Orchard Research Brief: Historical CPR and CDR Curve Construction
At the end of 2016, Orchard released a major update to our Cash Flow Simulator, which, among other things, introduced the ability to price loan pools using performance curves. For those unfamiliar with Cash Flow Analysis, it is a method for modeling the expected performance of a portfolio or pool of whole loans that involves projecting monthly cash receipts based on individual loan characteristics and projections of borrower behavior, including borrower prepayments, defaults, and recoveries. This is useful when considering a purchase of a pool of loans, or when considering the sale of one, for example.
The outputs of a Cash Flow Analysis are heavily dependant on the input assumptions for borrower behavior. In particular, prepayment (CPR) and default (CDR) assumptions have a strong impact on output cash flow and yield. I’ve spent the last few months analyzing historical performance of consumer lenders to generate a set of historical CPR and CDR curves. We’ve bundled this set of historical curves into a base Curve Library and made them available for use by our clients within the Cash Flow Simulator, helping to greatly simplify the process of beginning any performance analysis. The curves I’ve developed are for the U.S. Consumer Unsecured Lending industry using historical performance data from 2006-Present.
An excerpt from my latest Orchard Research Brief discussing the curve construction methodology in detail is below.
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CPR and CDR Curve Construction
Orchard has an extensive dataset of loan performance on the consumer unsecured lending industry. To construct these curves, we first segregated historical loan originations by vintage, term, interest rate, and FICO. For each loan population, we then calculated historical CPR and CDR curves as follows:
For every month i:
To address the noisiness of these historical curves, we apply a smoothing technique known as LOESS. LOESS is a non-parametric method that fits a series of polynomial regressions to local subsets of the underlying data, resulting is a smoothed curve that fits the structure of the raw curve but does not have the same degree of noise.