1. Calculating an Estimate Based on the Probability of Default Model
Dan Price, CPA, CFA
President
Twenty Twenty Analytics

2. Overview Example Implementation
The FASB example is omitted from the portion of this presentation because there isn’t one. In fact, if you ctrl+ f the only place you’ll find the word probability is where they mention it’s okay to use that methodology. This methodology is used within the Basel framework and IFRS 9. More information is available searching IFRS 9 than CECL

3. Compared to Other Models
Vintage Analysis
Probability of Default
Calculated at the Loan Level
Loss Magnitude
Loss Likelihood
Calculate at Pool Level
Based upon loss magnitude

4. Cost / Benefit - Greater Precision - More complex calculation
- Loan Level Application of Economic Impacts
- Automation
- More complex calculation
- Precision != Accuracy
- Generally requires longer loss and origination history

5. Expected Credit Losses
Overview
Probability of Default
Loss Given Default ($)
Expected Credit Losses
The probability of default (PD) is the likelihood that a loan will not be repaid and will fall into default.
Loss given default (LGD) ($) is the loss due to default.
You may sometimes see a formula PD*LGD*EAD.
That is the same formula. However, in that formula, LGD is referring to the percentage lost as a result of default. The total exposure to credit risk is the amount that the borrower owes to the lending institution at the time of default; the exposure at default (EAD). Our example is a simplified example, where LGD ($) = LGD (%) * EAD ($)
Expected Value
Expected value, in general terms, is calculated as the sum of all possible values multiplied by the probability of its occurrence. For example, if I were to flip a coin, giving you $5 if it landed on heads, or taking $5 if it landed on tails, the expected value of that coin flip would be calculated as [($5*50%)-($5*50%)]=$0.
Realistically, there is a 0% probability of you walking away from that coin flip with the same amount of money as you started. However, that does not change the scenario's expected value.
Expected Credit Losses
Twenty Twenty Analytics takes the above approach with credit losses. Using the Metro Area Analysis tool, you have the ability to set up to 5 economic scenarios that will impact your expected credit losses, and also set the likelihood of that scenario occurring. Weighted Expected Credit Losses (CECL reserve for loans not included in our analysis) is calculated as the expected value of those scenarios.

6. Loss Given Default Loss Given Default ($) Collateral Fair Value
Costs to Sell
Loss Given Default
Loss Given Default is presented above, and can be evaluated several ways:
Using actual collateral values and costs to sell
Creating some sort of loss percentage based upon your history and a high-level perception of changes in collateral quality

7. Loss Given Default ($) (LGD) Expected Credit Loss [(PD) * (LGD)]
Basic Example
Loan Number
Current Balance (A)
Probability of
Default (PD)
Collateral Value (B)
Superior Mortgage (C)
Costs to
Sell (D)
Loss Given Default ($) (LGD)
[(B)-(C)-(D)-(A)]
Expected Credit Loss [(PD) * (LGD)] 1
5,000
5.00%
-5,000
-250 2
25,000
2.00%
18,000
1,800
-8,800
-176 3
150,000
100.00%
250,000 4
7,500
-7,500
-375 5
3.00%
125,000
19,000
-19,000
-570
Total
212,500
-40,300
-1,371
Loan #3 – You’ll see that the Probability of Default for that loan is 100%, meaning it has defaulted or is in the process of defaulting. However, it is in the first lien position and very well-collateralized. Despite the fact that it has defaulted, we don’t expect to realize any of that loss, so the Expected Credit Loss is $0 (100% * $0 = $0)
Loan #5 – At first glance this loan appears to be adequately collateralized. However, after considering costs to sell the outcome is about an 80% loss. The point being, be sure to consider the actual cash flows that you’ll receive in the event collateral has to be liquidated. It’s also important to understand how the superior position (if any) fits in to the equation.
Continuing with the expected value example, there is virtually no actual outcome where this credit union would lose $250 on Loan #1, or $570 on Loan #5, but that remains our expected credit loss applied to those loans.

8. Probability of Default
Improving FICO Scores
Loan Aging
Longer Terms
Becoming Delinquent
All else equal, the above factors will move probability of default in the noted direction. Of course, these metrics moving in the opposite direction will have the opposite impact.
A loan with a declining FICO score will have a greater probability of default
A loan that has a longer time to maturity will have a greater probability of default
A loan with a shorter term will have a lower probability of default
A loan that has become current on its payments will have a lower probability of default
In addition to these pressures on probability of default:
Type of loan will also impact the probability of default
Collateral position, depending on asset class, could potentially impact the probability of default (e.g. strategic defaults on real estate loans). However, modeling this may be difficult and more appropriately addressed within your Q&E factors

9. Probability of Default
Complete Internal Model
Best
Hybrid Internal Model
Better
Supportable External Model
Okay
The Global Public Policy Committee (GPPC), which is comprised of representatives from the Big 4 Accounting Firms, BDO and Ernst & Young, released some specifics as to what will and will not be acceptable in assigning default probabilities
Difference Between IFRS and CECL
FASB’s CECL model requires entities to recognize lifetime expected credit losses for all assets, not just those that have had a significant increase in credit risk since initial recognition. There is no material difference in the methodology, simply the types of assets in which the methodology is applied
Under the CECL model, estimates of expected credit losses must reflect the time value of money explicitly only when a discounted cash flow approach is used to estimate expected credit losses.

10. Complete Internal Model
Identify Risk Drivers
Compile Historical Data
Evaluate Predictive Power
Calibrate Time Period
Best
If the bank develops a new model to produce lifetime PDs, it will be necessary to ensure all key risk drivers and their predictive power are identified and calibrated based on historical data over a suitable time period. This could take the form of a scorecard approach.

11. Supportable External Model
Understand the Model
Model Validation
Document Reasonableness
Document Appropriate Adjustments
Okay
2.3.4 What is not compliant
Leveraging existing models without, based on reasonable and supportable information, validating that these models are fit for purpose under IFRS 9 and/or making and documenting appropriate adjustments. [IFRS (c), B , BC5.283]
Assuming a constant marginal rate of default over the remaining lifetime of a product without appropriate supporting analysis. [IFRS (c), B ]
Grouping together exposures that are not sufficiently similar. [IFRS 9.B5.5.5]

12. Hybrid Internal Model Annual Charge Off Data
Appropriately Segment Portfolio
Understand Changing Default Rates
Document Appropriate Adjustments
Better

13. Historical Data Data Elements Performance Data Loan Quality Data
Probability of Default
Likelihood of Default
Volume, not Magnitude
Increases as
FICO score drops
Unemployment rates go up
Member becomes delinquent
Decreases as loan moves towards maturity

14. Hybrid Internal Model Historical Default Data Vintage Trend Analysis
Construction of Lifetime Probability Curve
Vintage Trend Analysis
Historical Default Data
Two types of PDs are used for calculating ECLs:
■ 12-month PDs – This is the estimated probability of default occurring within the next 12 months (or over the remaining life of the financial instrument if that is less than 12 months). This is used to calculate 12-month ECLs.
■ Lifetime PDs – This is the estimated probability of a default occurring over the remaining life of the financial instrument. This is used to calculate lifetime ECLs for ‘stage 2’ and ‘stage 3’ exposures.
To determine lifetime PDs, the bank either builds from the 12-month PD model or develops a lifetime PD model separately.
If the bank builds from the 12-month PD model, it develops lifetime PD curves or term structures to reflect expected movements in default risk over the lifetime of the exposure. This involves:
■ Sourcing historical default data for the portfolio.
■ Performing vintage analysis to understand how default rates change over time.
■ Extrapolating trends to longer periods where default data are not available for the maximum period of exposure.
■ Performing analysis at an appropriately segmented level, such that groups of loans with historically different lifetime default profiles are modelled using different lifetime default curves.

15. Hybrid Internal Model June 30, 2016 A B 2 4 6 8 10 12 14 16 18 20 22
One challenge for the PD method is that taking a pool of loans and tracking them through their life can take a lot of data. One way to get around that is what The GPPC considers a hybrid internal model
Lifetime probability of default is essentially the sum of all monthly probabilities of default.
A 12 month history is inadequate to estimate lifetime probability of default, but I bet if I asked you to calculate a monthly probability of default using that data for any month, you could do it.
Well, let’s just do that for all the months.
ABC Credit Union – 2,500 Loans
Pool A – 1,000 Loans
Pool B – 1,500 Loans 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Loan Age (in Months)

16. Hybrid Internal Model June 30, 2016 to June 30, 2017 A B 1,000 Loans
Pool A - 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Loan Age (in Months)

17. Hybrid Internal Model June 30, 2016 to June 30, 2017 A B 1,000 2,500
1,500
1,000 Loans
1,500 Loans A B
Pool A - 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Loan Age (in Months)

18. Hybrid Internal Model June 30, 2016 to June 30, 2017 1,000 2,500 1,500
1,000 Loans
1,500 Loans
Charge Offs 1 2 2 4 2 1 3 2 5 2 2 4 3 2 2 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Loan Age (in Months)

19. Hybrid Internal Model Month # of Loans # of Charge Offs % Charged Off8
1,000 1
0.10% 9 2
0.20% 10 11 4
0.40% 12
2,500
0.08% 13
0.04% 14 3
0.12% 15 16 5 17 18 19
0.16% 20
1,500 21
0.13% 22 23

20. Hybrid Internal Model June 30, 2016 to June 30, 2017 Month 10 - 21
Pool A - 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Loan Age (in Months)

21. Hybrid Internal Model Loan Type Direct Used Auto
Beginning of Year (BoY)
June 30, 2016
Ending of Year (EoY)
June 30, 2017
Charge Off Period
12 Months
Loan Count
% of BoY
Loans – BoY
16,275
Charge Offs
153
0.94%
Pay Offs
3,639
22.4%
Loans – EoY
12,483
76.7%

22. Modeling Example Charge-Off Month Default Volume Loan Volume
Monthly PD 8 2
4,326
0.05% 9 5
4,775
0.10% 10
5,234
0.04% 11
5,733
0.14% 12 3
5,873 13
5,639
0.20% 14
5,401
0.17% 15 4
5,227
0.08% 16
5,075 17
4,898
0.06% 18
4,771
0.19% 19
4,617
0.11% 20
4,440
0.09% 21
4,290 22
4,102
0.12% 23 7
3,905
0.18% 24
3,833
Charge-Off Month – The month in which a charge off occurred. If a loan was originated in June 2016 and charged off if February 2017 it would have been charged off in its 8th month
Default Volume – This is mean to be our numerator. The number of loans in our 12-month observation period that defaulted.
Default Volume Narrative: Of the 16,275 used direct auto loans that existed as of June 30, 2016, 2 of them charged off in the 8th month of their life.
Loan Volume – This is meant to be the denominator Remember, the beginning of our observation period is June 30, 2016 to June 30, 2017.
Default Volume Narrative – Of the 16,275 used direct auto loans that existed as of June 30, 2016, 4,326 passed through the 8th month of their life over this 12-month period. As of June 30, 2016, these loans:
Were in the 1st-7th month of their lives
Were originated between November 2015 and June 2016
Monthly PD – The probability that the loans that pass through each month charge off within that month.
Summary Narrative – Of the 4,326 loans that existed as of June 30, 2016 and passed through their 8th vintage month between June 30, 2016 and June 30, 2017, 2 defaulted (0.05%).

23. 12-Month Loss History
This illustration shows the construction of the 12-month loss history using the table on the previous slide. For example:
A 12-month curve for a loan in month one (that just originated) would be the sum of:
Months 0-7 – NO LOSSES
Month 8-11 (0.05% % % %) = 0.33%
A 12-month curve for a loan in month 12 (that is one year old) would be the sum of the monthly PD from month (1.43%)

24. Survival Probability Months on Book # of Loans (6/30/16)
Remaining Pool (6/30/17)
12-Month Survival
24-Month Survival
36-Month Survival
48 Month Survival
60 Month Survival
354
301
85.0%
62.5%
44.2%
24.5%
11.3% 12
449
330
73.5%
52.0%
28.8%
13.3%
0.0% 24
325
230
70.8%
39.2%
18.0% 36
159 88
55.3%
25.5% 48 89 41
46.1%
The probability that a loan still exists at a given time in its life.
Some loans pay off.
Some loans are charged off.
Some loans survive
We only have 12 months of history, but you can estimate longer term survival probabilities using the available data. For example, if you flip a coin, you have a 50% chance of landing on heads. If you flip a coin twice, there is a 25% chance the coin will land on heads both times (50% * 50%). If a loan in Month 0 has an 85% chance of making it to Month 12, and a loan in Month 12 has a 73.5% chance of making it to Month 24, a loan in month 0 has a 62.5% chance of making it to Month 24 (85% * 73.5%)

25. Life of Loan Probability
Month of Life
Default Probability
Survival Probability
Weighted Default Probability
0.33%
100.00% 12
1.38%
85.03%
1.17% 24
0.97%
62.49%
0.60% 36
44.23%
0.27% 48
0.92%
24.48%
0.23% 60
0.00%
11.28%
Lifetime Probability of Default
2.60%
Probability of Default
Likelihood of Default
Volume, not Magnitude
Increases as
FICO score drops
Unemployment rates go up
Member becomes delinquent
Decreases as loan moves towards maturity
Transition Guidance:
55-20
The historical credit loss rate already factors in prepayment history, which it expects to remain unchanged. Community Bank A considered whether any adjustments to historical loss information in accordance with paragraph were needed, before considering adjustments for current conditions and reasonable and supportable forecasts, but determined none were necessary.

26. Life of Loan Probability of Default
Months
0 – 11
24 – 35
36 – 47
48+
Grand Total
0.33%
1.17%
0.60%
0.27%
0.23%
2.60% 1
0.38%
1.08%
0.54%
0.21%
0.14%
2.35% 2
0.57%
1.05%
0.52%
0.30%
0.13%
2.57% 3
0.74%
0.44%
0.28%
0.10%
2.62% 4
0.82%
1.07%
0.42%
0.31%
0.09%
2.71% 5
0.92%
0.39%
0.02%
2.67% 6
0.98%
0.93%
2.64% 7
0.87%
0.34%
2.73% 8
1.23%
0.95%
2.86% 9
1.21%
0.36%
2.81% 10
1.27%
0.00%
2.68% 11
1.25%
0.78%
0.29%
2.63% 12
1.38%
0.71% 13
1.29%
0.64%
0.25%
0.16%
2.34% 14
1.28%
0.63%
0.37%
0.15%
2.44%

28. Loss Given Default Months on Book Active Loans Average Current Balance
Probability of Default
Projected Number of Defaults
Expected Losses
(50% LGD)
444
21,676
2.60%
11.5
124,927 1
993
22,090
2.35%
23.4
257,941 2
1018
21,574
2.57%
26.2
282,351 3
996
22,094
2.62%
26.1
288,316 4
976
20,850
2.71%
26.4
275,351 5
995
21,520
2.67%
26.6
286,390 6
678
20,340
2.64%
17.9
182,253 7
776
20,391
2.73%
21.2
216,065 8
787
20,597
2.86%
22.5
231,875 9
717
19,993
2.81%
20.1
201,235 10
740
17,761
2.68%
19.8
175,827 11
775
17,681
2.63%
20.3
179,865 12
594
15,293
15.8
121,120 13
575
15,248
2.34%
13.5
102,691 14
555
14,523
2.44%
98,290

29. Expected Loss Summary Historical 12-Month Probability 0.94%
June 30, 2017 Loans
21,118
Projected Charge Offs
446
Weighted Lifetime Probability
2.11%
Increase in Volume
224.65%
June 30, 2017 Balance
330,000,000
Expected Charge Offs
3,800,000
Lifetime Loss Rate
1.15%

30. Adjusting for Credit QualityB C D E NR
Total
Annual Probabilities
0.15%
0.44%
0.52%
0.90%
1.56%
3.53%
4.97%
0.94%
Adjustment Factor
15%
47%
55%
95%
166%
376%
529%

31. What Can Go Wrong? Treating Incomplete Data as Complete Inadequate
Inconsistently Applied Methodology
Treating Incomplete Data as Complete
Inadequate
Loss
Experience

32. Summary Pros Cons Easy to Apply at the Record (Loan) Level
Dynamically Adjusts for Changing Portfolios
Pros
More Complex Calculations
Longer First Time Setup
Cons

33. Twenty Twenty Analytics
Thank You!
Questions?
Dan Price
President
Twenty Twenty Analytics
(877)