 Crouhy et al (2006: 370) suggest an alternate definition and describe economic capital as the sum of risk and strategic risk capital, whereby strategic risk capital consists of two components: goodwill and burnedout capital. While this definition is more comprehensive as it includes potential losses from bad strategic investments, it is impractical for a general definition of economic capital given that strategic investments are not observable

6 The expected loss (EL) is dependent on three input variables: the expected size of the credit exposure at default (L), the borrower s expected default frequency (EDF) and the loss given default (LGD). The EL can be calculated as: EL = L EDF LGD (1) In practice we estimate the potential credit exposure at default (L) to equal the face value of the loan. The borrower s EDF is obtained from publicly available data as published by Standard & Poor s (S&P) or Moody s for various time horizons 3. Given that economic capital is usually dealt with on a one-year time horizon, we consider the following one-year EDFs that apply to various S&P credit ratings. Table 1: Cumulative Average Default Rates by Rating Multiplier, (%) Rating Year 1 Rating Year 1 AAA to AA 0.00 BB AA BB 0.86 A BB A 0.07 B A B 7.10 BBB B BBB 0.25 CCC/C BBB Source: Standard & Poor s (2007: 12) In so far as loss given default is dependent on loss experiences, it is difficult to obtain accurate LGDs for bank loans. Thus this figure is often approximated using recovery rates on publicly issued or privately placed debt. Table 2 shows recovery rates and corresponding 3 EDF measures can also be internally determined by financial institutions using past loss experience on loans of similar quality

7 LGDs for private debt portfolios by seniority class, while Table 3 shows the respective data for publicly placed debt by credit risk rating. Table 2: Recovery Rates and Corresponding LGDs in Private Debt Portfolios by Seniority Class Seniority Average recovery ($) Average LGD ($) Senior secured Senior unsecured Senior subordinated Subordinated Junior subordinated Source: Carey (1998: 1373) Table 3: Recovery Rates and Corresponding LGDs for Publicly Placed Debt by Credit Risk Rating Credit rating Average recovery rate (%) Average LGD (%) AA A BBB BB B < B Source: Carty and Lieberman (1996: 13) Assuming credit exposure at default (L) and LGD as fixed factors, unexpected loss (UL) can be calculated as follows 4 : UL = σ = EL ( LGD L) (2) 4 Matten (2000: 193) states that most credit risk models use this measure, which assumes that default on a loan is a single binomial event. A more sophisticated approach would incorporate volatility in the LGD

8 Following Ong (1999: 57) and Kiefer and Larson (2006: 2), we define economic capital as the number of standard deviations from the expected loss. Thus, economic capital is simply a multiple (m) of the exposure s UL: EC = UL m (3) While UL is dependent on the borrower s creditworthiness as observed in their credit rating, the multiple m is dependent on the institution s chosen confidence level and thus, ultimately, on the institution s targeted credit rating. As implied by Table 1, the higher the targeted credit rating, the lower the EDF and thus the higher the confidence level. When determining the multiplier it is important to choose a probability distribution that captures the limited upside risk and large downside risk of credit risk. One distribution that provides a good fit for credit risk, for which loss distributions are typically highly skewed and leptokurtic, is the beta distribution. 3. The Use of the Beta Distribution in Economic Capital Calculations The beta distribution belongs to the family of parametric probability distributions and is dependent on two constants: α which controls the steepness of the function, and β which controls the fatness of the tail. The use of the beta distribution in economic capital calculations has a twofold justification. First, on a theoretical level the beta distribution is appropriated by the need to capture the likelihood of extreme losses via the tail of the distribution. Second, on an empirical level the beta distribution simplifies the economic capital calculation as it does not allow for multiple defaults by a borrower during the tenor of the loan. Default is one parameter used to calculate - 8 -

9 expected loss. The expected loss (EL) is represented by the mean (µ) of the distribution and is defined as: µ α = EL = α + β (4) It follows from (4) that both shape parameters are dependent on the mean of the distribution and thus on the size of EL: α β + EL = (5) EL α β = EL (6) EL The variance (σ 2 ) of the distribution is defined as: σ = UL = 2 2 αβ α β α β 2 ( + )( + + 1) (7) The square root of the variance represents the unexpected loss (UL) of the distribution. Given that the variance is determined by the shape parameters α and β, and that α and β are in turn driven by the mean, it follows that the ultimate drivers of the variance and thus UL, are the expected size of the credit exposure at default (L), the borrower s expected default frequency (EDF) and the loss given default (LGD). Similarly, using a beta distribution the multiple m is driven by expected and unexpected losses: - 9 -

10 ( x µ ) m = (8) σ wherein x represents the value at which to evaluate the probability function for a desired confidence level. In equation (3) we showed that economic capital is the product of the standard deviation of a loan loss distribution and the multiple m. Substituting (2) and (8) into (3) gives: EC = EL ( LGD EL) x EL EL ( LGD EL) (9) The significance of Equation (9) is to highlight the strong dependence of economic capital on expected loss levels and, given the drivers of expected losses, even more prominently LGDs. 4. Implications for Loan Pricing based on Economic Capital From a risk measurement and management perspective, pricing loans based on economic capital is preferred to regulatory capital for its ability to better capture the unique risks and cash flows associated with an exposure. One reason is that economic capital is partially dependent on the borrower s creditworthiness. Further, economic capital captures the risk appetite of the lending institution by aligning the level of capital held against a given exposure with the institution s external credit rating. If a financial institution prices its assets based on a target return on economic capital, then the asset price will be primarily driven by the required profit on the loan. The required profit (π)

11 is the product of the economic capital held against the exposure and the institution s target hurdle rate (h): π = EC h (10) If we consider h to be fixed, the required profit on a loan is determined by the amount of capital held. The level of economic capital, it will be remembered, is dependent on unexpected losses and the multiple m. While the UL is dependent on the borrower s credit quality via the EDF and LGD, the multiple m is determined by the bank s target solvency standard, i.e. their target credit rating. A financial institution with a higher credit rating is required to hold comparatively more capital than one with a lower rating to achieve the corresponding higher solvency standard. A higher credit rating will also increase the multiple m and the corresponding required profit on a transaction. We use Carty and Lieberman (1996: 3) LGDs to summarise the impact of a change in a financial institution s credit rating on economic capital levels for BB, BBB and A rated borrowers. EDFs are taken from S&P s annual global default study (2007: 12). The full set of results, including information on EL, UL, m and economic capital, is provided in Appendix

12 Figure 1: Economic Capital Requirements as Percentage of Exposure by Bank and Borrower Credit Rating % Economic Capital (% of Exposure) % % % % % % AAA AA A BBB Bank Target Rating BB borrower BBB borrower A borrower Consistent with the higher default probability associated with more lowly rated borrowers, we observe from Figure 1 that economic capital increases with a decrease in the borrower s credit rating. A higher EDF will result in higher EL and UL for the exposure and consequently a higher multiple m. The implication is that a financial institution granting a riskier exposure needs to hold more capital. We can also observe that for all borrower ratings economic capital increases with an increase in the institution s target rating. The implication is that it is not only the credit rating of the borrower, but also the targeted credit rating of the lending institution that drives economic capital consideration 5. Targeting a higher external credit rating may however have negative consequences for either the borrower and/or the lending institution. Following Equation (10) it can be seen that a higher economic capital level combined with a constant hurdle rate will yield an increased 5 This finding is in line with Ford and Sundmacher (2007)

13 required profit on a loan and, all else equal, an increased loan price 6. The increased capital level in this scenario is driven by the higher targeted solvency standard of the lending institution, as the EDF of any borrower category is constant. The borrower is subsequently penalised for the institution s changing risk appetite by the increased loan price, but in targeting an increased rating and passing the resulting pressure on the required profit onto borrowers, the institution also runs the risk of diminished market share if borrowers fail to accept the higher interest charge. Alternatively the institution could adopt a pricing strategy that does not fully capture the risks and costs associated with the transaction. For instance, the institution could hold an increased capital level without varying the required income on the loan but consequently would need either to revise its target profitability, or to reduce operating expenses such as loan loss provision or monitoring costs. This latter however may expose the institution to increased default and/or operational risks. The ideal scenario for the financial institution would be to target a higher solvency standard without having to hold more economic capital and thereby avoid upward pressure on loan prices. Given the above discussion, this seems difficult to achieve. Re-examining the underlying drivers of UL and the multiple m in the beta distribution, a means of achieving this goal can be shown. The three input variables of interest here are the exposure at default, EDF and LGD. The size of the exposure can be assumed to be constant for non-revolving loan facilities. Given that EDFs are readily observable if the borrower already has rated debt, this variable is likewise assumed to be constant. This leaves us with LGD and the question of whether an institution targeting a higher credit rating and thus higher solvency standard is able to maintain the economic capital charge stable by varying LGD levels. 6 Though Jackson et al (2002) assert that a bank with a higher credit rating benefits from reduced wholesale funding costs and reduced costs in derivative markets, Ford and Sundmacher (2007) show that reduced wholesale funding cost are generally insufficient to offset loan price pressures arising from the higher economic capital requirement

14 The following Figures 2-4 illustrate the sensitivity of economic capital to LGD levels for BB, BBB and A rated borrowers respectively given various target credit ratings for the lending institution. Data corresponding to these figures is provided in Appendix 2 for each exposure level. Summarising the findings of Figures 2 4, economic capital as a percentage of exposure increases with increasing LGD for all borrower ratings given a lender target rating of BBB or A. Further, BBB or A rated lenders overall capital levels decrease with increasing borrower creditworthiness. The reason is the decreased borrower EDF associated with a higher rating, resulting in a lower EL, UL, multiplier m and consequently capital charge. For AA and AAA rated institutions however we observe capital levels that are at or close to 100% in Figures 2 4, and for AA lenders specifically we observe a kink in the economic capital versus LGD relation for all borrower ratings in the figures 7. Furthermore this kink becomes more pronounced with increased borrower rating from BB to A. The kink itself is a product of the estimating procedure described by the above equations for the calculation of the economic capital under the conditions that the cumulative default probability remains a constant for a given lender / borrower combination The marginal differences in capital between an AA and a AAA rated bank arise from the implied one-year solvency standards. According to Standard & Poor s (2007: 13) both target ratings imply a 0% default probability. In order to distinguish between the ratings we used the beta distribution and evaluated multipliers and resulting capital levels using the upper boundary of the 100% solvency standard for AAA rated and lower boundary for AA rated banks. For LGD values below the average LGD in Table 1, the value at which to evaluate the beta distribution is constant (100%) for AA rated lending institutions. At the average LGD the value at which to evaluate the beta distribution decreases and is increasing thereafter. More pronounced kinks are due to the initial decline in the value at which to evaluate the function being greater for more highly rated borrowers. For AAA rated lending institutions the value at which to evaluate the beta distribution is constant for all LGDs in the specified range, hence resulting in a constant (100%) LGD

15 Figure 2: Economic Capital Sensitivity to LGD BB borrower % % Capital (% of exposure) 90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 29% 32% 35% 38% 41% 44% 47% LGD AAA AA A BBB Turning to Figure 2 we see that given a BB rated exposure, a BBB rated lending institution is able to target an A rating without any corresponding in increase capital as a percentage of the exposure. This is achieved by initially assuming LGDs in the range 47% - 49% and then revising these to as low as between 29% - 31% once it moves to the A rating

16 Figure 3: Economic Capital Sensitivity to LGD BBB borrower % % 90.00% Capital (% of exposure) 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 23% 26% 29% 32% 35% 38% 41% LGD AAA AA A BBB In both Figures 3 and 4 economic capital levels are below the regulatory minimum of 8 % for specific LGDs and lending institution credit ratings. In Figure 3, for a BBB rated borrower and a BBB rated lender regulatory capital requirements are not satisfied for any LGD 30%. Similarly in Figure 4, for A rated borrowers regulatory minimums are not fulfilled for any LGD given a BBB rated lender and for any LGD 30% given an A rated lender

17 Figure 4: Economic Capital Sensitivity to LGD A borrower % % 90.00% Capital (% of exposure) 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 14% 17% 20% 23% 26% 29% 32% LGD AAA AA A BBB Based on results provided in Figures 2 4, there is limited opportunity for financial institutions to increase their solvency standard while maintaining capital levels by varying LGDs only. While there is some manipulation potential for a BBB rated institution with a BB exposure targeting an A rating, it might be difficult to justify the necessary decrease in the LGD given that the riskiness of the exposure has not changed. By varying the riskiness of assets and LGD levels it is possible however for institutions to target higher ratings without having to increase their capital levels. Indeed, there is even opportunity to decrease capital and subsequently loan price given a higher target rating for the lending institution. This ratings arbitrage opportunity is shown in Figures 5-7 and the supporting data tables in Appendix 2. We begin with the case of a lending institution with an initial rating of BBB and exposure to a BB rated borrower. For LGDs in the range 29% - 49%, capital as a percentage of exposure ranges from 27.80% % respectively. Now for an A rated lending institution with a

18 BBB exposure, capital levels range between 21.87% % given LGDs between 23% - 43%. Comparing these risk and LGD combinations shows that a BBB rated lender can maintain or even decrease its capital levels if it targets borrowers with a higher credit rating. This is shown in Figure 5. In this scenario a decrease in LGD can be easily justified by the expected lower default probability that arises from the higher credit rating of the borrower. Figure 5: Economic Capital Levels for BBB rated banks / BB rated Exposures and A rated banks / BBB rated Exposures by LGD 60.00% Economic capital (% of exposure) 55.00% 50.00% 45.00% 40.00% 35.00% 30.00% 25.00% 20.00% 23% 26% 29% 32% 35% 38% 41% 44% 47% LGD BBB bank rating / BB exposure A bank rating / BBB exposure Similarly a BBB rated lender with a BBB exposure is able to maintain or decrease capital if it increases its solvency standard congruent to an A rating and targets A rated borrowers, as shown in Figure

19 Figure 6: Economic Capital Levels for BBB rated banks / BBB rated Exposures and A rated banks / A rated Exposures by LGD Economic capital (% of exposure) 12.00% 11.00% 10.00% 9.00% 8.00% 7.00% 6.00% 5.00% 4.00% 3.00% 2.00% 14% 17% 20% 23% 26% 29% 32% 35% 38% 41% LGD BBB bank rating / BBB exposure A bank rating / A exposure Given the case of a BBB/BBB and an A/A combination of lender rating and borrower rating, capital levels however fall below the required regulatory minimum of 8%, and our ratings arbitrage opportunities are limited here to the 30% LGD 34% range. Notwithstanding this, the findings again show the potential for lending institutions to target a higher rating without having to increase their capital levels. A third scenario is shown in Figure 7. In this case the initial lender rating is A with a BB rated exposure. For this combination, LGD levels between 41% - 49% attract capital levels from 71.01% % respectively. A corresponding AA rated lender with an A rated exposure and LGD levels between 24% - 31% percent needs to hold between 69.68% and 82.63% in capital

20 Figure 7: Economic Capital Levels for A rated banks / BB rated Exposures and AA rated banks / A rated Exposures by LGD 85.00% Economic capital (% of exposure) 80.00% 75.00% 70.00% 65.00% 60.00% 24% 27% 30% 42% 45% 48% LGD A rated bank / BB exposure AA rated bank / A exposure While the lending institution is able to maintain or decrease capital levels similar to the first two scenarios, the structural change required in the riskiness of the loan portfolio might take a longer time to be achieved in this instance. 5. Conclusions As financial institutions increasingly use economic capital to measure and manage their risk exposures and to optimise capital levels, issues relating to economic capital and loan pricing have become increasingly important. In this paper we address the issue of credit ratings and loan pricing calculations using economic capital. Using a beta distribution, we identify the underlying components of economic capital and their corresponding drivers, namely exposure size at default, the default probability of the borrower and loss given default (LGD). Using published LGDs we show the potential for financial institutions to maintain or even lower capital levels while increasing solvency standards to achieve a higher credit rating. The resulting advantages for the institution of this ratings arbitrage are manifold. More highly

21 rated institutions are perceived to be less likely to default and thus lenders are generally willing to accept lower income on provided funds. If at the same time the institution is able to maintain capital levels, it is able to keep the price of its loans constant or even lower the price as there is no pressure on the required profit on a transaction arising from higher capital levels. The effect on the neutral loan price would be even more pronounced if the institution targeted a more highly rated borrower as expected losses that are associated with the transaction decrease as a result of the borrower s lower EDF. We could even argue that the hurdle rate for a more highly capitalised institution could be revised downward due to the lower leverage of the institution that results from the increased solvency standard. The effect would be a lower required profit on the loan transaction this in combination with lower funding costs and a lower level of loan loss provisions would put the lending institution into a situation in which it could either drastically reduce loan prices or keep loan prices stable in order to subsidise other products. That said however one problem does arise with respect to the quality of LGD data. Financial institutions can either estimate their own LGDs based on historic loss experiences or approximate LGDs using data from publicly available loss default studies such as the ones undertaken by Carey (1998) or Carty and Lieberman (1996). Both alternatives are not entirely desirable. A problem with internally generated data is the potential for manipulation it is generally difficult for regulatory authorities or credit rating agencies to verify the data s validity. On the other hand, published data on corporate defaults predominantly relates to issued bonds and is often not appropriate given the structural differences between bonds and bank loans. Yet it is the chosen LGD level, together with the riskiness of the loan portfolio that drives capital levels

22 In the absence of high quality data, it is up to credit rating agencies and regulatory authorities to either validate internally generated data or to judge the appropriateness of publicly available data. This might prove to be a difficult task given the limited man power of regulatory authorities and credit rating agencies and the complex nature of financial institutions lending activities. Thus it is questionable if the ratings arbitrage opportunities we have identified will be limited through supervisory rigor

23 References Basel Committee on Banking Supervision Basel II: International Convergence of Capital Measurement and Capital Standards: a Revised Framework Comprehensive Version, Bank for International Settlements, Basel, June. Berg-Yuen, P.E.K. and Medova, E.A Economic Capital Gauged. Research Papers in Management Studies. Working Paper no 07/2004. University of Cambridge: Judge Institute of Management. Carey, M Credit Risk in Private Debt Portfolios. Journal of Finance. 53(4) Carty, L.V. and Lieberman, D Corporate Bond Defaults and Default Rates: Special Report. Moody s Investor Service, January. Crouhy, M., Galai, D. and Mark, R The Essentials of Risk Management. New York: McGraw-Hill. Ford, G. and Sundmacher, M Bank Credit Rating Dynamics. International Review of Business Research Papers. 3(4) Hull, J.C Risk Management and Financial Institutions. New Jersey: Pearson Education. Jackson, P., Perraudin, W. and Saporta, V Regulatory and Economic Solvency Standards for Internationally Active Banks. Journal of Banking and Finance

24 Jokivuolle, E. and Peura, S Rating Targeting and the Confidence Levels Implicit in Bank Capital. Bank of Finland Research Discussion Papers. 27. Kiefer, N.M. and Larson, C.E Evaluating Design Choices in Economic Capital Modeling: A Loss Function Approach. Economics Working Paper No Washington DC: Office of the Comptroller of Currency. Matten, C Managing Bank Capital: Capital Allocation and Performance Measurement. 2nd ed. Chichester: John Wiley & Sons. Ong, M.K Internal Credit Risk Models: Capital Allocation and Performance Measurement. London: Risk Books. PWC and Economist Intelligence Unit Effective Capital Management: Economic Capital as an Industry Standard? PWC FS Briefing Programme. 13th Briefing. Smithson, C.W Credit Portfolio Management. New Jersey: John Wiley & Sons. Standard & Poor s Annual 2006 Global Corporate Default Study

25 Appendix 1: Level of Economic Capital for Various Bank Ratings by Borrower Rating Table A1.1: BB rated Borrower Target Bank Rating AAA AA A BBB Borrower EDF 0.86% 0.86% 0.86% 0.86% LGD 39% 39% 39% 39% Alpha Beta EL % % % % UL % % % % Target Solvency % % 99.93% 99.75% Multiplier Economic capital % % % % Table A1.2: BBB rated Borrower Target Bank Rating AAA AA A BBB Borrower EDF 0.25% 0.25% 0.25% 0.25% LGD 33% 33% 33% 33% Alpha Beta EL % % % % UL % % % % Target Solvency % % 99.93% 99.75% Multiplier Economic capital % % % % Table A1.3: A rated Borrower Target Bank Rating AAA AA A BBB Borrower EDF 0.07% 0.07% 0.07% 0.07% LGD 24% 24% 24% 24% Alpha Beta EL % % % % UL % % % % Target Solvency % % 99.93% 99.75% Multiplier Economic capital % % % %

26 Appendix 2: Sensitivity of Economic Capital to LGD by Bank and Borrower Rating Table A2.1: BB rated borrower Target Bank Rating LGD AAA AA A BBB 29% 99.75% 99.75% 50.21% 27.80% 30% 99.74% 99.74% 52.00% 28.93% 31% 99.73% 99.73% 53.78% 30.08% 32% 99.72% 99.72% 55.55% 31.25% 33% 99.72% 99.72% 57.32% 32.43% 34% 99.71% 99.71% 59.08% 33.63% 35% 99.70% 99.70% 60.83% 34.85% 36% 99.69% 99.69% 62.57% 36.08% 37% 99.68% 99.68% 64.30% 37.33% 38% 99.67% 99.67% 66.01% 38.60% 39% 99.66% 98.09% 67.70% 39.98% 40% 99.66% 98.36% 69.37% 41.20% 41% 99.65% 98.58% 71.01% 42.53% 42% 99.64% 98.77% 72.64% 43.88% 43% 99.63% 98.93% 74.23% 45.25% 44% 99.62% 99.06% 75.80% 46.64% 45% 99.61% 99.17% 77.33% 48.05% 46% 99.60% 99.26% 78.82% 49.48% 47% 99.60% 99.33% 80.28% 50.93% 48% 99.59% 99.38% 81.70% 52.41% 49% 99.58% 99.42% 83.07% 53.90%

27 Table A2.2: BBB rated borrower Target Bank Rating LGD AAA AA A BBB 23% 99.94% 99.94% 21.87% 6.10% 24% 99.94% 99.94% 22.95% 6.37% 25% 99.94% 99.94% 24.04% 6.63% 26% 99.94% 99.94% 25.15% 6.90% 27% 99.93% 99.93% 26.27% 7.17% 28% 99.93% 99.93% 27.40% 7.44% 29% 99.93% 99.93% 28.55% 7.71% 30% 99.93% 99.93% 29.72% 7.98% 31% 99.92% 99.92% 30.89% 8.25% 32% 99.92% 99.92% 32.09% 8.51% 33% 99.92% 92.03% 33.31% 8.79% 34% 99.92% 92.97% 34.53% 9.05% 35% 99.91% 93.83% 35.78% 9.32% 36% 99.91% 94.61% 37.04% 9.59% 37% 99.91% 95.31% 38.32% 9.86% 38% 99.91% 95.94% 39.62% 10.13% 39% 99.90% 96.50% 40.94% 10.40% 40% 99.90% 97.00% 42.28% 10.67% 41% 99.90% 97.44% 43.64% 10.94% 42% 99.90% 97.82% 45.02% 11.21% 43% 99.89% 98.16% 46.42% 11.48%

28 Table A2.3: A rated borrower Target Bank Rating LGD AAA AA A BBB 14% 99.99% 99.99% 3.69% 0.15% 15% 99.99% 99.99% 3.96% 0.15% 16% 99.99% 99.99% 4.22% 0.16% 17% 99.99% 99.99% 4.49% 0.16% 18% 99.99% 99.99% 4.76% 0.16% 19% 99.99% 99.99% 5.02% 0.17% 20% 99.99% 99.99% 5.29% 0.17% 21% 99.99% 99.99% 5.55% 0.17% 22% 99.98% 99.98% 5.82% 0.17% 23% 99.98% 99.98% 6.09% 0.17% 24% 99.98% 69.68% 6.36% 0.17% 25% 99.98% 71.77% 6.62% 0.17% 26% 99.98% 73.79% 6.89% 0.17% 27% 99.98% 75.72% 7.16% 0.17% 28% 99.98% 77.58% 7.43% 0.17% 29% 99.98% 79.34% 7.69% 0.16% 30% 99.98% 81.03% 7.96% 0.16% 31% 99.98% 82.63% 8.23% 0.16% 32% 99.98% 84.15% 8.50% 0.15% 33% 99.98% 85.58% 8.76% 0.15% 34% 99.98% 86.93% 9.03% 0.14%

29 ECONOMIC CAPITAL, LOAN PRICING AND RATINGS ARBITRAGE Maike Sundmacher = University of Western Sydney School of Economics & Finance Locked Bag 1797 Penrith South DC NSW 1797 Australia. Phone: m.sundmacher@uws.edu.au Craig Ellis University of Western Sydney School of Economics & Finance Locked Bag 1797 Penrith South DC NSW 1797 Australia. Phone: c.ellis@uws.edu.au Keywords: economic capital, loan pricing JEL codes: G210, G280, G320 =Contact author - 1 -

30 ECONOMIC CAPITAL, LOAN PRICING AND RATINGS ARBITRAGE Abstract The role of economic capital has grown significantly in recent years. Although not a regulatory requirement, an increasing number of financial institutions use economic capital for such purposes as measuring and managing the performance of people, products, risk exposures, and to manage and optimise capital levels. From a risk management perspective, pricing loans based on economic capital is preferred to regulatory capital for its ability to better capture the unique risks and cash flows associated with an exposure. This paper examines the issue of economic capital and its use in loan pricing. Using a loan pricing model based on economic capital we examine the impact of ratings on loan price and show how financial institutions can engage in ratings arbitrage to target higher external credit ratings without having to increase capital levels. The potential implications for regulatory authorities of such arbitrage are also discussed

31 ECONOMIC CAPITAL, LOAN PRICING AND RATINGS ARBITRAGE 1. Introduction The Basel II capital framework published by the Basel Committee on Banking Supervision (BCBS) in June 2006 requires financial institutions to hold minimum capital levels against their market, credit and operational risk exposures. For credit risk the BCBS provides financial institutions with a choice of three increasingly sophisticated approaches: Standardised, Foundations Internal Ratings-Based, and Internal Ratings-Based. By providing a spectrum of approaches the BCBS addresses one of the major criticisms associated with the existing capital guidelines, namely that capital calculations are the same for all institutions, independent of their size, the complexity of their activities, and their sophistication in risk management and measurement. While the calculation for credit risk capital is pre-determined by the BCBS under the Standardised approach, the Internal Ratings-Based approaches allow financial institutions to use internally generated data in their capital calculations. To be eligible to use the Internal Ratings-Based approaches a financial institution needs to satisfy certain qualifying quantitative and qualitative criteria 1. Compliance with the criteria may require significant investment by the institution. The incentive however is that the use of an Internal Ratings-Based approach is likely to result in a better alignment of risk and capital. This is important as excess capital is expensive for institutions, in both monetary terms and with regards to performance measurement, while too low capital levels might threaten the survival probability of an institution in case of financial distress. 1 The minimum requirements for the Internal Ratings-Based approaches are outlined in Basel Committee on Banking Supervision (2006: )

32 In addition to mandatory regulatory capital calculations, institutions may also use internally derived data to estimate their capital requirements. These internal estimates are typically based on the concept of economic capital, which is generally considered to be a better indicator of the riskiness of assets as it considers the unique risks and cash flows associated with the institution s exposures. PWC (2005: 3) find that an increasing number of financial institutions use economic capital to measure and manage the performance of people, products, risk exposures and to optimise capital levels. This combined with the imminent implementation of the Basel II framework, suggests that economic capital is gaining greater importance in financial institutions risk measurement and management activities. This paper examines the issue of economic capital and its use in loan pricing. We adopt the approach outlined by Ford and Sundmacher (2007) and assume that financial institutions price their loans with the aim to generate a target return on employed capital by applying a bottom-up approach, in which the specific risks, costs and revenues associated with the loan are each considered. The advantage of the approach is that financial institutions hold neither excess nor insufficient capital against their exposure and thus avoid mis-pricing their risks and costs. While overpricing loans might render financial institutions uncompetitive, underpricing increases the financial institution s risk exposure as risks and costs are not adequately captured in the price of the loan and thus the institution will be more susceptible to financial distress. Taking this into consideration, economic capital can be regarded as a form of risk currency in financial institutions (Hull, 2007: 365) as it directly reflects the risk levels taken by a bank. The paper is structured as follows. In the next section we define economic capital and identify its different components to isolate the variables that ultimately drive capital levels. Next we discuss the choice of the beta distribution in determining economic capital levels. The third section introduces a loan pricing approach based on - 4 -

33 economic capital. In the fourth we demonstrate the potential for ratings arbitrage through model adjustments in economic capital calculations using the beta distribution. The final section concludes and highlights potential implications for regulatory authorities and other bank stakeholders, such as credit rating agencies. 2. The Nature of Economic Capital Economic capital is commonly described as the amount of capital required to capture potentially large losses in a financial institution (Ong, 1999: 57; Berg-Yuen and Medova, 2004: 7), where the level of capital is dependent on the institution s chosen confidence level and time horizon (Jokivuolle, 2006: 7; PWC, 2005: 3) 2. The confidence level can be linked to the target credit rating of the institution. Institutions with high levels of capitalisation are perceived to have a low default probability. Thus, a higher capital level usually attracts a higher credit rating. Alternatively, an institution that targets a particular external credit rating such as AA, will be required to hold a certain level of capital. Hence, Jokivuolle s (2006: 7) definition of economic capital as the amount of capital required for a given credit rating is practical, particularly given that external credit ratings are publicly observable. In order to better understand the nature of economic capital it is beneficial to decompose it into its different components. The concepts of expected and unexpected losses form the basis of the measure of economic capital. The expected losses (EL) of a loan or loan portfolio are seen as a normal cost of doing business (Smithson 2003: 8) and as such should not attract capital. Rather financial institutions should consider the EL in the pricing of a loan transaction. 2 Crouhy et al (2006: 370) suggest an alternate definition and describe economic capital as the sum of risk and strategic risk capital, whereby strategic risk capital consists of two components: goodwill and burnedout capital. While this definition is more comprehensive as it includes potential losses from bad strategic investments, it is impractical for a general definition of economic capital given that strategic investments are not observable

34 The expected loss (EL) is dependent on three input variables: the expected size of the credit exposure at default (L), the borrower s expected default frequency (EDF) and the loss given default (LGD). The EL can be calculated as: EL = L EDF LGD (1) In practice we estimate the potential credit exposure at default (L) to equal the face value of the loan. The borrower s EDF is obtained from publicly available data as published by Standard & Poor s (S&P) or Moody s for various time horizons 3. Given that economic capital is usually dealt with on a one-year time horizon, we consider the following one-year EDFs that apply to various S&P credit ratings. Table 1: Cumulative Average Default Rates by Rating Multiplier, (%) Rating Year 1 Rating Year 1 AAA to AA 0.00 BB AA BB 0.86 A BB A 0.07 B A B 7.10 BBB B BBB 0.25 CCC/C BBB Source: Standard & Poor s (2007: 12) In so far as loss given default is dependent on loss experiences, it is difficult to obtain accurate LGDs for bank loans. Thus this figure is often approximated using recovery rates on publicly issued or privately placed debt. Table 2 shows recovery rates and corresponding 3 EDF measures can also be internally determined by financial institutions using past loss experience on loans of similar quality

35 LGDs for private debt portfolios by seniority class, while Table 3 shows the respective data for publicly placed debt by credit risk rating. Table 2: Recovery Rates and Corresponding LGDs in Private Debt Portfolios by Seniority Class Seniority Average recovery ($) Average LGD ($) Senior secured Senior unsecured Senior subordinated Subordinated Junior subordinated Source: Carey (1998: 1373) Table 3: Recovery Rates and Corresponding LGDs for Publicly Placed Debt by Credit Risk Rating Credit rating Average recovery rate (%) Average LGD (%) AA A BBB BB B < B Source: Carty and Lieberman (1996: 13) Assuming credit exposure at default (L) and LGD as fixed factors, unexpected loss (UL) can be calculated as follows 4 : UL = σ = EL ( LGD L) (2) 4 Matten (2000: 193) states that most credit risk models use this measure, which assumes that default on a loan is a single binomial event. A more sophisticated approach would incorporate volatility in the LGD

36 Following Ong (1999: 57) and Kiefer and Larson (2006: 2), we define economic capital as the number of standard deviations from the expected loss. Thus, economic capital is simply a multiple (m) of the exposure s UL: EC = UL m (3) While UL is dependent on the borrower s creditworthiness as observed in their credit rating, the multiple m is dependent on the institution s chosen confidence level and thus, ultimately, on the institution s targeted credit rating. As implied by Table 1, the higher the targeted credit rating, the lower the EDF and thus the higher the confidence level. When determining the multiplier it is important to choose a probability distribution that captures the limited upside risk and large downside risk of credit risk. One distribution that provides a good fit for credit risk, for which loss distributions are typically highly skewed and leptokurtic, is the beta distribution. 3. The Use of the Beta Distribution in Economic Capital Calculations The beta distribution belongs to the family of parametric probability distributions and is dependent on two constants: α which controls the steepness of the function, and β which controls the fatness of the tail. The use of the beta distribution in economic capital calculations has a twofold justification. First, on a theoretical level the beta distribution is appropriated by the need to capture the likelihood of extreme losses via the tail of the distribution. Second, on an empirical level the beta distribution simplifies the economic capital calculation as it does not allow for multiple defaults by a borrower during the tenor of the loan. Default is one parameter used to calculate - 8 -

37 expected loss. The expected loss (EL) is represented by the mean (µ) of the distribution and is defined as: µ α = EL = α + β (4) It follows from (4) that both shape parameters are dependent on the mean of the distribution and thus on the size of EL: α β + EL = (5) EL α β = EL (6) EL The variance (σ 2 ) of the distribution is defined as: σ = UL = 2 2 αβ α β α β 2 ( + )( + + 1) (7) The square root of the variance represents the unexpected loss (UL) of the distribution. Given that the variance is determined by the shape parameters α and β, and that α and β are in turn driven by the mean, it follows that the ultimate drivers of the variance and thus UL, are the expected size of the credit exposure at default (L), the borrower s expected default frequency (EDF) and the loss given default (LGD). Similarly, using a beta distribution the multiple m is driven by expected and unexpected losses: - 9 -

38 ( x µ ) m = (8) σ wherein x represents the value at which to evaluate the probability function for a desired confidence level. In equation (3) we showed that economic capital is the product of the standard deviation of a loan loss distribution and the multiple m. Substituting (2) and (8) into (3) gives: EC = EL ( LGD EL) x EL EL ( LGD EL) (9) The significance of Equation (9) is to highlight the strong dependence of economic capital on expected loss levels and, given the drivers of expected losses, even more prominently LGDs. 4. Implications for Loan Pricing based on Economic Capital From a risk measurement and management perspective, pricing loans based on economic capital is preferred to regulatory capital for its ability to better capture the unique risks and cash flows associated with an exposure. One reason is that economic capital is partially dependent on the borrower s creditworthiness. Further, economic capital captures the risk appetite of the lending institution by aligning the level of capital held against a given exposure with the institution s external credit rating. If a financial institution prices its assets based on a target return on economic capital, then the asset price will be primarily driven by the required profit on the loan. The required profit (π)

39 is the product of the economic capital held against the exposure and the institution s target hurdle rate (h): π = EC h (10) If we consider h to be fixed, the required profit on a loan is determined by the amount of capital held. The level of economic capital, it will be remembered, is dependent on unexpected losses and the multiple m. While the UL is dependent on the borrower s credit quality via the EDF and LGD, the multiple m is determined by the bank s target solvency standard, i.e. their target credit rating. A financial institution with a higher credit rating is required to hold comparatively more capital than one with a lower rating to achieve the corresponding higher solvency standard. A higher credit rating will also increase the multiple m and the corresponding required profit on a transaction. We use Carty and Lieberman (1996: 3) LGDs to summarise the impact of a change in a financial institution s credit rating on economic capital levels for BB, BBB and A rated borrowers. EDFs are taken from S&P s annual global default study (2007: 12). The full set of results, including information on EL, UL, m and economic capital, is provided in Appendix