[Updated on:  February 7, 2017]

## LendingRobot’s Expected Return

We recently wrote a blog post going into lengthy detail about how we calculate Expected Return (newly improved since July 2016). For those who are unfamiliar with our Expected Return and how it is calculated, we suggest reading the aforementioned article and then returning to this one. As a brief summary, LendingRobot’s Expected Return creates a single array of historical and forecasted monthly cashflows (which take into account historical default rates) and uses this array to compute the Internal Rate of Return of your portfolio. Some important aspects of Expected Return:

1. Every cashflow that ever occurred is included in the Expected Return calculation. This means that twenty years from now, when we generate the aggregated cashflow array for your portfolio, the cashflow array will still start with cashflows from the very first loans you bought.
2. Expected Return is forward looking if your account still has ongoing loans. We use the historical default rates to generate expected cashflows for your ongoing loans to give investors a sense of what portfolio return they should expect based on the past performance of similar loans.

So Expected Return is a combination of how your portfolio has done since inception with an expectation of how your portfolio will do with the ongoing loans it currently has.

## Lending Club’s (a)NAR

Lending Club’s explanation of (a)NAR can be found here. Below is an explanation of (a)NAR in our own words (we use the equation below, from Lending Club’s website, as guidance).

While the formula may look intimidating, the underlying concept is simple. Each month:

1. Sum all the interest portions of monthly payments received.
2. Add any recoveries amounts collected that month.
3. Subtract all applicable fees from that month.
4. Subtract any amounts being charged off that month. If calculating aNAR, subtract an expected loss amount for notes that are not current.
5. Divide the total from the previous four steps by the total remaining outstanding principal at the beginning of the month. This is (adjusted) the monthly return.
6. Repeat the (adjusted) monthly return calculation for every month for your account since inception, and weight each by the fraction of outstanding principal of each month to the sum of all outstanding principal each month. Take the average.
7. Annualize the result from 6 to arrive at (a)NAR.

1. (a)NAR is a snapshot of how your portfolio is doing from inception until today, weighted more towards the earlier months if you’ve stopped reinvesting. Done loans will not be included in present-day and future (adjusted) monthly return calculations, but will be included in the overall (a)NAR by means of dollar-weighted averaging over all (adjusted) monthly returns since inception.
2. aNAR will only take probability of default into account when the loan actually becomes late.

## Final Notes and Comparisons

Ultimately, there’s a fairly simple way to think about (a)NAR and Expected Return. (a)NAR gives you a sense of how your portfolio has done up until today, with months that have more outstanding principal having a larger contribution to the (a)NAR number. If you want to know how your portfolio has done since inception combined with how your portfolio is expected to do given the historical performance of loans similar to those in your portfolio, look at Expected Return. Now, for some final remarks about (a)NAR and Expected Return. For (a)NAR, notice the shape of the example graph displayed by Lending Club:

We see that the NAR trends downward as the weighted average age of the portfolio increases. The reason for this is due to the hazard rate for loan defaults; loans are in a “risky” period for the first third of their lives (e.g. 12 months for a 36 month loan). This period is where a loan that is “destined” to default is most likely default. The reasoning, from a soon-to-be-defaulting-borrower’s perspective, would be that “if I’m going to default anyway and ruin my credit score/file for bankruptcy, I might as well default as soon as possible to minimize the amount of monthly payments I paid and possibly get the rest of my debt discharged.” Since (a)NAR shows your return up until present day, we can see that the returns between months 0-12 look extraordinarily high. Loans that are going to default are not completely reflected in months 0-12. After 12 months, the majority of loans that will default have defaulted, and then (a)NAR stabilizes as the portfolio ages until it is wound down. Another thing to realize is that for any portfolio that has reinvestments, the weighted average age of notes in your portfolio is not likely to reach beyond 20 months. This is simply because you are constantly making your portfolio “younger” by investing in newly issued loans. Your portfolio will likely only reach the 20+ weighted average ages if you’re winding down your peer lending investments.

Recall that for Expected Return, cashflows use historical probabilities of default when being used for IRR computation. Notice the progression throughout one year for an example account in months 3-15:

Over the timespan of a year the Expected Return only changed by 0.12%. In general the Expected Return, especially for portfolios that are constantly reinvesting without changing their note selection criteria, will change very little over time as long as the underlying historical performance of the platforms remain constant. This is because Expected Return is forward looking, and uses past performance to predict future results via probabilities of default. With constant historical performance, the Expected Return is what you’re supposed to make if you wind down your portfolio today as well as what you’re expected to make if you wind down your portfolio several years from now. Of course, significant changes to interest rates/underwriting/default rates will cause Expected Returns to change.

We add the following table to summarize the similarities and differences.

(a)NAR Expected Return
Historical Yes, weighted more towards large principal months Yes
Forward Looking No Yes
Probability of Default Yes in aNAR, reduces value of principal on late loans Yes, in calculating expected value of cashflows
Accounts for platform fees Yes Yes