# Roll Rate Analysis: Estimating the Value of a Pool of Loans

Analyzing roll rates on a portfolio of unsecured consumer loans—or any type of loan for that matter—is an effective way to review overall trends and estimate future performance. Roll rates are the percentage of loans moving from one state of delinquency to another—e.g., 30 days past due (DPD) to Charged-off. Generally, when reviewing the health of a portfolio, one of the best assessments is the periodic change in a portfolio’s roll rates.

## Reviewing the “Roll”: Markov Chains

As shown below in Fig. 1, with Orchard’s performance analysis tool one can review the “roll” of balances from one delinquency bucket to another. This example is for an aggregate of consumer unsecured loans but, again, this kind of analysis can be done for various cohorts of loans from any originator or asset class on our platform. At a quick glance, you can see the high percentage of loans that roll from a particular delinquency bucket to further delinquency buckets. For example, 30-59 DPD to 60-89 DPD or 60-89 DPD to 90-119 DPD. This movement is typical for unsecured consumer loans and has been discussed in previous Orchard roll rate blog posts about Lending Club and Prosper.

*Fig. 1: 1–Month Roll Rate Matrix*

Investors can use roll rate transition matrices, as shown above, to forecast the performance of a portfolio of loans. This method of using transition matrices to calculate the probability of a loan moving from one state to another is also known as Markov Chains. In Fig. 2, I demonstrate how the transition matrix from Fig. 1 could be used to roll forward three months to estimate future performance for a sample portfolio.

*Fig. 2: Sample Portfolio Roll Forward Estimation*

We start with an initial distribution of loans in period 0. Then, we use the transition probabilities from Fig. 1 to calculate new distributions of loans iteratively in periods 1, 2, and 3. For example, we calculate the Current bucket for period 1 as:

When using roll rate transition matrices to forecast performance, most portfolio managers use a historical average of roll rates to create transition matrices to apply recent performance changes to their portfolio of loans. In general, the use of historical roll rate transitions does not account for external risk factors and macroeconomic conditions, so roll rate transition matrices may be better suited to short-term forecasting.

In Fig. 3, Orchard provides the 3-month roll rate matrix for an aggregate of unsecured consumer loans.

*Fig. 3: 3-month Roll Rate Matrix*

With the power of Orchard’s platform, users can use the 3-month roll rate matrix to forecast a 3-month outlook on an unsecured consumer loan’s performance without having to run the transition matrix per period, as done in the previous exercise. As shown in Fig. 3, a user could estimate current balance and overall charged-off and paid-off as of month 3. This is a great tool if you want to simply calculate expected performance as of a certain month.

*Fig. 4: Sample Portfolio 3–Month Roll Forward Estimation*

While the roll rate transition forecasting methodology is not perfect, the tool is well-suited to providing a top-down overview approach to estimating future performance and assessing the overall health of a portfolio in a relatively uncomplicated manner. If forecasting for exogenous factors—credit loan characteristics, or long-term performance—industry professionals typically use other statistical methods such as logistic/linear regressions, generalized additive models, decision tree ensembles, or neural networks to model expected performance.

## Using Roll Rates to Estimate the Value of a Pool of Loans

If estimating the value of a portfolio of loans, we could use the same roll rate methodology. We have found that a 12-month roll rate matrix can be useful for pricing a portfolio of loans. A 12-month roll rate matrix shows the “roll” of the delinquency status 12 months from a loan’s current transition state. For example, the percentage of loans in 30-59 DPD status in month 0 that were charged off in month 12.

As shown in Fig. 5 below, an unsecured consumer loan in delinquency status 30+ DPD has a high probability of being charged off within 12 months. This assessment of unsecured consumer loan performance has helped us develop a simple valuation for a portfolio of consumer loans.

*Fig. 5: Probability of Charged-off within 12 months*

For the matrix in Fig. 6, we created a modified 12-month roll forward matrix by delinquency status and remaining terms to calculate the probability of a loan being charged off. Loans in current status are valued at 100% of the current unpaid balance.

*Fig. 6: 3-12-month Forward Roll Rate by Remaining Terms and Delinquency Status*

When calculating a value for loans, users can use the above table to value a loan by current delinquency bucket and remaining term. Users are able to add or substitute other factors into the matrix such as origination FICO, originator, current unpaid balance, etc. If an investor were reviewing a loan within 30-59 DPD with a remaining term of five months, an investor would price the loan as 32.5% of the loan’s current unpaid balance, based on the 67.5% probability of the loan being charged off within twelve months.

The accuracy of this methodology is sufficient when calculating a portfolio that doesn’t have many credit-quality changes or exogenous factors affecting the performance of loans. As shown in Fig. 7, the use of a 12-month roll forward methodology is accurate in estimating the percentage of loans moving into charged-off.

*Fig. 7: 30+ DPD Expected Charged-off vs. Actual Charged-off*

The 12-month roll rate methodology provides a value that is less than 99 bps for a loan in 120+ DPD. If using the current tool to evaluate pricing on a loan, it would be beneficial for an investor, originator, or portfolio manager to review the historical recoveries and use that data to calculate an expected return on loans that go into charged-off. Orchard Platform will be looking into the recovery rate for unsecured consumer loans in future blog posts, but we have seen initial average recovery rates between 5%-12%, after recovery fees, for many unsecured consumer loans in the space.

Valuing a portfolio is just one of multiple uses for roll rates when analyzing a portfolio of unsecured consumer loans. The 12-month roll rate tool assists users in calculating an internal value for a portfolio of unsecured loans. In future a blog post, we will demonstrate how to value a portfolio of loans’ expected returns using a cash flow methodology.

Notes:

https://arxiv.org/pdf/1106.4513.pdf

https://www.orchardplatform.com/blog/revisiting-roll-rates-using-markov-chains/