Our New Expected Return

In March 2016, we started presenting two return numbers: Current Return and Forward-Looking Return. We did this believing that the two numbers would be more descriptive compared to what we presented previously, but we’ve concluded that by and large they are confusing and inconsistent. Now we’re changing to one Portfolio Expected Return number that is more accurate and simplifies understanding your portfolio’s returns. This article will cover how Current Return, Forward-Looking Return, and the new Portfolio Expected Return are calculated, and why the Portfolio Expected Return is a better way to present returns.

For those unfamiliar with Expected Return, we previously did a blog post about it but the abridged version is that we aggregate all of a loan’s cashflows, actual and expected, and calculate an annualized Internal Rate of Return for that loan. We choose to use Internal Rate of Return (IRR), rather than other metrics like Return on Investment (ROI), since IRR takes into account the time value of money and duration of investment.

We begin by defining return terminology that we will use:
Expected Return – The annualized Internal Rate of Return at the loan level.
Current Return – The weighted average of the Expected Returns of all loans in a portfolio. Weighted by percentage of amount invested.
Forward-Looking Return – The weighted average of the Expected Returns of ongoing loans in a portfolio. Weighted by percentage of amount invested.
Portfolio Expected Return – The Expected Return number generated from aggregating the whole portfolio’s cashflows. Each loan’s cashflows, actual and expected, are combined into one time series of cashflows and then a single annualized IRR is computed.

Now let’s examine example portfolios to understand how Current Return, Forward-Looking Return, and Expected Return are calculated, why they are different, and which return makes the most sense.

We’ll explain our reasoning using slightly modified loans and example portfolios from this blog post. Attached is this google spreadsheet so readers can follow along. We strongly recommend following along with the google spreadsheet for better understanding.

Our model portfolios consist of combinations of four hypothetical loans with the following characteristics:

Loan Funded ($) Term Rate (%) Status Installment ($) Issuance Date (Expected) Total Paid ($) Return on Investment (%) Expected Return (%)
L1 10,000 36 13.00 Fully Paid 336.94 Feb 2013 12,008.52 20.09 13.02
L2 7,500 36 13.00 Prepaid 252.70 Apr 2013 8,660.58 15.47 12.83
L3 10,000 36 13.00 Current 336.94 Jan 2016 11,664.34 16.64 10.91
L4 4,000 36 17.00 Defaulted 142.61 Dec 2014 1,270.66 -68.23 -91.22

First, note that all loans are finished except for L3, which is current and ongoing. For L3’s cashflows, we use actual cashflows up until present day, and then use expected (predicted) cashflows based on L3’s probability of default and hazard rate.

We start with a portfolio of all loans except L3. There are no ongoing loans in this portfolio; all loan activity ceased by February 2016. Examine the Averaged column, where we compute weighted averages of ROI and Expected Return. It is strange here that the averaged ROI is positive (2.05%) and the averaged Expected Return is negative (-6.44%); was money actually gained or lost? Looking at the aggregated column we see that \$21,500 was invested vs \$21,939.76 received which indicates a positive return. So we know that a positive return was earned but we’ve managed to calculate a contradictory negative return. This averaging of Expected Returns is how Current Return was calculated. The heart of the problem with averaging is that it is disproportionately affected by defaults and loses the information that a large loss occurred in a short amount of time. Now examine the Aggregated column; ROI is correctly the same as in the Averaged column, but the Expected Return of the aggregated cashflows is 1.83% and is the true IRR of the portfolio. Here, the ROI and Expected Return are in agreement, and the Expected Return is saying that the money you invested, adjusting for when you deployed it into loans, has earned an annualized rate of return of 1.83%. This method of aggregating cashflows and then computing the IRR is our new Portfolio Expected Return. As for Forward-Looking Return, there are no ongoing loans in this portfolio so there is no Forward-Looking Return. We summarize relevant numbers in the following table (see the “No L3 Portfolio Example” tab on the google spreadsheet for more details):

Loan L1 L2 L4 Averaged Aggregated
Return on Investment (%) 20.09 15.47 -68.23 2.05 2.05
Expected Return (%) 13.02 12.83 -91.22 -6.44 1.83
Current Return (%) Forward-Looking Return (%) Portfolio Expected Return (%) Initial Value ($) Ending Value ($)
No L3 Portfolio -6.44 N/A 1.83 21,500 21,939.76

Now let’s examine a portfolio containing all four loans. The key difference here is that for L3 not all the cashflows have been received yet so we have an Expected Total Paid based off actual and expected cashflows. As of writing, the date is July 2016 so all cashflows after July 2016 are future cashflows. July 2016 is marked by purple cells. Examining the Averaged and Aggregated columns again shows that when averaging the ROI and Expected Return are in disagreement showing a gain (6.68%) and a loss (-0.93%), while the aggregated ROI and Expected Return both show a gain (6.68% and 5.06% respectively). Again, the true IRR should be a positive return since the ending portfolio value (\$33,604.10) is greater than the initial value (\$31,500). Keep in mind that for this portfolio with ongoing loans, we use our best guess at future cashflows when calculating returns. Also, since this portfolio is ongoing there is a Forward-Looking Return (10.91%) based solely off ongoing loans (just L3 in this case). Again, relevant numbers are summarized below with details in the “All Loans Portfolio Example” google spreadsheet tab:

Loan L1 L2 L3 L4 Averaged Aggregated
Return on Investment (%) 20.09 15.47 -16.64 -68.23 6.68 6.68
Expected Return (%) 13.02 12.83 10.91 -91.22 -0.93 5.06
Current Return (%) Forward-Looking Return (%) Portfolio Expected Return (%) Initial Value ($) Ending Value ($)
All Loans Portfolio -0.93 10.91 5.06  31,500 33,604.10

The bases for our new Portfolio Expected Return are clarity and consistency. It was confusing to show a Current Return and a Forward-Looking Return that could have such a large spread (and even opposite signs depending on the defaults in your portfolio), or a negative return for a portfolio of completed loans in which the portfolio’s final value was greater than its beginning value. Hopefully this new Expected Return addresses all of these concerns.


  1. James says:

    I’m very optimistic that Lending Robot will find returns in general and have signed up for your service. I’m interested on how Lending Robot manages major market swings (high default rate enviroments) especially since these higher returns means a lot of exposure. Thank you.

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