Lost Given Default and the Credit risk Erika

2014 International Conference on Management, Education, Business, and Information Science(ICMEBIS 2014)
Lost Given Default and the Credit risk
Erika Spuchľáková1, a, Juraj Cúg2, b
1
Department of Economics, Faculty of Operation and Economics of Transport and Communications,
University of Žilina, Slovak Republic
2
Department of Economics, Faculty of Operation and Economics of Transport and Communications,
University of Žilina, Slovak Republic
a
email: [email protected], bemail: [email protected]
Keywords: Credit risk, Loss Given Default, Probability of Default, Exposure at Default
Abstract. Institution such as banks will determine their credit losses through an analysis of the
actual loan defaults. While quantifying some losses may be simple, in some situation it may be
quite difficult and require the analysis of multiple variables. Nowadays, measuring of credit risk is
considered as an important for financial institutions as well as for non-financial institutions. This
paper focuses on the Credit risk and its main components, which are Probability of Default,
Exposure of Default and Loss Given Default. These are included in the credit spread, which is the
difference in market prices between defaultable and default-free bonds.
Introduction
Credit risk is the oldest form of risk in the financial markets. If credit can be defined as nothing
but the expectation of a sum of money within some limited time, the credit risk is the chance that
this expectation will not be met. [14]
Usually is credit risk defined as (Resti, S. 2007) “unexpected change in a counterparty´s
creditworthiness may generate a corresponding unexpected change in the market value of the
associated cred exposure”. According to the Cisko, Klieštik (2013, p. 443) credit risk “is not so
limited only to the counterparty’s default and loss resulting from its insolvency, but also to losses
arising from the deterioration in credit quality, which is expressed by downgrading of its credit
rating.”
Credit risk techniques have undergone significant development in recent decades. This has led to
the development of new methods for the estimation of the potential bankruptcy of borrowing
entities and parameters specifying possible losses. These parameters include Loss Given Default,
expressing the percentage of an exposure which will not be recovered after counterparty defaults.
Many academic papers, publications and scientific books have demonstrated this approach, LGD
estimation model. Most famous is the model introduces by Moody´s (2005) also known as LossCals
model. This model applying a multivariate linear regression model that includes certain risk factors,
industry and macroeconomic factors, and that includes transformed risk factors. Other well-known
models were presented by Glößner (2006), this model consists of two steps, scoring and calibration
step. Hamerle, A. (2006), who presents an estimation model based on a linear regression in
connection with a logic transformation of the LGD and a time consideration by using lag variables
within the regression. See also Huang and Oosterlee (2008), Appasamy (2008) and Bastos (2010).
Main components of credit risk are Probability of Default (PD), Exposure At default (EAD) and
the Loss Given Default (LGD). These are included in the credit spread, which is the difference in
market prices between defaultable and default-free bounds. While much attention was paid to
modeling of the probability of default, the loss given default was often assumed to be constant and
exogenously given. [4]
Loss given default expressing the percentage loss incurred relative to exposure at default (EAD).
The EAD represents the legal claim by the bank on the obligor for credit extended including
principal and interest outstanding at the time of default. [7]
978-0-9917647-3-0/EDUGait Press, Canada
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Distribution of loses is shown in Figure 1. Risk-weighted functions produce the capital
requirements only for the Unexpected Losses (UL) portion, while Expected Losses (EL) are
considered to stand for ex-ante estimated average losses, therefore being already incorporated into
the price of the risky instrument. Generally, EL can be calculated as the product of PD, LGD and
EAD. [8]
Fig.1. Distribution of credit losses
Source: RBNZ (2005)
Loss Given Default
Loss Given Default (LDG) is usually defined as the loss rate experienced by a lender on a
credit exposure if the counterparty defaults.
The estimation of LGD is not so straightforward, because it depends on many driving factors,
such as the seniority of the claim, quality of collateral or state of the economy.
It is important to distinguish between LGD and actual loss incurred, which can be computed
as LGD x EAD. Given the default of counterparty, according to Seidler & Jakubik (2009), the
total loss consists of (i) the loss of principal, (ii) the carrying costs of non-performing loans and
(iii) the workout expenses. However, the carrying costs and other expenses are very small
relatively to the principal loss; therefore it is reasonable to assume they will not significantly
influence the loss given default rate. Following this assumption, recovery rate, the percentage
rate of exposure that lender receive after the obligor defaults can be defined as a complement to
LGD as:
R = 1 – LGD
(1)
One minus LDG is therefore called recovery rate (RR). In principle, LGD comprises also
other costs related to default of the debtor, and the correct formula should rather be:
LGD = 1 – RR + costs
(2)
Costs are relevant only in a specific type of LGD and are not usually so high to influence
losses markedly in comparison with recovery rate.
The measurement of LGD is a standard problem in finance. The valuation of uncertain future
cash flows. The only complication is that the cash flows relate to proceeds expected from postdefault resolution or sale of obligor assets, net of recovery costs incurred by the bank, and not the
original pre-default contractual promised payments. If δ is a fixed spread over a risk-free term
rate – rt, then the empirical LGD can be defined as (Maclachan, 2004):
(3)
Where, EAD is the exposure of default, δ is a fixed risk premium, Ct is the net cash flow at time t
inclusive of positive flows received under contract form the borrower, or through asset sales, and
negative cash flows arising from internal and external costs.
Moody´s defines Loss Given Default as the sum of the discounted present values of the
periodic interest shortfalls and principal losses experienced by a defaulted tranche. The coupon
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rate of the tranche is used as the discount rate. The formula for LGD is:
(4)
Where LGDk,t denotes the loss severity rate up to time t using time k as the reference date, ISs
and LPs denote the net interest shortfall and principal loss at time s, cs is the discount rate for
period s, and Bk is the outstanding principal balance at the reference date k. There are usually
three dates of interest: the origination date, the default date, and a cohort formation date,
Moddy´s (2010).
Types of LGD
Methods of loss given default measurement can be divided into the ex-post and ex- ante
default estimation. Schuermann (2004) divided the loss given default into three broadly
recognized concepts of measuring, (i) Market LGD, (ii) Workout LGD and (iii) Implied Market
LGD. [13]
(i) Market LGD – this methodology considers the price of bond after default as a proxy of
the recovered amount or marketable loans reflect the actual investors’ expectations about the
recovery. The main advantage is comparison to other ex-post methods and that data can be
observed immediately after the default. Market data are an objective and updated source of
information for LGD observations. However, post-default price is available only for the fraction
of the debt that is traded and for which after-default market exists. Market LGD is limited for
defaulted bank loans that are traditionally not traded.
(ii) Workout LGD – this type of LGD is based on the process of recovery workout. It
considers bank as an investor who invests into the defaulted assets. LGD is then determined by
loss of principal, carrying costs of non-performing assets and recovery and workout expenses.
The simple formula of Workout LGD could be:
(5)
Where NPV is the net present value and Rj(t), Cj(t) represent all recoveries and costs observed
from the time of default tDF to the end of workout process tE. Even though this formula is
mathematically simple, compared to directly observed market LGD, it is actually much more
difficult to calculate. Firstly, because it is not unambiguous, how these cash flows should be
discounted.
(iii) Implied Market LGD – the basis of the implied market LGD is to derive LGD estimates
from market price of non-defaulted loans, bonds or credit default instruments by structural or
reduced-form models. This approach is not yet widely used in banks, but it provides important
tools for pricing fixed-income securities and credit derivatives. Implied market LGD model
estimating the Credit risk parameters which are divided into structural models and reduced-form
model.
Some scientific literatures also mention Accounting LGD as one of the LGD type. This
approach is based on charge-off amounts, i.e. the amount of non-performing facilities. The
charge-off amounts are determined by product types, past due days, collateral and by accounting
standards which focus on prudence what may not be consistent with risk management policies.
[13]
Conclusion
Credit Risk techniques have undergone significant development in recent decades. This has led
to the development of new methods for the estimation of the potential bankruptcy of borrowing
entities and parameters specifying possible losses. These parameters include Loss Given Default,
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expressing the percentage of an exposure which will not be recovered after a counterparty default.
While the estimation of the probability of default has received considerable attention over the
past 20 years, LGD has gained greater acceptance only in recent years.
There are four types of LGD, Market LGD, Workout LGD, Implied Market LGD and some
authors also mention the Accounting LGD. Every one of these types has some advantages and
disadvantages.
Acknowledgement
The contribution is an output of the science project VEGA 1/0656/14- Research of Possibilities of
Credit Default Models Application in Conditions of the SR as a Tool for Objective Quantification of
Businesses Credit Risks.
References
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