Previous Document | Next Document | List of Regulations |

Loan loss rates are determined by applying the loss- frequency equation and the loss-severity factor to Farmer Mac loan-level data. Using this equation and severity factor, you must calculate loan losses under stressful economic conditions assuming Farmer Mac's portfolio remains at a "steady state." Steady state assumes the underlying characteristics and risks of Farmer Mac's portfolio remain constant over the 10 years of the stress test. Loss rates discussed in this section apply to all loans, unless otherwise indicated. The loan volume subject to loss throughout the stress test is then multiplied by the loss rate. Lastly, the stress test allocates losses to each of the 10 years assuming a time pattern for loss occurrence as discussed in section 4.3, "Risk Measures."

p = 1/(1+exp(-(BX))

Where:

BX = (-12.62738) + 1.91259 ˇ X

ˇ X

ˇ (1-exp((-0.00538178) ˇ X

Where:

- p is the probability that a loan defaults and has positive losses (Pr (Y=1|x));
- X
_{1}is the LTV ratio at loan origination raised to the power 5.3914596;^{2} - X
_{2}is the largest annual percentage decline in FCBT farmland values during the life of the loan dampened with a factor of 0.0413299 per year;^{3} - X
_{3}is the DSCR at loan origination; - X
_{4}is 1 minus the exponential of the product of negative 0.00538178 and the original loan balance in 1997 dollars expressed in thousands; and - X
_{5}is the D/A ratio at loan origination.

Intercept -12.62738 <0.0001

X

X

variable 0.33830 <0.0001

X

X

Hosmer and Lemeshow goodness-of-fit p-value 0.1718

Max-rescaled R

Concordant 85.2%

Disconcordant 12.0%

Tied 2.8%

Here is an example of the calculation of the dollar losses for an individual loan with the following characteristics and input values:

Loan Origination Year | 1996 |

Loan Origination Balance | $1,250,000 |

LTV at Origination | 0.5 |

D/A at Origination | 0.5 |

DSCR at Origination | 1.3984 |

Maximum Percentage Land Price Decline (MAX) | -23.52 |

$1,278,500 = $1,250,000 ˇ 1.0228

0.998972 = 1 – exp((-.00538178) ˇ $1,278,500 / 1000)

Where,

Z

(-16.6439443) - 0.19596 ˇ DSCR + 4.55390 ˇ 0.998972 +

- 2.49482 ˇ DA = (-1.428509)

- 1 / 1 + exp

Z

- (-16.7439443) – 0.19596 ˇ DSCR + 4.55390 ˇ 0.998972 +

Loss Frequency Probability at (-16.74%) =

- 1 / 1 + exp

0.05330776 = (0.19333111 - 0.19866189) / -0.1

Loss Frequency at -16.69 percent =

Z

- (-16.6939443) – (0.19596) (DSCR) + (4.55390)(0.998972) +

(2.49482) (DA) = -1.411594

1 / 1 + exp

Dampened Maximum Land Price Decline =

- (-20.00248544) = (-23.52)(1.0413299)

- 0.17637092 = 0.053312247 ˇ (-16.6939443 –

(-20.00248544))

0.37235371 = 0.19598279 + 0.17637092

- 0.077821926 = 0.37235371 ˇ 0.209

- $97,277 = $1,250,000 ˇ 0.077821926

$81,987 = $97,277 - $97,277 ˇ (0.157178762)

You must calculate the age-adjusted loss rates for these loans that include adjustments to scale losses according to the proportion of total submitted collateral to the guaranteed amount as provided for in the "Dollar Losses" column of the transformed worksheets in the Credit Loss Module based on new data inputs required in the "Coefficients" worksheet of the Credit Loss Module. Then, you must adjust the calculated loss rates as follows:

Loan | Origination Balance | Age-Adjusted Loss Rate (Percent) | Estimated Age-Adjusted Losses | Guarantee Amount Scaling Adjustment (2/2.2) (Percent) | Losses Adjusted for Overcollateral |

1 | $1,080,000 | 7.0 | $75,600 | 90.91 | $68,727 |

2 | $1,120,000 | 5.0 | $56,000 | 90.91 | $50,909 |

A | B | C | F | E | F | G |

Whole-Letter Rating | Default Rate (Percent) | Severity Rate (Percent) | V3.0 GOA Factor (Percent) | V4.0 GOA Factors (D x 3) (Percent) | Concentration Ratio (e.g., 25%) (Percent) | Factor with Concentration Adjustment 1-((1-E)x(1-F)) (Percent) |

AAA | 0.897 | 54 | 0.48 | 1.41 | 25.00 | 26.06 |

AA | 2.294 | 54 | 1.24 | 3.70 | 25.00 | 27.78 |

A | 2.901 | 54 | 1.57 | 5.13 | 25.00 | 28.84 |

BBB | 7.061 | 54 | 3.82 | 11.48 | 25.00 | 33.61 |

Below BBB and Unrated | 26.827 | 54 | 14.50 | 44.52 | 25.00 | 58.39 |

Loan A | Loan B | ||

1 | Guaranteed Volume | $2,000,000 | |

2 | Origination Balance of 2-Loan Portfolio | $1,080,000 | $1,120,000 |

3 | Age-Adjusted Loss Rate | 7% | 5% |

4 | Estimated Age-Adjusted Losses | $75,600 | $56,000 |

5 | Guarantee Volume Scaling Factor | 90.91% | 90.91% |

6 | Losses Adjusted for Total Overcollateral | $68,727 | $50,909 |

7 | Contractually Required Overcollateral on Pool (5%) | $100,000 | |

8 | Net Losses on Pool Adjusted for Contractually Required Overcollateral | $19,636 | |

9 | GOA Factor for “A” Issuer with 25% Concentration Ratio | 28.84% | |

10 | Losses Adjusted for “A” General Obligation | $5,664 | |

11 | Loss Rate Input in the RBCST for this Pool | 0.28% |

You must submit the outstanding principal, maturity date of the loan, maturity date of the AgVantage Plus contract (if applicable), and the rural utility guarantee fee percentage for each loan in Farmer Mac's rural utility loan portfolio on the date at which the stress test is conducted. You must multiply the rural utility guarantee fee by two to calculate the loss rate on rural utility loans under stressful economic conditions and then multiply the loss rate by the total outstanding principal. To arrive at the net rural utility loan losses, you must next apply the steps “5” through “11” of section 2.4.b.4 of this Appendix. For loans under an AgVantage Plus-type structure, the calculated losses are distributed over time on a straight-line basis. For loans that are not part of an AgVantage Plus-type structure, losses are distributed over the 10-year modeling horizon, consistent with other non-AgVantage Plus loan volume.

The stress test explicitly accounts for Farmer Mac's vulnerability to interest rate risk from the movement in interest rates specified in the statute. The stress test considers Farmer Mac's interest rate risk position through the current structure of its balance sheet, reported interest rate risk shock-test results,

HR. 15, "Selected Interest Rates." The stress test uses the 10-year CMT to generate earnings yields on assets, expense rates on liabilities, and changes in the market value of assets and liabilities. For stress test purposes, the starting rate for the 10-year CMT is the 3-month average of the most recent monthly rate series published by the Federal Reserve. The 3-month average is calculated by summing the latest monthly series of the 10-year CMT and dividing by three. For instance, you would calculate the initial rate on June 30, 1999, as:

Month End | 10-year CMT Monthly Series |

04/1999 | 5.18 |

05/1999 | 5.54 |

06/1999 | 5.90 |

Average | 5.54 |

Month End | 10-year CMT Monthly Series |

07/1998 | 5.46 |

08/1998 | 5.34 |

09/1998 | 4.81 |

10/1998 | 4.53 |

11/1998 | 4.83 |

12/1998 | 4.65 |

01/1999 | 4.72 |

02/1999 | 5.00 |

03/1999 | 5.23 |

04/1999 | 5.18 |

05/1999 | 5.54 |

06/1999 | 5.90 |

12-Month Average | 5.10 |

Calculation of Shock Amount |

12-Month Average Less than 12%: Yes |

12–Month Average: 5.10 |

Multiply the 12-Month Average by: 50% |

Shock in basis points equals 255 |

The stress test requires the initial financial statement conditions and income generating relationships for Farmer Mac. The worksheet named "Data Inputs" contains the complete data inputs and the data form used in the stress test. The stress test uses these data and various assumptions to calculate pro forma financial statements. For stress test purposes, Farmer Mac is required to supply:

Farmer Mac I program loan data fields |

Loan Number Ending Scheduled Balance Group Pre/Post Act Property State Product Type Origination Date Loan Cutoff Date Original Loan Balance Original Scheduled P&I Original Appraised Value Loan-to-Value Ratio Debt-to-Assets Ratio Current Assets Current Liabilities Total Assets Total Liabilities Gross Farm Revenue Net Farm Income Depreciation Interest on Capital Debt Capital Lease Payments Living Expenses Income & FICA Taxes Net Off-Farm Income Total Debt Service Guarantee/Commitment Fee Seasoned Loan Flag |

Condition: | Apply: | |

1. | Total Assets = 0 | Proxy D/A |

2. | Total Liabilities = 0 | Proxy D/A |

3. | Total assets less total liabilities <0 | Proxy D/A |

4. | Total debt service = 0 or not calculable | Proxy DSCR |

5. | Net farm income = 0 | Proxy DSCR |

6. | LTV ratio = 0 | Proxy LTV |

7. | Total assets less than original appraised value. | Proxy LTV, D/A |

8. | Total liabilities less than the original loan amount. | Proxy D/A |

9. | Total debt service is less than original scheduled principal and interest payment. | Proxy DSCR |

10. | Depreciation, interest on capital debt, capital lease payments, or living expenses are reported as less than zero. | Proxy DSCR |

11. | Original Scheduled Principal and Interest is greater than Total Debt Service. | Proxy DSCR |

12. | Calculated LTV (original loan amount divided by original appraised value) does not equal the submitted LTV ratio. | The greater of the two LTV ratios |

13. | Any of the fields referenced in "1." through "12." above are blank or contain spaces, periods, zeros, negative amounts, or fonts formatted to any setting other than numbers. | Proxy all related ratios |

In addition, the following loan data adjustments must be made in response to the situations listed below:

Situation: | Data adjustment: |

Original loan balance is less than scheduled loan balance. | Substitute scheduled balance for origination. |

Purchase (commitment) date (a.k.a. "cutoff" date) field and Origination date field are both blank. | Insert the quarter end "as of" date of the RBCST submission. |

Origination date field is blank. | Model based on Cutoff date. |

Seasoned Standby loans that include loan data. | Proxy data applied.^{*} |

Mac in favor of other criteria and frequently not origination data.

Further, because it would not be possible to compile an exhaustive list of loan data anomalies, FCA reserves the authority to require an explanation on other data anomalies it identifies and to apply the loan data proxies on such cases until the anomaly is adequately addressed by the Corporation.

FCA Ratings Category | AAA | AA | A | BBB | Below BBB and Unrated |

Standard & Poor's Long-Term | AAA | AA | A | BBB | Below BBB and unrated |

Fitch Long-Term | AAA | AA | A | BBB | Below BBB and Unrated |

Standard & Poor's Short-Term | A-1+ SP-1+ | A-1 SP-1 | A-2 SP-2 | A-3 | SP-3, B, or Below and Unrated |

Fitch Short-Term | F-1+ | F-1 | F-2 | F-3 | below F-3 and Unrated |

Moody's | Prime- MIG12 VMIg1 | Prime-2 MIG2 VMIG2 | Prime-3 MIG3 VMIG3 | Not Prime, SG and Unrated | |

Fitch Bank Ratings | A | B A/B | C B/C | D C/D | E D/E |

Moody's Bank Financial Strength Rating | A | B | C | D | E |

Ratings Classification | Non-Program Investment Counterparties (Excluding Derivatives) (Percent) |

Cash | 0.00 |

AAA | 1.41 |

AA | 3.70 |

A | 5.13 |

BBB | 11.48 |

Below BBB or Unrated | 44.52 |

Fixed Spread = Weighted Average Yield less 10-year CMT

0.014 = 0.0694 - 0.0554

Yield = Fixed Spread + 10-year CMT

.0994 = .014 + .0854

The worksheet labeled "Loan and Cashflow Data" contains the categorized loan data and cashflow accounting relationships that are used in the stress test to generate projections of Farmer Mac's performance and condition. The steady-state formulation results in account balances that remain constant except for the effects of discontinued programs, maturing AgVantage Plus positions, and the LLRT adjustment. For assets with maturities under 1 year, the results are reported for convenience as though they matured only one time per year with the additional convention that the earnings/cost rates are annualized. For the pre-1996 Act assets, maturing balances are added back to post-1996 Act account balances. The liability accounts are used to satisfy the accounting identity, which requires assets to equal liabilities plus owner equity. In addition to the replacement of maturities under a steady state, liabilities are increased to reflect net losses or decreased to reflect resulting net gains. Adjustments must be made to the long- and short-term debt accounts to maintain the same relative proportions as existed at the beginning period from which the stress test is run with the exception of changes associated with the funding of defaulted loans during the LLRT period. The primary receivable and payable accounts are also maintained on this worksheet, as is a summary balance of the volume of loans subject to credit losses.

The "Capital" worksheet contains the results of the required capital calculations as described below, and provides a method to calculate the level of initial capital that would permit Farmer Mac to maintain positive capital throughout the 10-year stress test period.

_____________________

The Gauss-Newton method is the selected iterative solving process. As described in the preamble, the loss-frequency function for the nonlinear model is the negative of the log-likelihood function, thus producing maximum likelihood estimates. In order to obtain statistical properties for the loss-frequency equation and verify the logistic coefficients, the estimates for the nonlinear transformations are applied to the FCBT data and the loss-frequency model is re-estimated using the SAS Logistic procedure. The SAS procedures, output reports and Excel spreadsheet used to estimate the parameters of the loss-frequency equation are located on the Web site

[71 FR 77255, Dec. 26, 2006; as amended at 73 FR 31940, June 5, 2008; 76 FR 23467, Apr. 27, 2011; 78 FR 21037, April 9, 2013]

[