Analyzing Lending Club Payment History
There are several ways to determine the Return on Investment (“ROI”) for an individual note and thus derive a return of a portfolio of notes. Below is a quick summary of various prevailing methods and their limitations
|Adjusted Net Annualized Return (“ANAR”)||
A much better methodology to calculate ROI would be to use the internal rate of return (“IRR”) using borrowers’ payment history and discount for future losses. Peer Lending Server (“PLS”) calculates the internal rate of return for non-periodic payment history cash flows of all historical loans on Lending Club’s platform to address the payment history issue. For discount on future losses, we use survival analysis cox proportional hazard regression to determine future cash flows for a more accurate projected return on investment.
Obtaining the Data
Lending Club provides historical statistics to investors by clicking on the Statistics tab and selecting Download Data:
However, this historical data does not provide borrower payment history. For that, Lending Club provides this additional data at http://additionalstatistics.lendingclub.com:
As of January 2015, there are over 5.5MM records for borrower payment history, which are used by PLS to calculate the IRR. On this data, we also apply cox proportional hazard model to understand future loss using survival curves.
Survival Rate of Loans
The Kaplan-Meier plot provides a measure of survival rate over time to a future event (Fully Paid or Charged Off) sometimes referred to as a survival curve. We can visualize loans over a period of time to estimate the time it takes to be fully paid or charged off. Let’s first take a look at survival times for all 36 and 60 month loans:
95% confidence intervals are provided above and below the center line for each survival curve. Not surprisingly, as time increases the rate of charged off notes also increases. 36 month loans have a higher survival rate than 60 month loans. For example, at 30 months approximately 10% of 36 month notes have charged off while 14% of 60 month notes. Note that as 36 month loans age beyond their term, there is less confidence as to their survival rate.
It is also informative to look at the hazard rate of loans over time. The hazard rate is the risk of charging off over a specific period of time (month). The hazard rate helps to understand when the loan is at most risk of charging off. The following two charts show the hazard rate for 36 and 60 month loans using a kernel density smoothing:
For both 36 and 60 month notes, the highest risk of charge off is approximately 18 months. Now let’s examine the survival curves by loan grade:
As expected, the risk of charge of significantly increases as the loan grade increases. However, notice how F and G grade notes have a similar curve and crossover at several points in time. There are other additional inferences here that can be made but the point is the survival rate is consistent by grade.
Calculating the Internal Rate of Return
Unfortunately, there is no easy way to process 5MM+ rows of payment history. Parallelized processes break up the job into a manageable effort for a modern server. Payment history is collected including the monthly contract amount, interest rate, principal balance, payment, date and other data points. For each current note, you can determine the payments left using the following formula:
i=Interest Rate, l=Payments, p=Principal
Note that the expected cash flows are not guaranteed and therefore should be discounted appropriately. If the current note is in late status, we can discount expected cash flows using Lending Club’s probability of default:
Based on the existing and expected cash flows, you can determine the effective annualized rate of return. Next we need to convert the effective rate to a nominal rate as expressed to the borrower:
With mature notes (Charged Off or Fully Paid), we know the exact payment history and use a similar method to calculate the internal rate of return. Up to this point, we have determined the instantaneous ROI for current notes without considering the possibility of future loss. In PLS, this value is represented as “Instant ROI” in the filter window. However, as previously mentioned, this provides an optimistic view of return as it is likely that some current notes will eventually default in the portfolio. Using survival analysis, we can use a cox proportional hazard model to project the expected return using evidence from all available 380K historical notes.
Projecting Return of Current Notes
Current notes in a portfolio may eventually become fully paid and provide a return equal to the instantaneous ROI. However, it is important to accurately reflect ROI based on the loan profile. Fitting a semiparametric cox model, we can estimate the survival curve for all historical notes which can be used to discount expected cash flows. Given we know the status and existing cash flow for each note, we can determine the periods and event used by the model. We used a step-wise Akaike Information Criterion (“AIC”) regression to select the following covariates used in the cox model:
After fitting the model on over 380K historical loans, we create survival curves for each historical loan. Based on the survival probability, we can discount future cash flows and project a more realistic return. This value is represented in Peer Lending Server by “Projected ROI” in the filter summary window.
Peer Lending Server provides an accurate estimate of return by incorporating both borrower cash flows and future loan losses in its model. This information can easily be used in your filter creation strategy along with reactive, real-time plots of expected return. When selecting loan filtering parameters, this information is critical to understanding the most likely return based on statistical evidence.