This framework has various applications, most notably IFRS 9/CECL impairment calculations. The private firm converter leverages RiskCalc™ Credit Cycle Adjustment (CCA) and term structure. Resulting PD measures are country- and industry-specific.

The RiskCalc Private Firm Converter v1.3 builds on our Private Firm Converter v1.2, originally released in June 2019. Private Firm Converter v1.2 transforms one-year TTC PD measures into one-year PIT PD measures and estimates a typical term structure, depending on the risk level. V1.3 maintains this functionality, while also providing the option of entering the five-year TTC PD as an input, and then converting both the one-year and five-year TTC measures to PIT, replicating RiskCalc methodology.

**1. Introduction**

The International Accounting Standards Board (IASB) and the Financial Accounting Standards Board (FASB) issued new accounting standards,^{1} commonly known as IFRS 9 and CECL, which require calculating expected losses, given current economic conditions. Entities can leverage existing internal models or use new tools to comply with the new standards.

Since most banks must follow the Basel Capital Standards, current internal models may include Foundation Internal Ratings-Based (FIRB) approaches and Advanced Internal Ratings-based (AIRB) approaches, which estimate one-year PDs based on long-run averages of one-year default rates for borrowers within a rating grade. These are often regarded as TTC PD measures. Since the recent accounting standards require firms to incorporate information regarding current conditions, TTC PDs require a cycle adjustment. Further, firms must also express PDs for different time horizons.

The Private Firm Converter leverages Moody’s Analytics RiskCalc CCA and term structure to calculate PIT term structures for private companies, beginning with any TTC PD. The Private Firm Converter v1.3 includes the following improvements over v1.2:

- Optional five-year TTC PD input. If users have a five-year TTC PD estimate (along with the one-year TTC estimate), they can use it as an additional input, to convert both one-year and five-year measures to PIT, and build a term structure using the same methodology as in RiskCalc.
- When the five-year TTC PD input is not provided, the model will continue using the RiskCalc static mapping term structure to inform the estimation, but the treatment for the obligors within the highest risk category (Caa/C bucket) is more conservative than v1.2.
^{2}

**2. Leveraging RiskCalc to Convert TTC PD to PIT PD**

The Moody’s Analytics RiskCalc model suite provides credit risk measures for various countries and industry segments throughout the world. RiskCalc EDF™ (Expected Default Frequency) credit metrics can be calculated using two different modes: Financial Statement Only (FSO) and Credit Cycle Adjusted (CCA). The FSO mode calculates an obligor’s probability of default based purely on the information found in the company’s financial statements and industry information. The CCA mode incorporates the current position of the credit cycle in addition to financial statement information.

Most RiskCalc models use the Distance-to-Default (DD) calculation from the Moody’s Analytics Public Firm Model to capture the credit cycle position in a particular country and industry sector. A public firm’s DD reflects the equity market's current assessment of the firm’s default risk, and is, hence, a forward-looking measure of default risk. When changes in the equity market impact public firm DD measures, it leads to a similar change in the default probability of private firms in that sector. Some models also combine the industry-specific signal with additional macroeconomic variables to arrive at the credit cycle adjustment.

As financial ratios are relatively stable over time, FSO EDF metrics are stable as well. CCA EDF metrics are more cyclical. As a result, RiskCalc CCA EDF metrics are similar to PIT PDs, while FSO EDF metrics are similar to TTC PDs. Figure 1 shows the Average FSO and CCA EDF credit measures by year for the RiskCalc U.S. 4.0 Corporate Model. We see that the average FSO EDF tends to be more stable through time when compared to the average CCA EDF. We also see that the CCA EDF aligns with the observed default rate through time.

_{𝑖}, … , 𝑥

_{𝑁}are the input ratios/factors; 𝐼

_{1}, … , 𝐼

_{𝐾}are indicator variables for each of the industry classifications; β and γ are estimated coefficients; Φ is the cumulative normal distribution; 𝑇

_{𝑖}𝑠 are non-parametric transforms of each financial statement variable;

^{3}

*F*is the final transform, (i.e., the final mapping), which captures the empirical relationship between the probit model score and actual default probabilities; and FSO EDF is the financial statement only EDF credit measure. In CCA mode, the functional form becomes

where the Credit Cycle Multiplier is a function of the DD factor.^{4} When the multiplier is one, the average level of credit risk in the economy is neutral, and the FSO EDF value equals the CCA EDF value. When the Credit Cycle Multiplier is less than one (indicating low credit risk), the CCA EDF results in a lower value than the FSO EDF value. Conversely, when the Credit Cycle Multiplier is greater than one (indicating high credit risk), the CCA EDF results in a larger value than the FSO EDF value.

The PIT converter leverages RiskCalc CCA functional form and parameters to adjust any TTC PD measure. The starting TTC PD may have been calculated using an internal rating system, a qualitative factor-adjusted PD derived initially from a RiskCalc FSO EDF or any other TTC PD measure. The first step in converting a TTC PD is calculating its implied probit score using Equation (1):

**3. Using RiskCalc to Obtain a PD Term Structure
**

**3.1 Five-Year TTC optional input is provided**

When a five-year TTC estimate is available, the converter will transform both one- and five-year TTC values to PIT using the methodology described on Section 2. The converter then uses the one-year and five-year estimates to fit a Weibull function and obtain two-, three-, and four-year PIT estimates.

**3.2 Using only the One-Year TTC estimate**

When a five-year TTC estimate is not available, the converter leverages RiskCalc static mapping, which provides a term structure for each rating category.

Although a PD Term Structure may be based on observed default rates by credit risk categories for different time horizons, due to the lack of data in certain categories, the realized default rates may not be monotonic as credit risk changes. Taking this into consideration, as well as other objectives,^{5} RiskCalc designed a term structure using Moody’s bond rating categories, for both one-year and five-year horizons, also known as RiskCalc static mapping. Table 1 shows its lower and upper boundaries:

This mapping table expands to include a term structure between years two and four, using the two-point estimates for the one-year and five-year estimates to fit a Weibull function and, thus, achieve a continuous term structure of EDF values for each rating bucket.

To obtain the term structure of any one-year PD, we first use Table 1 to obtain the implied rating and then find the PD between years two and five using linear interpolation within the rating bucket. Specifically, we first calculate the natural logarithm of the starting PD and boundaries by bucket. We then perform a linear interpolation using the boundaries for the rating bucket at each time horizon. Figure 2 illustrates the process.

When the one-year PIT estimate goes beyond the RiskCalc one-year boundary of 35%, the converter assumes that the obligor’s annualized PD for the entire term structure is equal to the one-year PIT PD.

**3.3 Term Structure beyond Five Years **

If a term structure beyond five years is needed, we estimate the forward rate between years four and five and assume this is the constant forward rate for the next years, as follows:

CEDF_{t} = 1-(1-CEDF_{5})×(1-FEDF_{4,5})^{(t-5)}

where *CEDF _{t}* is the cumulative EDF for year

*t*, and

*FEDF*

_{}_{4,5}is the forward EDF from year

*four*to

*five*.

*FEDF _{}*

_{4,5}= (

*CEDF*)/(1-

_{5}-CEDF_{4}*CEDF*), where

_{4}*FEDF*

_{}_{4,5}is the forward EDF from year

*four*to

*five*, and

*CEDF*is the cumulative EDF for year

_{4}*four*.

**4. Assumptions and Limitations**

As with all models, the Private Firm Converter relies upon a number of assumptions, and its usage is subject to some limitations.

**ASSUMPTIONS**

The credit cycle signal that most RiskCalc models use is derived from Moody’s Analytics public firm model. This approach assumes that public and private companies of the same sector share the same credit signal. To verify this assumption, we compare the output from the model against observed default rates of private companies over time.

Since some PIT converter users typically estimate a one-year TTC PD only, not a term structure, the private firm converter estimates a term structure for a typical firm on that risk category. The term structure methodology assumes that the implied rating at longer horizons is the same as the one-year implied rating. Although we observe that, in practice, companies may have a better or poorer implied rating at a longer horizon, it is more common to have the same rating.

If a term structure beyond five years is needed, the model assumes a constant forward rate, equal to the forward rate between years four and five. This forward rate represents the probability that a firm will default between years four and five, assuming the firm survived to year four, and, therefore, represents a long-term view of the default risk of a particular firm. This assumption is consistent with our recommendation for RiskCalc users.

If a term structure for an obligor with a one-year PIT PD above the RiskCalc boundary of 35% is needed, the converter assumes that the obligor’s annualized PD for the entire term structure is equal to the one-year PIT PD. The PD measures above 35% are not covered by RiskCalc, and there is very limited data to inform a term structure above the threshold.

**LIMITATIONS**

Given that the private firm converter leverages RiskCalc methodology, its applicability is limited to the types of companies RiskCalc covers. For example, RiskCalc corporate models typically exclude financial institutions and real estate companies. Similarly, the correct model should be used for each provided geography. For countries where we have not yet developed a RiskCalc model, we generally recommend a proxy RiskCalc model that can also be used in the Private Firm Converter.

The list of industries available in Private Firm Converter matches the sectors covered by RiskCalc, and it is specific to each corresponding RiskCalc model. For example, the RiskCalc United States 4.0 Corporate sectors are: Agriculture, Business Products, Business Services, Communication, Construction, Consumer Products, Health Care, HiTech, Mining, Services, Trade, Transportation, Unassigned, and Utilities.

The Private Firm Converter assumes that the provided input PD is a TTC PD, similar to RiskCalc FSO EDF. The input PD may be derived using an internal rating system, a qualitative factor-adjusted PD derived initially from a RiskCalc FSO EDF, or any other TTC PD measure.

**5. Ongoing Monitoring**

We conduct model operation monitoring to ensure that the external factors underlying the model are validated, and that the model continues to operate properly. This consists of quality assurance checks on the CCA factors and data input/output validation.

During a RiskCalc monthly production cycle, we perform several CCA factors checks — focusing primarily on the month-over-month change of the DD factors, using history trends as a benchmark. In the event that we see an unusual change in the DD factor, we perform a detailed case study. Most often, exceedances are found to be justified. In the rare cases when inaccurate DD factors are identified, the issue is resolved, CCA factors are re-calculated, and then published. Under extremely rare circumstances where published CCA factors are found to be inaccurate, an immediate investigation takes place, followed by a timely resolution, and re-calculation and re-publishing of the corrected CCA factors to RiskCalc. An impact analysis report is also distributed to address the impact of previously inaccurate results, if any, on the scoring and/or implied ratings.

**6. Outcome Analysis**

Private Firm Converter testing is covered by the regular RiskCalc model performance assessment, as they both share the same underlying methodology. For each RiskCalc model in each year, we decide if a performance assessment is warranted. The decision to conduct a performance assessment depends upon a variety of factors, but a key one is whether enough new data is available to undertake a meaningful performance assessment. Performance assessment tests can be broken into three groups: (i) a test as to whether or not the model calibration is working as intended; (ii) the rank ordering ability of the model; and (iii) a level validation of the model. In general, the data requirements for assessing (i) are less than that of assessing (ii), which is less than assessing (iii). When data is unavailable, we formulate a plan for acquiring new data from the relevant population.

**7. Summary**

This document presents the RiskCalc approach to incorporate a Credit Cycle signal and how to leverage it to convert any TTC PD to a PIT PD. The TTC PD may be sourced from an internal rating system, an FSO qualitative-adjusted PD, or any other TTC PD. The resulting PIT PD measures are country- and industry-specific. The document also presents an approach to calculate the term structure, starting from either a one-year PD, or both a one-year and a five-year PD. Resulting PIT PD term structures can be used for various applications, such as the IFRS 9/CECL accounting standards requirements.

^{1} In 2014 and 2016, respectively.

^{2} In particular, for v1.2, the one-year upper boundary for the term structure interpolation within the Caa/C bucket was 100%, while for v1.3, the boundary is 35%, consistent with the RiskCalc one-year boundary. When the one-year PIT estimate is beyond 35%, v1.3 assumes that the obligor’s annualized PD for the entire term structure is equal to the one-year PIT PD.

^{3} The non-parametric transforms capture the non-linear impacts of financial ratios on the default likelihood.

^{4} The actual construction of the DD factor differs somewhat by country. Please refer to the methodology paper of the specific RiskCalc model that you are using for more details.

^{5} See FAQ – Static Mapping

^{6} The Private Firm Converter v1.3 upper boundary for the Caa/C bucket is 35%, for the one-year horizon, and 88.3971% for the five-year horizon, differing from v1.2, which had 100% as the upper boundary at both one- and five-year horizons.