on a PD approach
On 31 December 2018, Bank A originates a 10 year bullet loan with a gross carrying amount of $1,000,000, with
interest being due at the end of each year and the principal due at maturity. In line with IFRS 9, Bank A must
recognise an impairment allowance for the ECLs, considering current and forward looking credit risk information.
The ECLs are a probability-weighted estimate of the present value of estimated cash shortfalls – i.e. the
weighted average of credit losses, with the respective risks of a default occurring used as the weights. For
this purpose, the following parameters must be estimated:
• Probability of Default (‘PD’) – Estimate of the likelihood of default over a given time horizon (e.g. from ti–1
to ti). A default may only happen at a ti horizon if the facility has not been previously derecognized and is
still in the portfolio. An early exit (‘EE’) may occur in case of default unless the facility reverts to performing
without significant modification of the contractual terms. The marginal probability of default for the period
ti–1 to ti is then adjusted from the probability that an early exit occurred during the previous periods:
J=j–1
PD
(1 – EE )
t ×
t
i
J=1
j
We note that, for simplicity, Bank A may decide to model EE within the PD component.
• Loss Given Default (‘LGD’) – Estimate of the loss arising in case a default occurs at a given time (e.g. ti). It
is based on the difference between the contractual cash flows due and those that the lender would expect to
receive, including from the realisation of any collateral. It is usually expressed as a percentage of the EAD.
• Exposure at Default (‘EAD’) – Estimate of the exposure at a future default date, taking into account
expected changes in the exposure after the reporting date, including repayments of principal and interest,
whether scheduled by contract or otherwise, expected drawdowns on committed facilities, and accrued
interest from missed payments.
• Discount Rate (‘r’) – Rate used to discount an expected loss to a present value at the reporting date.
Based on these parameters, an ECL can be computed for any horizon – typically for each due date of an
exposure. The computation formula can be expressed as follows:
t = t
i
n
J=j–1
PD
(1 – EE ) × LGD × EAD
t ×
t
t
t
i
J=1
j
i
i
ECL tn =
(1 + r ti
i )
t = t
i
1
Where:
i
= each future payment
ti
= maturity of the payment i
tn
= horizon considered (either 12-month or lifetime)
Note that the figures in the tables below have been rounded to one or two decimal points.
3754 Chapter 47
Stage 1: 12-month ECLs of $422
At origination, the loan is in stage 1. Thus a corresponding 12-month ECL allowance is recognised, i.e. the
portion of the lifetime ECLs that result from default events that are possible within 12 months after the
reporting date.
Based on statistical and qualitative information, Bank A has computed the following ECL parameters at origination.
As interest is paid on a yearly basis, ECLs are calculated using annual periods.
Each year EAD equals the outstanding principal plus accrued interest due at the end of the year. This bullet
loan does not allow any prepayment, therefore the EAD is constant.
The effective interest rate of the loan is assumed to be the contractual rate, which is 3%.
Bank A sets EE = PDn–1 × 0.8, on the basis that a proportion of the loans which default are expected to cure
and will once again be at risk of default.
Based on provided guarantees and collateral, LGD is estimated at 25% of EAD, whatever the date of default.
Cumulative
Cumulative
Discount
PD @
Marginal
EE t–1 @
Marginal
Year EAD rate
origination
PD
origination LGD
ECL
2018 1,000,000
2019 1,030,000
3%
0.17%
0.17%
0.00% 25%
$422
12m ECL
2020 1,030,000
3%
0.49%
0.32%
0.14% 25%
$775
2021 1,030,000
3%
0.86%
0.37%
0.39% 25%
$877
2022 1,030,000
3%
1.38%
0.53%
0.69% 25%
$1,196
2023 1,030,000
3%
1.84%
0.47%
1.11% 25%
$1,027
2024 1,030,000
3%
2.37%
0.54%
1.47% 25%
$1,141
2025 1,030,000
3%
2.85%
0.49%
1.90% 25%
$1,014
2026 1,030,000
3%
3.30%
0.46%
2.28% 25%
$912
2027 1,030,000
3%
3.84%
0.56%
2.64% 25%
$1,073
2028 1,030,000
3%
4.50%
0.69%
3.07% 25%
$1,280
Lifetime
$9,717
ECL
1 – Cum PDi
Marginal PDi = 1 –
1 – Cum PDi–1
PDi × (1 – Cum EEi–1) × LGDi × EADi
Marginal ECLi =
(1 + ri)i
Financial instruments: Impairment 3755
Stage 2: lifetime ECLs of $50,285
On 31 December 2021 – 3 years after origination, the loan shows signs of significant deterioration in credit
quality based on the creditworthiness of the obligor and forward looking information, and Bank A moves it
to stage 2. Example 47.10 below shows the calculation underlying this assessment.
Consistent with the significant increase in credit risk, the PD of the obligor has increased. In consequence, the
probability of an early exist has also increased, because of the higher level of default. For the purposes of this
example, we assume that there are no significant fluctuations in collateral values and the LGD remains constant.
Discount
Cumulative
Marginal
Cumulative
Marginal
Year EAD rate
PD
PD
EE t–1
LGD
ECL
2021 1,000,000
0.00%
2022 1,030,000
3%
1.40%
1.40%
0.00%
25% $3,495
12m ECL
2023 1,030,000
3%
3.87%
2.51%
1.12% 25% $6,017
2024 1,030,000
3%
8.82%
5.15%
3.10% 25% $11,7
56
2025
1,030,000 3% 12.84%
4.40% 7.06%
25%
$9,366
2026
1,030,000 3% 16.04%
3.67% 10.27%
25%
$7,322
2027
1,030,000 3% 18.98%
3.50% 12.83%
25%
$6,585
2028
1,030,000 3% 21.60%
3.23% 15.18%
25%
$5,745
Lifetime
$50,285
ECL
Stage 3: lifetime ECLs of $262,850
In the following year, on 31 December 2022, the obligor does not pay the amount due. Based on credit
information available, it is already considered to be in default and is moved to stage 3 – credit-impaired. At
this time, the exposure is $1,030,000.
Once a facility becomes credit-impaired, impairment must still represent ECLs. Therefore, it must be
probability-based. At the reporting date, Bank A updates the appraisal value of the collateral and considers 3
probable scenarios:
• Scenario 1 – Cure: the obligor eventually pays past dues and the loan reverts to performing. In this case,
ECL corresponds to lifetime losses expected from loans that have recently defaulted. Based on its
historical data and using the methodology described above, Bank A expects an ECL of $130,000.
• Scenario 2 – Restructure: Bank A comes to a restructuring agreement with the obligor. After 6 months
of negotiation, the loan is written off and a new loan is initiated with a net present value of $800,000.
• Scenario 3 – Liquidation: The loan is written off and the bank starts the collection of the contractual
collateral. Bank A expects to sell the collateral within a year and to collect $700,000 net of recovery costs.
3756 Chapter 47
The ECL of each scenario can be calculated as follows:
t = t
i
n
CFt – RC
i
ti
ECL = EAD –
(1 + r ti
i )
t = t
i
1
Where:
CF
= expected future cash flows
RC
= expected recovery costs
Expected net
Expected
ECL of
Probable
Discount
Weighted
Probability EAD
future cash
recovery
each
scenarios
rate
ECL
flows
time
scenario
Scenario 1:
20% 1,030,000
3%
900,000
0.0 $130,000
$26,000
Cure
Scenario 2:
40% 1,030,000
3%
800,000
0.5 $241,737
$96,695
Restructure
Scenario 3:
40% 1,030,000
3%
700,000
1.0 $350,388 $140,155
Liquidation
Weighted
Lifetime
$262,850
average ECL
ECL
% of
26%
EAD:
ECL = EAD − Exp. net future CF
(1+r)exp recovery time
Most sophisticated banks have developed their IFRS 9 solutions by adjusting and
extending their Basel models. This is true for all types of model component: PD, LGD
and EAD. This is perhaps unsurprising given the historical investment large banks have
made in their Basel models, and the fact that IFRS 9 shares fundamental similarities in
expected loss modelling. But, for many banks, creating lifetime estimates and altering
models to satisfy the complex and detailed IFRS 9 requirements will still require
significant work.
5.4.2
Loss rate approach
Not every entity calculates a separate risk of a default occurring and an LGD, but instead
uses a loss rate approach. Using this approach, the entity develops loss-rate statistics on
the basis of the amount written off over the life of the financial assets. It must then adjust
these historical credit loss trends for current conditions and expectations about the
future. The following Illustrative Example 9 from IFRS 9 is designed to illustrate how
an entity measures 12-month ECLs using a loss rate approach. [IFRS 9 IG Example 9, IE53-IE57].
Example 47.4: 12-month expected credit losses measurement based on a loss
rate approach
Bank A originates 2,000 bullet loans with a total gross carrying amount of $500,000. Bank A segments its
portfolio into borrower groups (Groups X and Y) on the basis of shared credit risk characteristics at initial
recognition. Group X comprises 1,000 loans with a gross carrying amount per client of $200, for a total
gross carrying amount of $200,000. Group Y comprises 1,000 loans with a gross carrying amount per
client of $300, for a total gross carrying amount of $300,000. There are no transaction costs and the loan
Financial instruments: Impairment 3757
contracts include no options (for example, prepayment or call options), premiums or discounts, points paid,
or other fees.
Bank A measures ECLs on the basis of a loss rate approach for Groups X and Y. In order to develop its loss
rates, Bank A considers samples of its own historical default and loss experience for those types of loans. In
addition, Bank A considers forward-looking information, and updates its historical information for current
economic conditions as well as reasonable and supportable forecasts of future economic conditions.
Historically, for a population of 1,000 loans in each group, Group X’s loss rates are 0.3 per cent, based on
four defaults, and historical loss rates for Group Y are 0.15 per cent, based on two defaults.
Number
of
Estimated
Total
Historic
Estimated
Present
Loss rate
clients in
per client
estimated
per
total gross
value of
sample
gross
gross
annum
carrying
observed
carrying
carrying
average
amount at
loss (a)
amount at
amount at
defaults
default
default
default
Group
A
B
C = A × B
D
E = B × D
F
G = F ÷ C
X 1,000 $200 $200,000
4
$800
$600 0.3%
Y 1,000 $300 $300,000
2
$600
$450 0.15%
(a) ECLs should be discounted using the EIR. However, for purposes of this example, the present value of the observed loss is assumed. [IFRS 9.5.5.17(b)].
At the reporting date, Bank A expects an increase in defaults over the next 12 months compared to the
historical rate. As a result, Bank A estimates five defaults in the next 12 months for loans in Group X and
three for loans in Group Y. It estimates that the present value of the observed credit loss per client will remain<
br />
consistent with the historical loss per client.
On the basis of the expected life of the loans, Bank A determines that the expected increase in defaults does
not represent a significant increase in credit risk since initial recognition for the portfolios. On the basis of its
forecasts, Bank A measures the loss allowance at an amount equal to 12-month ECLs on the 1,000 loans in
each group amounting to $750 and $675 respectively. This equates to a loss rate in the first year of 0.375 per
cent for Group X and 0.225 per cent for Group Y.
Number
of
Estimated
Total
Expected
Estimated
Present
Loss rate
clients in
per client
estimated
defaults
total gross
value of
sample
gross
gross
carrying
observed
carrying
carrying
amount at
loss
amount at
amount at
default
default
default
Group
A
B
C = A × B
D
E = B × D
F
G = F ÷ C
X 1,000 $200 $200,000
5
$1,000
$750
0.375%
Y 1,000 $300 $300,000
3
$900
$675
0.225%
Bank A uses the loss rates of 0.375 per cent and 0.225 per cent respectively to estimate 12-month ECLs on
new loans in Group X and Group Y originated during the year and for which credit risk has not increased
significantly since initial recognition.
The example above illustrates that under the loss rate approach, an entity would
compute its loss rates by segmenting its portfolio into appropriate groupings (or
sub-portfolios) based on shared credit risk characteristics and then updating its
historical loss information with more forward-looking information. The loss rate
was derived simply by computing the ratio between the present value of
observed losses (the numerator) and the gross carrying amount of the loans
3758 Chapter 47
(the denominator). Although the loss rate approach does not require an explicit risk
of a default occurring, there has to be an estimate of the number of defaults in order
International GAAP® 2019: Generally Accepted Accounting Practice under International Financial Reporting Standards Page 742
