# What is the value of a Portfolio?

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?

## Outstanding Principal

One option is to value a note at its outstanding principal. Imagine you lent \$100 to Bob last week, but need the money now and would like to sell me his debt. Since Bob owes you \$100, I could give you a Benjamin in exchange for you to tell Bob that I’m the one he’ll need to pay back. \$100 is the Outstanding Principal.

This is the valuation method that Lending Club and Prosper are showing on their websites.

## Principal and Accrued Interest

What if Bob and you agreed that he would pay back your \$100 plus \$20 in three days? In that case, your receivable is worth more than \$100. The closer we are to the three days limit, the closer to \$120 I’ll be willing to pay you. If I was to buy Bob’s debt from you a split second before Bob hands you the \$120, the price would be exactly \$120. More than this and I’d be losing money, any less and the deal wouldn’t make sense for you. This is called ‘Principal plus Accrued Interest’.

## Probability of Default

Alas, Bob is not anymore the trustworthy friend he used to be, and you may have doubts about his ability (or willingness) to pay you back. For instance, if he was supposed to give you some money yesterday, but you haven’t heard from him and he’s not even answering your calls. In that case, you would be very happy to offload me the loan for \$120 or even \$100, but I wouldn’t buy it at that price. If we both estimate that Bob has only 60% chance of paying back, then the price should be \$120 * 60% = \$72.

Lending Club takes that imminent risk of default into account, by displaying an “Adjusted account value for past-due Notes”. For instance, the outstanding principal of notes that are between 31 and 120 days late is discounted by 75%. Prosper accounts for this risk of default by showing the split between borrowers that are current and borrowers that are late with their payment.

## Discounting by the Risk-free rate

The further away we are form Bob’s payment date, the less I’ll be willing to pay for the debt. I have another option for my money; for instance, I can put the \$120 into a savings account and earn at least \$0.0003 in interest between now and Bob’s payment (savings accounts are that good). And if you had the \$120 now, you too could earn the same impressive \$0.0003. In that case, we could agree on exchanging Bob’s debt at \$120 – \$0.0003 = \$119.9997 . This is the outstanding principal (plus accrued interest) discounted by what is called the risk-free rate.

## 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.

- Alex Neporozhniy
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