Downturn LGD: a More Conservative Approach for Economic Decline Periods

Downturn LGD: A More Conservative Approach for Economic Decline Periods

Mauro Ribeiro de Oliveira Júnior Armando Chinelatto Neto

Electronic copy available at: http://ssrn.com/abstract=2416500 43

Abstract

The purpose of this paper is to identify a relevant statistical correlation between rate of default (RD) and loss given default (LGD) in a major Brazilian financial institution’s Retail Home Equity exposure rated using the IRB approach, so that we may find a causal relationship between the two risk parameters. Therefore, according to Central Bank of Brazil requirements, a methodology is applied to add conservatism to the es- timation of the Loss Given Default (LGD) parameter at times of economic decline, reflected as increased rates of default.

Keywords: A-IRB, Loss Given Default, Rate of Default.

1. Introduction Financial institutions that wish to aches, and allows larger banks to use the use IRB (Internal Ratings Based) approa- advanced approach based on the internal ches pursuant to the recommendations of rating of exposures according to their cre- the Basel Committee on Banking Supervi- dit risk, that is, the Advanced IRB approa- sion as provided in the document titled "In- ch, to which the literature refers as A-IRB. ternational Convergence of Capital Measu- Central Bank of Brazil Circular Let- rement and Capital Standards: a Revised ter No. 3.581, dated March 8, 2012, addres- Framework", or simply Basel II, must cal- ses the standards governing the use of in- culate the following risk parameters: Pro- ternal credit risk systems. In practice, Cir- bability of Default (PD), Loss Given De- cular Letter No. 3.581 tropicalized the con- fault (LGD), Exposure at Default (EAD) and cepts of Basel II. Effective Maturity (M). According to Carvalho and San- Central Bank of Brazil Communi- tos (2009) the A-IRB approach requires the qué No. 18.365 (2009) established the pre- most sophisticated models and is therefore liminary guidelines for using these appro- more complex than the other approaches

Electronic copy available at: http://ssrn.com/abstract=2416500 44

that Basel II discusses. compromise obligors’ capacity to honor Under A-IRB, Central Bank autho- their debts. rized institutions will be able to used their Therefore, during economic down- own estimates for Probability of Default turns, a portfolio’s loss rates may be gre- (PD), Loss Given Default (LGD), Exposu- ater than during normal periods, and the re at Default (EAD) and Effective Maturity portfolio’s downturn LGD must reflect this (M), subject, at all times, to minimum cri- volatility. teria set forth by the supervising authority. Circular Letter No. 3.581 addres- LGD corresponds to the percen- sed this point explicitly, as it provides that tage loss relative to total exposure at the LGD estimates must be more conservative time of default, and must be determined in the presence of a relevant positive cor- for every contract in the portfolio that is in relation between the frequency of default default status. and the magnitude of LGD. According to article 75 of Circu- Given the above, calculating a do- lar Letter no. 3.581 and to paragraph 468 wnturn LGD is justified because, in al- of Basel II, banks using the A-IRB method most every case, the LGD obtained from must estimate LGD parameters so that they the historic average of recovery rates may cover a full economic cycle and are equal not be independent from rates of default, to or greater than the long-term weighted requiring an added penalty for LGD esti- average of observed LGD percentages. mates for the duration of economic down- According to Communiqué No. turn periods. 18.365 and Circular Letter No. 3.581, whe- In light of the foregoing, this re the losses show cyclicality characteris- paper’s research problem is to propose tics, the LGD parameter must reflect perio- a downturn LGD for a Retail Home Equi- ds of adverse economic conditions, a prac- ty portfolio that can reflect added conser- tice that is referred to in the literature as vatism at times when default rates are on “downturn LGD”. the rise. Indeed, at times of economic do- Section 2 analyzes an overview of wnturn, obligors in arrears may have incre- the available literature on rates of recovery ased difficulty honoring their obligations, and rates of default. Section 3 shows the leading to higher loss rates for banks’ por- application of the methodology developed tfolios. In this case, the mean historic LGD, in the literature to calculation of a down- which may include a previous period of turn LGD. Finally, Section 4 presents the “economic normalcy”, will not provide an paper’s conclusions. accurate indicator of the future losses fa- ced as an adverse period arises, and will, in fact, underestimate the portfolio’s real 2.Literature Review loss potential. The academic studies reviewed It is during recessive periods that show that economic adversity and periods both retail and wholesale loan portfolios of high default imply greater expected los- face their greatest rates of default: as the ses. It is therefore a mistake to regard LGD economic scenario deteriorates, it may as independent from rates of default (RD) 45

and use only the long-term average LGD to The document describes the pro- estimate the portfolio’s future LGD. cess to be followed to evaluate the poten- The conservatism supervisors re- tial effects of worsening economic condi- quire in connection with LGD estimates, tions on recovery rates. According to the according to Altman and Ssabato (2005), is guidelines, the first step is to identify a his- due to the fact that Pillar 1 capital require- toric period that can be characterized as a ments under Basel II are highly sensitive to period of economic downturn. the magnitude of LGD, particularly as con- One understanding that can be de- cerns retail asset classes. Therefore, requi- rived from the document is that, if the reco- ring the calculation of a more conservati- very rates observed during the periods of ve – downturn – LGD is intended to make highest defaulting are lower than the ave- sure that capital requirements accurately rage long-term rates of recovery, there is a reflect the capital needed to face unexpec- potential for increased losses in periods of ted losses arising from credit portfolio ex- rising default. Therefore, failing to adopt a posures over long periods of time. conservative LGD estimate for this period Most of the academic studies on may underestimate the capital needed to the dependence between the behavior of cover unexpected losses. LGD and variables indicating economic We thus conclude that the appro- downturns analyze data for debt issued by priate approach to identify a period of eco- large businesses. For example, Altman et nomic decline must be based on tracking al. (2005) examine the rates of recovery of the historic observed rates of default and, corporate obligations in 1982-2002 to con- as a result, periods in which historic obser- clude that macroeconomic variables do ved rates of default are high will be then answer for a small part of the variation in associated to a specific period of econo- rates of recovery. mic downturn for each credit portfolio. Arguments for evidence of de- Our review of the literature reve- pendence between the recovery of de- aled a single article that uses data for re- faulting exposures and variables associa- tail assets: Sabato (2009). According to ted with recessive economic conditions the author, it was the first study that pro- can be found in Frey (2009), where the au- posed to analyze the ties between rates of thor shows that, during recessions, the re- recovery and an economic downturn for covery of defaulted obligations is around this asset class. 30% lower than during periods of econo- In the paper’s results, the author mic growth. His study, however, also exa- showed a high and positive Pearson corre- mines American corporate bonds, where lation coefficient of .77 between LGD and a high correlation between default and re- default rates. The correlation was obtained covery can be found. using data from a portfolio of products ca- Basel Committee 2005 document tegorized, as per Basel II, as Other Retail “Guidance on Paragraph 468 of the Fra- Exposures - ORE. mework Document” helps banks interpret On the other hand, in the same paragraph 468 of Basel II as concerns the study, the author demonstrated the ab- demand for downturn LGD. sence of significant correlation between 46

variables in retail portfolios of products ca- dependence between the rates of default tegorized as Qualified Revolving Exposu- and LGD will imply increased conserva- res (-.84) and in Exposures to Small and tism in A-IRB models may vary significan- Medium Enterprises (-.12), suggesting that tly from one financial institution to another, these two asset classes do not require cal- given that the methodologies take internal culation of a downturn LGD. databases into consideration for the pur- Identification of a statistical con- poses risk-parameter calculation. nection between two variables may not es- Therefore, the purpose of this stu- tablish a casual tie between them. In this dy – that is, to calculate downturn LGD ba- paper, we use a method supported by the sed on historic data for the Home Equity literature and known as the Granger Cau- Retail sub-class, is to make sure that LGD sality Test, which allows finding a cau- includes future predictions of loss rates re- sal link (or temporal precedence) between lative to the risks that increased defaulting any two variables, in the sense that varia- may create. ble X Grange-causes variable Y if the observed X in the present or past helps pre- dict the future values of Y for a given hori- 3. Methodology zon (GRANGER, 1969). The method proposed above to Within the context of this paper, if calculate downturn LGD consists of iden- the granger RD causes LGD, then chan- tifying the period of economic downturn ges in RD must precede changes in LGD and then calculating how much, in percen- over time. tage terms, loss given default increases re- However, the two variables must lative to periods of lower-than-average ra- be stationary, as the stationary condition is tes of default. crucial to application of the Granger causa- Illustrating the method with data lity test (GUJARATI, 2004). from Other Retail Exposures, as in Saba- Data constraints are a significant to (2009), the economic downturn period challenge in estimating LGD parameters showed an average 17% increase in LGD in general and downturn LGD parameters for the category relative to the period in its in particular. Furthermore, there is no cer- entirety. This factor must be added to the tain, supervisor-provided, methodology in portfolio’s LGD to increase the variable’s terms of what methods are appropriate for conservatism for the period of deteriora- conservative estimates of LGD under eco- ting economic conditions, that is, when the nomic downturn conditions. frequency of default starts rising to above- Therefore, according to the me- -average levels. thod proposed in Sabato (2009), we regard This paper adopted the downturn an economic downturn as a minimum pe- LGD development model proposed in Sa- riod of six months during which the obser- bato (2009) and applied the technique to ved rate of default is consistently higher Home Equity Retail exposures of a major fi- than the long-term historic rate plus one nancial institution active in the domestic fi- standard deviation. nancial market. The extent to which potential The LGD database consisted of 47

monthly observed LGD data for the pe- the same period, that is, January 2008 to riod from January 2008 to November 2011 November 2011. (see graphic 1). The rate of default da- The .71 correlation between loss tabase was obtained from the Central given default and the rate of default is sig- Bank of Brazil Website and comprehend nificant for the purposes of the study. 48

3.1. Granger Causality today’s RD is impacted by the LGD from 5 Test for RD and LGD periods ago, at a 5% significance level. Although a strong Pearson correlation exists between the variables invol- ved in our study, this alone does not mean 3.2. Economic that a causal tie is present, that is, that an Downturn Period increase in RD in a certain period does As noted, the approach to identi- affect the increase in LGD in a subsequent fying a period of economic downturn will period. be based on historic observed rates of The Granger Causality test is a default. VAR model, that is, a Vector Autoregressi- We therefore considered a period ve model that examines linear relationships of economic downturn to be a minimum between each variable and the lagged va- period of six months during which the ob- lues of itself and every other variable. Such served rated of default is consistently hi- models consider the presence of interde- gher than the historic long-term rate plus pendence between variables and may as- one standard deviation. sess the dynamic impact of random dis- Give the information from our data- turbances on the variables system, which base, the period from January 1208 to Au- makes them particularly useful and effi- gust 2008 show rates of default in excess cient in predicting the future behavior of of 2.99%, which is the historic average plus interrelated time series (CAIADO, 2002). one standard deviation. Therefore, this pe- The stationary condition of the RD riod will be regarded as a period reflecting and LGD series is crucial to application of adverse economic conditions. the Granger Causality Test method for the purposes of capturing causal ties between the variables. It is important to point out 3.3. Expected Average that if a series displays a unit-root, then it is Increase in LGD non-stationary. More conservatively, the The analyses show that LGD does average expected increase in LGD may be have a unit-root, that is, is non-stationary. calculated as the relationship between the On the other hand, RD is stationary, as it downturn period’s weighted average LGD lacks a unit-root. However, given the cons- plus one standard deviation and the avera- traints of the data period, we decided not ge LGD of the period of lowest rates of de- to develop vector models based on the fault minus one standard deviation. cointegration of the variables. Our result is an LGD that is 7.73% Assuming LGD to be stationary, higher during recessive periods than in the results we found using Eviews 5 and periods of low defaulting. This implies an adopting a 5% significance level for each LGD that is 2 percentage points higher. of the two tests, is that LGD causes RD In this case, the formula for the se- (for 5 lags). lected portfolio would be: This means that today’s changes in LGD will affect RD in 5 periods, that is, dLGD1= 0.02 + ELGD (graphic 3) 49

On the other hand, according to a that is 7% higher during recessive perio- slightly less conservative view, the average ds than for the portfolio’s entire period. expected increase in LGD may be calcula- This implies an LGD that is 1.83 percenta- ted as the relationship between the down- ge point higher. turn weighted average LGD plus one stan- In this case, the formula for the se- dard deviation and the average LGD for the lected portfolio would be: entire period minus one standard deviation. In this case, the result is an LGD dLGD2= 0.0183+ ELGD (graphic 3)

4. Conclusion default follow a rising path, may have a fu- This paper investigated a methodo- ture impact on increased economic losses logy that adds conservatism to LGD estima- arising from defaults. tes at times when the beginning of an eco- However, despite not having found nomic downturn is perceived. We developed that RD Granger-causes LGD, LGD must a methodology that has been established for even so, as per the Central Bank’s recom- retail portfolios, but had never been applied mendations, be more conservative in perio- to a Home Equity Retail portfolio. ds when default begins to rise. This paper Despite the high statistical correla- attempted to determine how much more tion between RD and LGD, we cannot, ba- conservative we should be by applying an sed on the statistical tools available, claim added penalty to estimations of LGD. that the period marked by an economic do- We therefore tried to meet the wnturn, that is, the period in which rates of Central Bank of Brazil’s requirements for 50

the LGD estimates used in A-IRB. For futu- recovery and collateral value, since, if such re and supplementary studies, we suggest a relationship can be found, the deteriora- calculating more conservative metrics for tion of collateral values will bring about a portfolios where a significant correlation potential increase in default-related losses and time causality exist between rates of and, consequently, in LGD.

Mauro Ribeiro de Oliveira Júnior Autores

Bachelor of Mathematics, Universidade Federal de São Carlos, Master of Mathematics, Universidade Estadual de Campinas, MBA in Risk Management, Fundação Instituto de Pesquisas Contábeis, Atuarias e Financeiras – FIPE- CAFI. Currently a Doctor of Statistics candidate at Universidade Federal de São Carlos and employed at a domestic retail bank. Contact the author: [email protected]

Armando Chinelatto Neto

Bachelor of Economics and Master and Doctor of Applied Economics, Universidade Federal de Viçosa – UFV. MBA in Risk Management, Fundação Instituto de Pesquisas Contábeis, Atuarias e Financeiras – FIPECAFI. Con- sultant to the CEO at a domestic retail bank. Contact the author: [email protected]

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