How To Calculate Hypothetical Performances

Introduction

At LendingRobot we are often asked two important questions: “how have the peer lending marketplaces performed to date?” and “how does the performance compare between LendingRobot and platform automated loan selection?”. These questions all involve examining returns (past through present) and do not have a simple answer due to the lack of a perfect return metric. At LendingRobot we choose to use Expected Return \(E(r)\) for reasons explained here and here, and with it as our basis we attempt to answer the aforementioned questions in the following discussion.

We use Lending Club as our example marketplace. Assume that all cashflows and expected returns are net of servicing and collection fees unless otherwise specified. LendingRobot performance is net of LendingRobot fees. Also note that numbers may be slightly off due to rounding.

Definitions & Assumptions

We count a loan in a specified month if:

1. The loan was issued in the month.
2. The loan was paid/prepaid or charged-off in the month.
3. The loan was issued before the month, and still has scheduled payments after the month.

This means a loan issued, still paying, making its last payment, or becoming charged-off in January 2010 is considered to count towards January 2010. Note that the minimum number of months a loan is considered ongoing is five months, as it takes at least 151 days to charge off.

We also make the following assumptions for our methodology in determining performance numbers:

1. Loans are bought and sold on the secondary market at prices such that the loan’s annualized return from buying/selling in specified month equals its calculated expected return in said month, \(E(r)\), based on our methodology. The amount invested in each selected note is equal such that each selected note takes the same initial weight in the loan portfolio. Note that every loan has a positive expected return at issuance based entirely on its term, interest rate, and loan grade’s historic default rate. Also note that we do not take into account the potential costs of transacting on the secondary market. Inclusion of such transaction costs would impact Lending Club and LendingRobot performance equally (\(1\%\) of all sale proceeds). We make these assumptions because:
   1. One can already list their portfolio holdings or buy notes on the secondary market. It is just a matter of what price one might buy or sell at.
   2. We believe that the secondary Peer Lending markets will trend towards reaching the efficiency of secondary stock markets.
   3. We wish to capture the performance of the entire marketplace at any given month, which includes all loans ongoing in said month. Note that this is significantly different from examining the loan performance by issuance date.

2. Any recoveries, if applicable, of a charged-off loan are ignored.

1. Recoveries are ignored because of the various ways that platforms deal with charged-off loans, whether it is to try and pursue recoveries or to sell the debt to a third party. Regardless, the timing and size of a recovery cashflow, if any, is subject to large fluctuations and thus we exclude them.

3. For calculating LendingRobot fees, we assume a steady account size of \($12,500.00\) which is approximately the average account size across our clients. Annualization is done with compounding to match annualization as calculated with \(E(r)\). The annualized impact of LendingRobot fees is \(0.27\%\).

1. To apply the first \($5,000\) managed for free, we approximate the average account size at time of writing. Fees are determined as follows:

\[monthlyLRfee = \frac{0.45\%}{12} = 0.0375\%\]

\[monthlyLRCharges = (\$12,500.00 – \$5,000.00) * monthlyLRfee = \$2.81\]

\[annualizedLRfee = ((1 + \frac{\$2.81}{\$12,500})^{12}-1) * 100 \% = 0.27\%\]

And now, a quick sanity check on the secondary market buy/sell assumptions:

Below we have the \(E(r)\)s of three loans, as calculated with the aforementioned \(E(r)\) methodology (specific cashflows for loan 887606 in this article).

From the table we see that the annualized return of owning loan 887606 in September 2011 is \(7.60\%\). Our assumption is that if you own loan 887606 for the month of September 2011, you will have a monthly return of \(7.60\%)\). This means that if you invested \($100.00\) in the loan at the start of the month and sold it by the end, you’d have \($107.60\). The increase in value was due to the loan remaining current throughout the period, reducing its apparent risk of default. Skip ahead to February 2012 where the loan first enters grace period, and now investing \($100.00\) in this loan would result in having only \($93.00\) after selling. This decrease could be understood as the discount you have to offer to get rid of the note for because of its increased risk of default with its non-current status. Similar reductions in value can be seen for the later months as the loan approaches being charged-off. We consider that these values, while not perfect, are within reason when thinking about how seasoned loans increase their value and how late loans are offered at steep discounts to remaining outstanding principal.

Methods and Methodology

In the following, we walk through the steps of determining the returns for one month. Steps marked LR are only used for determining LendingRobot loan selection.

LR: Score every loan using LendingRobot’s Scoring algorithm. Loans are scored at issuance and scores remain constant over a loan’s life. This algorithm is the basis for LendingRobot’s selection criteria.

1. Select all loans that are ongoing during the month. Similar to how stock market performance in January 2010 is not only dependent on the stock performance of IPOs in January 2010, peer lending performance is not only dependent upon loans issued in January 2010. Instead, their performance includes IPOs and firms that are still alive, and excludes the stock of companies now defunct or not in existence yet. We think that peer lending returns should be the same; encompassing loans that are newly issued or ongoing, but excluding those that have finished or not originated yet.
   1. LR: Select the top 20% of LendingRobot scored loans, and then construct a portfolio targeting a 75% aggressive and 25% conservative portfolio. Aggressiveness/conservativeness is determined by applying a weighting factor to scale down the LendingRobot Scores of higher interest rate loans. We believe that the top quintile of scored loans is representative of loans that would be selected by solely relying on any combination of the LendingRobot Score filters or using fully automated mode. It is important to note that additional filters are likely to change the loan selection and performance.
2. Select the expected return of each loan during the month and adjust the expected return’s weight based on maturity. Expected returns of loans that are close to maturity take nearly full weight, while expected returns of newly issued loans take almost no weight. The maturity based on weight is scaled linearly from one to zero. We make this adjustment in recognition of the fact that at issuance, a loan’s expected return is based purely on prediction of future cashflows.
3. Take the average of the maturity weight-adjusted expected returns of all ongoing loans in the month. With the assumptions of equal amounts invested in each selected note and the monthly return of a note being equal to the note’s expected return for the month, the average maturity weight-adjusted expected returns is a simple calculation that can answer our two questions.

Results

See our performance graphs here. Graphs are updated upon availability of new data. Note that bond performance is based on the “Total US Bond Market”, as represented by the historical trailing twelve month returns of the AGG iShare ETF adjusted close prices. We chose this ETF because we believe the US Bond Market is a comparable alternative to peer lending and  AGG’s inception date was before the earliest inception date for US peer lending platforms. Bond performance does not include any trading costs.