Whether you invest in stocks, in ETFs, you put your money in a savings account or you invest in peer lending, the first thing you’ll see on your statements is the value of your account.

The value of your bank account is obvious; it’s the number of dollars you have in it. For publicly traded assets, it is the value that the market is currently willing to pay for the asset. Your portfolio holding of 99 Amazon shares may go down from \$76,496 to \$76,353 without any action on your part, but you haven’t lost actual money. The market simply has a slightly smaller appetite for the company, which is reflected in the dollar amount you will receive should you choose to liquidate the stock. An AMZN share is an AMZN share, and the ones traded right now are perfectly identical to the ones you own, and should therefore be priced identically.

When a market is so fragmented that identical assets are seldom traded, valuation is more complex. This is the case for peer lending. Even though Lending Club and Prosper support a secondary market, since both platforms issue hundreds of thousands of different loans with each divided into tens of notes of different denominations, the market activity is not immediately applicable to your portfolio.

Another situation is prevalent when an asset is not publicly traded. If no public market data is available, how do you value a portfolio?

## Future Cash Flow

Now imagine you agreed with Bob that he will reimburse you by paying you \$10 every month, for one year. If we’re both absolutely sure that Bob will fulfill his due, then the total ‘value’ of your loan to him is 12 x \$10 = \$120 (maybe discounted by the risk-free rate). And if there’s some risks involved, we should discount payments accordingly. Imagine that in any given month, there is a 3% risk that Bob stops paying. The first month, Bob is likely to pay \$10 * 97% = \$9.70. The second month, Bob is likely to pay \$10 times 97% he made the first payment times 97% he makes the second payment, or 10 x 97% x 97% = \$9.41. If there’s a 3% risk that Bob stops paying every month, the probability that he pays the last installment, on the 12th month is only 97% to to the power of 12 = 69%. Therefore the last payment is only worth \$6.94. Summing all those probable payments gives a total of \$99. That would be the value we could agree on, so neither of us loose or make money, on average. By the way, it shows that lending \$100 to Bob was a bad idea, to start with…

Please note that the ‘average’ part is very important. As a matter of fact, trading Bob’s loan at \$99 is never a neutral operation for us, because Bob will never pay exactly \$99. If he defaults the first month, he would have repaid me \$0 for a loan that I purchased for \$99, which would be quite a bad transaction for me. But if he pays up to the 11th month before default, Bob would have paid \$110. Now that’s a good transaction for me, while you sold the loan too cheaply. The value of \$99 will only be neutral if we trade not one, but hundreds of Bob’s loans.

This valuation method is also very dependent upon the accuracy of the probabilities of default. Any change in Bob’s situation should reflect upon the future, discounted cash-flows of the loan. which make this method quite complicated, and frankly, a bit obscure.

## Early re-payment

What if, Bob could decide, at any time, to pay back his loan before waiting for its maturity? In such a case, I’d be willing to buy you the loan only at its principal plus outstanding interest. Or, more precisely, the higher the probability that Bob makes an early re-payment, the more the loan should be valued at its principal plus outstanding interest, and the less as future, discounted cash-flows.

As a conclusion, calculating the value of a portfolio of loans as the sum of the principal plus accrued interest, discounted by late payments, looks like the simplest and most transparent solution, while still being reasonably accurate. Furthermore, it has the extra benefit of not requiring any other assumptions than the decrease in value due to late status.