# How Do We Predict Cash Flows

Our ‘Summary’ page shows how much money a LendingRobot client could withdraw on a monthly basis from their loans payments. We improved this graph a few months ago by adding the options of getting estimates when withdrawing all funds as fast as possible, reinvesting the principal and interest payments, and withdrawing some payments while keeping the portfolio value constant.

## Re-investing everything

The simplest case is when someone wished to re-invest all loans payments into new loans. Then whatever is paid from existing loans is reinvested, and the amount that can be withdrawn every month is… zero. Duh.

## Cashing out entirely

At the opposite end is cashing out everything. To calculated how much money one will receive from their investments, we must to predict when and how much each borrower will repay. All loans installments are paid monthly, so the ‘when’ is fairly easy, but the ‘how much’ is slightly more complicated. Imagine a \$50 note from a 36-month, 21% interest loan. The amount paid every month in theory is \$1.88. The formula to calculate the installment *p* is:

\[p = A \times \frac{1-(1+\frac{r}{12})^{-n}}{\frac{r}{12}}\]

Where *A* is the loan amount, *r* the annual interest rate, and *n* the number of payments.

Unfortunately, defaults do sometimes occur. So we need to discount future payments by the cumulative probability that a loan stops paying before reaching that month. We base that probability on historical data (average default probability, evolution of risk over time, etc…) and build a vector of discounted payments [p1, p2, p3, …., pn] for each note by multiplying *p _ the installment by (1- *dt_ ) where *dt* is the probability that the loan stops paying before the time *t* . To calculate the payments received at the portfolio level, we sum all of the payment vectors. For instance, if we invest in 3 different notes, 2 of them reaching maturity in the next 2 months, we’d have something like:

Month | Note #1 | Note #2 | Note #3 | Total |
---|---|---|---|---|

1 | \$1.56 | \$1.95 | \$1.98 | \$5.49 |

2 | – | \$1.94 | \$1.96 | \$3.90 |

3 | – | – | \$1.95 | \$1.95 |

… | – | – | … | … |

36 | – | – | \$1.79 | \$1.79 |

Please note that payments decreases other time, because of the increasing probability that the loan has stopped paying before reaching each subsequent installment.

The vector [\$5.49, \$3.60, \$1.95,…, \$1.79] is that we would show as a cash-flow forecast in case someone wanted to cash out entirely.

## Keep portfolio constant

The last and most complex case is when someone wants to withdraw as much money as possible while still keeping the portfolio value constant. Peer lending loans are fully amortized, meaning that the payments received are both for the interest and for reimbursing the outstanding principal. Without any reinvestment, the portfolio value will drop to zero after all loans have matured, and no more payments will be received.

If the loans were only to pay interest, never default nor repay the principal, the portfolio value would remain unchanged. This would be equivalent to a perpetuity with the same annual net return. Said otherwise, a perpetuity with the same annual net return than the loans portfolio tells us how much one can cash out from payments without lowering the portfolio value. The rest needs to be re-invested in new loans (that we assume will generate, on average, an identical return).

This would be accurate if the risks of charge-offs, and therefore the returns, were constant over time. However, many of our studies have shown that the risk of default of a loan increases during the first third of its life, then progressively decreases until maturity. To get a more precise estimate, we need, on a note-per-note basis, to subtract from the payments the decrease in outstanding principals, and consider this re-invested in a perpetuity with the same return. Over time, the initial portfolio value decreases to zero, but is replaced by a perpetuity portfolio of equal value and equal returns. In particular, the cash flow forecast will show, initially, numbers that vary greatly because of when defaults are expected to happen most. The predicted cash-flow will become smoother as more payments are factored into the perpetuity calculation.

- Alex Neporozhniy
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