Roll Rate Model In Excel

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Quantifying these impacts allows them to be included in a forecast or to change them in a scenario. What is the intrinsic quality of an account or a consumer? An account opened in a bad environment can be expected to perform worse than an account opened in a good environment, but it seems that such behavior should be assigned to the environment, not the account. Credit scores usually have a similar goal.

Most scores are designed with the intent that a change in the environment does not change the relative ranking of accounts. Naturally, credit scores are the primary tool for measuring account quality.

However, other issues can also play a role in explaining originations quality. Loan-tovalue, first versus second lien position, product mix, channel mix, and geographic mix are just some of the other factors that can drive quality. Some factors driving quality are less predictable or controllable, such as system breakdowns and adverse selection due to things like competitor actions. For this reason, score monitoring must always be accompanied by direct measurement of quality from the performance data with proper adjustments for changes in the environment and differences in maturity.

Keep in mind that a simple vintage plot does not convey this kind of information. Although a visual comparison of vintages is useful, vintage plots are ambiguous as to the cause of the differences between vintages. Economic cycles tend to create industry-wide reactions. Although every portfolio has its unique aspects, similar patterns in vintage quality can be observed through most. Figure 1 shows a schematic representation of how vintage quality has changed over the last several years.

Again, this is not vintage performance, but rather the component of performance attributable to the intrinsic quality of the accounts. Much discussion has surrounded the Vintage for its poor performance. Credit scores and economic conditions are not enough to explain this performance.

In fact, none of the usual metrics revealed anything abnormal. The best hypothesis seems to be adverse selection.

As the economic shocks began in early , better-quality consumers in any given score band became more cautious about taking on debt. The result was a vintage of unexpectedly poor quality. Conversely, and were years of directed action. Most portfolio managers dramatically tightened their criteria because of the worsening economic environment and worrying delinquency trends.

The resulting higher-quality vintages typically will not dominate portfolio losses for several more years, yet the reaction of being conservative in a bad economic period is quite common. Anecdotal evidence suggests that this trend may be reversing. As managers see better economic prospects ahead, they may again start loosening underwriting criteria in a battle for market share.

The established pattern repeats. Fundamental to any portfolio is an understanding of the life cycles in any performance metric.

New accounts follow a natural life cycle. A credit card account that starts empty will tend to mature by building a balance and increasing the risk of delinquency. When environmental impacts are removed, almost all performance metrics show accounts maturing relative to months-onbooks. The maturation process is one of the most predictable aspects of the portfolio.

When cleaned of variation in originations quality and environmental impacts, it provides an immediate boost for portfolio forecasting efforts. The specific shape of the maturation curve varies across products and demographic segments. Figures 2 and 3 show examples of maturation curves. Prime versus subprime creates one of the strongest disparities in the shape of maturation curves. Figure 2 compares charge-off rates for prime and subprime credit cards.

Subprime products in general tend to peak high and fast compared to prime products. It may be a bit optimistic to have subprime drop below prime even after years of maturing, as shown in the figure, but one can always hope. Although subprime loss rates can be quite high, the good side is that the origination-to-attrition cycle is short, and therefore the portfolio can be actively managed.

For prime products, the lag between origination and peak delinquency is so long that course corrections are very slow to affect portfolio performance. Today's prime portfolio performance is often a remnant of the actions of previous management. With prepayment rates, the patterns tend to be reversed.

Prime auto loans, for example, will show important levels of prepayment in the first few years as the lowest-risk customers pay off their loans.

With subprime, few consumers have surplus funds with which to make advance payment, so loan payoffs tend to occur predominantly at the end of the term. Life cycles are important in understanding portfolio performance, because yesterday's accounts perform differently tomorrow, even if nothing in their universe changes. Accounts booked today may have peak revenue or delinquency up to several years in the future.

Although conceptually simple, this effect creates a great deal of confusion when interpreting performance data. Changes in originations criteria today can dominate the portfolio years into the future under a different economic environment.

Many portfolios have poor vintages from dominating their portfolios today. For those same portfolios, a recovery in would coincide with a portfolio composed largely of today's highquality bookings. Timing originations policies to the environment is one of the most difficult aspects of portfolio management. Underwriting criteria are set by calibrating to the most recent year or two of data. This is how credit scores are commonly used.

New accounts are originated, and peak delinquency risk may not occur until several years into the future. This can, and often does, make origination policies exactly out of phase with the environment, where the worst loans mature in the worst environment and the best loans mature in the best environment.

Maturation curves and originations quality describe vintage performance in isolation. Consumers live in the real world, so we must consider shocks to this idealized behavior. Seasonality, management actions, and macroeconomic impacts all have the power to alter the observed vintage performance. Seasonality is the most obvious of all portfolio impacts.

Holidays, tax refunds, summer vacations, and back-to-school spending are the most common examples. Almost all portfolio metrics show the effects of seasonality.

Seasonality is not difficult in concept, nor particularly difficult to measure. The key to success is keeping long time series. A two-year rolling database is insufficient to provide a reliable estimate.

Seasonality can be masked by recurring policies, e. Seasonality tends not to vary significantly across demographic segments, which can provide additional clues about seasonal patterns. Every portfolio history includes course corrections.

This is what management is paid to do. Yet management actions can confound any portfolio analysis. Embedded in the portfolio performance metrics are changes in collections policies, credit line assignment, system outages, database changes, etc. These effects must be identified and extracted so that the forecast does not implicitly assume a replay of past actions.

Few organizations maintain detailed logs of policy changes. This must change with the Basel II focus on operational risk, but it is also extremely valuable to forecasting and management.

Measuring these impacts and extracting them is much easier when a process is employed that first removes the portfolio variability caused by origination changes and vintage maturation. The business cycle is not dead. Intuitively, everyone knows the economy drives portfolio performance.

Quantification, however, is quite difficult. Long time series are essential. Originations volume and quality, vintage maturation, management actions, and seasonality must all be removed before macroeconomic impacts become clear. Yet, early warning of these changes is extremely valuable, allowing managers to implement contingency plans. Industry-wide indices can help, but they can be masked by industry-wide management trends.

For example, the recent move to higher-quality originations will affect any industry-average performance metric. Therefore, an accurate internal measurement is always essential to understanding how macroeconomic impacts are affecting the portfolio.

The current macroeconomic environment for losses continues to be difficult. Many portfolios are at recent highs for losses driven by macroeconomic factors. This is not to say that total portfolio performance is at its worst. Some of the better-quality vintages from may be starting to bring down overall loss rates.

Nevertheless, most portfolios are showing the contribution to losses from the outside environment to be at recent highs. The real question, of course, is where do we go from here? The preceding discussion lays out the components of historical behavior that should be measured and understood.

The key to success is to estimate them such that they are roughly independent of each other. Achieving statistical independence in the measurement is not easy, but very valuable. This article has not focused on how those pieces are measured, but a thorough discussion of that subject can be found in"Becoming a Better Vintner," The RMA Journal, September Predicting where you're going. Historical analysis is necessary, but everyone's burning question is, "Where is the portfolio headed?

Further confounding the effort are an endless number of hybrids incorporating aspects of different techniques. For these reasons, no overview can be truly exhaustive, but we will try to review some of the dominant techniques in use and under development.

Forecasting techniques differ greatly in their handling of scenarios. Some provide explicit and extensive support for scenarios, while others operate more as a black box with no obvious controls. Nevertheless, all forecasts make certain assumptions:.

A forecasting approach that does not allow users to input scenarios for these items must be either assuming "no change" or creating scenarios using some form of extrapolation.

Therefore, all forecasting approaches should be viewed as scenario based. The only question is whether you can change the scenario. What follows is a short encyclopedia of forecasting techniques, providing a brief description along with the pros and cons of each.

Although some are more sophisticated and seemingly more capable than others, the correct choice of forecasting technology is a multi-faceted question that will be addressed later. Accounts are segmented into many small cohorts based upon a range of criteria. Recent historical averages are computed for each segment and taken as a prediction of future performance.

Cohort averages had to be included in this list because they are so simple to create. However, they are so prone to failure that no important decision should be based solely upon a cohort average forecast.

Many industry-wide data and forecasts have become available from consortia, bureaus, or other vendors. These can be used as a proxy or starting point for an internal forecast. Industry-wide indices or forecasts are really best when integrated with an internal forecasting methodology in order to overcome data shortcomings. The classic roll-rate model is a structural model of the net rate at which accounts roll through delinquency buckets. Predictions are made by computing a moving average of historical roll rates.

Roll-rate models are a simplified subset of the broader class of Markov models. State transitions are modeled by transition probabilities. Probabilities are usually computed as a moving average on the historical data. Markov models have seen some limited use, but they are not generally flexible enough to be used across the range of portfolio forecasting problems. Vintage models start by estimating rates as a function of months-on-books by computing average curves from the historical data.

Vintage models are often used as the starting point in hybrid approaches. Many sophisticated statistical approaches have been tested on consumer loan portfolios.

Desktop computing power has ushered in an era of nonlinear models for many applications. The current generation of nonlinear statistics packages is probably best suited to account level scoring. To be effective in portfolio forecasting, these seemingly sophisticated techniques are best hybridized with a more structural approach that understands retail lending.

Unmodified off-the-shelf implementations are rarely useful. As a categorical term, nonlinear decomposition is not in wide use. It is defined here to refer to techniques that attempt to quantify all the historical components first originations quality, life cycle, seasonality, management impacts, and economic impacts and then combine those components at the vintage level to create a forecast.

Many different approaches are in use today within this category. They cover the spectrum from completely manual and labor-intensive techniques to fully automated modeling engines and many stages in between. Modeling macroeconomic impacts is of great interest for portfolio forecasting today. Although in some texts econometric modeling is even defined to include simple regression, here we are interested in relating macroeconomic variables to portfolio performance. The goal is to understand and predict the economy's impact on the portfolio.

A wide variety of models are used to create this relationship. Then we use dplyr to group the data, and then create the new column you need. By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. Prad Prad 98 9. Not clear to me - don't you already have the results you're after? I have the results from Column D.

Is this structure repeated for different months? Assuming you always have groups of three rows with the same date, we can use dplyr. Juan Bosco Juan Bosco 1, 2 12 Hi Juan, Thankyou for your help, i tried it and i understood the code. But i have few doubts. I was able get the results, in my actual dataset the range is [1:

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