This article explains how we calculate returns at the portfolio level, and why we make a distinction between what we call ‘Current Return’ and ‘Forward-looking Return’.

## Averaging Returns

We calculate the return of a portfolio as a weighted average, based on the amount invested in each note. A portfolio made up of n loans, each one of amount a and giving a return r, then R the portfolio return is:

$R = \frac{\sum_{i=1}^n{a_i \cdot r_i}}{\sum_{i=1}^n{a_i}}$

Loans can be either paid, defaulted, or on-going. Dead loans are not expected to make any more payment, and therefore their return calculation is simple and accurate. Dead loans, like human beings, may have had an admirable life (in case of loans, they made fully payment) or may have disappointed (for loans, they were charged-off).

Live loans are the ones that are still expected to make further payments. They can be current or late (past a payment due), and more or less mature. The mechanism to predict the returns of live loans has been described in a previous article. There are two important facts to remember. First, because the probability of defaulting decreases over time, the expected return of a live note increases as the loan becomes for mature. Second, the risk of default is not uniform over time and loans have a significantly higher risk to default during the first half of their life.

For instance, a fictitious loan with a 10-month maturity returns at best 13.5% upon reaching maturity. Its expected return over time could look like this:

Month Expected Return
0 (issuance) 9.0%
1 9.1%
2 9.3%
3 10.0%
4 11.0%
5 11.8%
6 12.5%
7 12.9%
8 13.2%
9 13.4%
10 13.5%

At issuance, the expected return is only 9%. After one payment this return increases, but only slightly, because few loans miss at least one payment. At the 4th month, the growth in expected return accelerates. A loan is unlikely to miss the last payment once 9 payments have been made; therefore the ‘discount’ for the risk of default only lowers the return to 13.4%.

## Aggregation at the Portfolio level

Since there is still some uncertainty regarding live loans, it seems at first more reliable to calculate the return of a dead one.

However, because defaults happen, by definition, prior to maturity, an investor is likely to see those charged-offs accumulating only a few months after initial investment, while he’ll have to wait several years for the surviving loans to reach maturity.

Let’s imagine a portfolio, made up of 7 identical loans similar to the one described above. Each loan is issued at the same time. However, loan #1 stops paying after only 2 months, and loan #2 defaults after making a total of 4 payments. The 5 remaining loans reach maturity. The returns we have for each loans are:

Month Loan #1 Loan #2 Loan #3 Loan #4 Loan #5 Loan #6 Loan #7
0 (issuance) 9.0% 9.0% 9.0% 9.0% 9.0% 9.0% 9.0%
1 9.1% 9.1% 9.1% 9.1% 9.1% 9.1% 9.1%
2 9.3% 9.3% 9.3% 9.3% 9.3% 9.3% 9.3%
3 –30.0% 10.0% 10.0% 10.0% 10.0% 10.0% 10.0%
4 11.0% 11.0% 11.0% 11.0% 11.0% 11.0%
5 –15.0% 11.8% 11.8% 11.8% 11.8% 11.8%
6 12.5% 12.5% 12.5% 12.5% 12.5%
7 12.9% 12.9% 12.9% 12.9% 12.9%
8 13.2% 13.2% 13.2% 13.2% 13.2%
9 13.4% 13.4% 13.4% 13.4% 13.4%
10 13.5% 13.5% 13.5% 13.5% 13.5%

Depending upon which loans we take into account for calculating the portfolio returns, numbers are very different. There are 3 options:

1) Consider only the dead loans. We’ll call this ‘Past Return’
2) Consider only the live loans. We’ll call this ‘Forward-Looking Return’ because it doesn’t take into consideration what already happened.
3) Consider all the loans, both live and dead. We’ll call this the ‘Current Return’.

Month Loan #1 Loan #2 Loan #3 to #7 Past Return Current Return Forward-Looking Return
0 (issuance) 9.0% 9.0% 9.0% 9.0% 9.0%
1 9.1% 9.1% 9.1% 9.1% 9.1%
2 9.3% 9.3% 9.3% 9.3% 9.3%
3 –30.0% 10.0% 10.0% –30.0% 4.3% 10.0%
4 11.0% 11.0% –30.0% 5.1% 11.0%
5 –15.0% 11.8% –22.5% 2.0% 11.8%
6 12.5% –22.5% 2.5% 12.5%
7 12.9% –22.5% 2.8% 12.9%
8 13.2% –22.5% 3.0% 13.2%
9 13.4% –22.5% 3.1% 13.4%
10 13.5% –22.5% 3.2% 13.5%
11 3.2% 3.2%

As shown above, the Past Return shows meaningless numbers, until all the loans have been able to reach maturity. The Current Return is a much more accurate measurement. However, it is also heavily penalized by early defaults. At the 5th month, the Current Return indicates 2.0%, which is almost one-half under the final performance.

As for the Forward Looking Return, it tends to be too optimistic (even more so on this example. For real portfolio the discrepancy is much lower). However, this is an important measurement, because it allows to track, over time, the performance of a strategy.

# A Note for Our Clients

Because of the way we calculate Current Returns and Forward-Looking Returns, many clients who invested on their own before switching to LendingRobot are likely to encounter this kind of summary information:

Account Current Return Forward-Looking Return
Managed by LendingRobot 7.72% 9.76%
Not Managed by LendingRobot 4.61% 11.29%

Here the forward-looking return of the loans we do manage is significantly lower than the one for the investments we do not manage (9.76% vs 11.29%). Is LendingRobot doing a bad job? Not necessarily.

Because the non-managed loans are older than the ones managed by LendingRobot, more of them have already defaulted. This is why, on the ‘few’ remaining ones, the return is so high. This can be easily verified by comparing the current returns: it’s at 7.72% for the loans managed by LendingRobot, while it’s only 4.61% for the loans purchased before switching to LendingRobot. A discrepancy that can only be explained by two reasons: the non-managed is older, so more loans have defaulted already, and LendingRobot selected better loans.

Considering that in this case, LendingRobot is 1.53% below for the forward-looking return, but 3.11% above for the current return, both reasons seem valid.

Nota Bene: the numbers above are real numbers from my personal account.

1. Lincolnf says:

Thanks for the article. Since you have the expected returns for each loan in a portfolio, wouldn’t it be a fairly simply matter to on a monthly basis calculate the expected return for the entire portfolio, given the behavior of the dead and live loans? Would it be possible to add this to the dashboard? I think this would be a very useful number, allowing investors to see how close their performance is fitting with their original expectations.