Meauring returns from your peer lending portfolio can be challenging. You have to account for notes starting in different periods with different rates, defaults, and prepayments. For notes that have completed we can calculate the present value of all payments made for all notes. Whichever interest rate gives back a present value of the exact amount paid for the notes is the interest rate you actually recieived on your initial investment. This is an ideal calculation that assumes all payments were reinvested in an equivalent portfolio of notes. The minimum investment at Lending Club is $25 so every month there will be some cash sitting in your account unused. This lowers your real return rate by a bit, but the more money you have invested the less that matters. 

This is the formula to calculate the present value of a stream of note payments. r is the interest rate you could expect to get on your money in general. If we find r such that the present value of a note is equal to what we paid for it, then that note was equivalent to getting interest rate r.

$$Present Value = \sum_{i=1}^{term}\frac{Monthly Payment}{(1+r)^{i}}    \ \ \       (1)$$

Let's work through some examples we'll start with evaluating performance of 1 completed loan at a time.

Full Performing Note

1 $100 note bearing 15% interest for 36 months with monthly payments of $3.47. The note never defaulted and finished on time.

$$Present Value = \sum_{i=1}^{36}\frac{3.47}{(1+\frac{.15}{12})^{i}} = 100.1$$

We assumed an interest rate of the actual stated interest rate of 15%. We divided this by 12 because payments are made every month. The result was 100.1 almost exactly what we paid for the note ($100). It was only slightly higher becuase we rounded the monthly payments up a few cents. This means we did get a 15% return on this note.

Defaulting Note

1 $100 note bearing 15% interest for 36 months with monthly payments of $3.47. The note defaulted after 30 payments.

Now we change the sum to stop at the 30th month. We still use an interest rate of 15%.

$$Present Value = \sum_{i=1}^{30}\frac{3.47}{(1+\frac{.15}{12})^{i}} = 86.36$$

Now the present value is only $86.36. What does this mean? It means if we expect to get 15% returns we should only be willing to pay $86.36 for this note. We can use exhaustive search to find the expected interest rate that makes the note worth the $100 we paid for it. 

$$Present Value = \sum_{i=1}^{30}\frac{3.47}{(1+\frac{.031}{12})^{i}} = 100$$

So it turns out this note was worth the same as a %3.1 return investment. Much less than the stated 15%.

Note Paid Off Early

What if a note gets paid off early how does that affect our return? Let's calculate return for the same note as above but this time all the remaining principal gets paid off in month 10. Now we must find the present value of the monthly payments up to month 9 and add it to the present value of the bulk principal payment that paid off the loan. The remaining principal when the loan was paid off plust the interest for that period was $80.02.

$$Present Value = \sum_{i=1}^{9}\frac{3.47}{(1+\frac{.15}{12})^{i}} + \frac{80.02}{(1+\frac{.15}{12})^{10}}= 100$$

Even thought the loan was paid off early we still got a 15% return on that note. So it looks like prepayments don't affect your returns. In isolation they don't, but in a portfolio where some notes default prepayments can make your portfolio look better than it is.

If you measure your portfolio performance by default rate prepayments can be  a problem.

Prepayments can keep your default rate low while your portfolio is actually performing very poorly. Imagine 3 scenarios involving prepayments:

In scenario A 100% of loans get paid off after 1 month. You have a portfolio of 100 notes and they all get paid off after just 1 month. So each month you have all your principal back to buy more notes. You go buy more from the same pool of notes that always prepays early. You can do this each month and even though the notes are paid off early you make your expected return because you can alwyas buy more giving you the same rate.

In scenario B 90% of loans get paid back early and 10% default immediately. You buy 100 notes. After 1 month 90 paid back in full and 10 defaulted. So you reinvest in 90 new notes. The next month 81 pay back in full and 9 defaulted. Now you can only buy about 81 notes, just 2 months after you started with 100. If you keep reinvesting you will quickly lose all your money.

In scenario C 90% of loans perform for their entire term and 10% default immediately. You buy 100 notes. After 1 month 10 defualt but the other 90 keep performing for 35 more months. In this situation the defaults don't hurt your portfolio nearly as badly as they do in the prepayment scenario B. 

Putting it all together: Evaluating an entire portfolio of notes

The calculations done above for the single note can be applied to an entire portfolio of notes. Just sum the present values of all the notes together. If you find the equivalent interest rate that gives a portfolio present value that equals the value actually paid for all the notes in the portfolio then that is the rate you earned from that portfolio. In future articles we will call that the Portfolio Equivalent Interest Rate or PEIR. Remember this can only be calculated for notes that are finished. One thing to keep in mind is that you should not add notes that defaulted but would not have finished if they did not default to a PEIR calculation. This would inflate the number of defaulting loans in your portfolio calculation because defaults would get added as soon as they default but good loans don't get added until the loan is completed.