At liwwa, we connect small businesses in need of financing to individual investors through our online platform. For this platform to work well, investors need some way of assessing the risk of the investment opportunities we offer. To this end, we conduct a thorough credit assessment of all businesses we work with.

Out of respect for our borrowers' privacy, we don't publish our full credit assessments online. Instead, we present investors with a number of summary indicators, the most succinct of which is the *credit score*. You can read more about how the score is calculated here. This post explores how well our credit scores work in practice. How much riskier is a liwwa loan with a low credit score, compared to one with a high credit score?

##### Credit scores as a predictor of repayments

The key concern for investors in any fixed-income asset is getting repaid on time. This is especially true of *Murabaha* and other Islamic finance products where investors make a return in the form of a fixed fee, rather than through an interest rate that compounds over time.

For this reason, it would be helpful to quantify the relationship between the credit score and the probability of repayment. We could model this relationship in a number of ways, but in this case, we choose to use a survival model to describe the relationship.

Survival models are frequently used in medical research to quantify how administering some treatment or drug is related to patient survival. We can use the same basic model to describe the link between credit scores and loan repayments.

A survival model can help us estimate the probability that a loan has a late payment in any given month, given that it has a certain credit score. This can easily be extended to tell us how many late payments we expect a loan to have after a certain period of time, conditional on its credit score. For example, given that a loan has a score of 8, what is the expected number of late payments for the loan after 12 months? How would the expectation change if the credit score was 4? This information can help investors better gauge the risk they take when investing through liwwa.

To answer this question, we use historical liwwa data to fit a type of regression model known as a Cox proportional hazards model. This model starts by assuming that there is some adverse event that has a certain probability of occurring -- known as the *failure rate* or *hazard rate* -- in any given period. The model estimates how this hazard rate changes as some input variables change. In our case, we're interested in the probability of a loan installment being repaid late in any given month, as a function of the loan's credit score.

We fitted this model with data on liwwa loans from to July 2015 to July 2017. Of course, our credit models have developed throughout this period, so we can think of this as testing the average effectiveness of our credit scores over the time period.

The model, summarized in the appendix below, tells us that each one-point increase in the credit score is associated with a 32% reduction in the probability of a late payment in any given period, other things being equal.

Roughly speaking, if a loan with a credit score of 4 has a 3% chance of being late in any given month, the model suggests that a loan with a credit score of 5 would have a 2% chance of being late -- roughly one-third lower.

##### Simulating future late payments

Using this model, we can get the expected number of late payments for a loan after a certain period of time, given its credit score. To get this, we combine the coefficient calculated above with a baseline hazard rate. This lets us run the simulation illustrated in Figure 1 below.

Here, the x-axis represents the number of months a loan has been outstanding, and the y-axis represents the number of late payments. The lines plot the estimated relationship between the two for a loan of a certain credit score. The shaded areas give 95% confidence intervals.

As we would expect, this shows a significantly lower number of expected late payments for a loan with a high credit score (8) than for a loan with a low credit score (4). After twelve months, we'd expect 0.08 late payments from the former campaign -- roughly equivalent to one in twelve such campaigns having a late payment. By contrast, the latter campaign with credit score 4 has an expected 0.46 late payments after 12 months -- equivalent to almost one in two such campaigns having a late payment.

This type of analysis can give investors an idea of what to expect when investing in a liwwa loan of a certain credit score. It also helps us internally at liwwa, as we strive to develop even more accurate scoring algorithms in a data-driven way.

###### Appendix: The Cox proportional hazards model

*We specified a model with the following form:*

```
h(t) = h_0(t) * exp(b_1 * credit_score)
```

*where h(t) is the hazard in period t, h_0(t) is the baseline hazard before considering covariates, and credit_score is the credit score varaible. The coefficient b_1 tells us the impact of the credit score of the rate of late repayment.*

*The main regression results are summarized in Table 1. The coefficient of the credit score variable ( b_1) is equivalent the natural logarithm of the factor by which the probability of a repayment changes as the credit score increases by one point. This is not very intuitive to interpret, so we take the antilog of the coefficient to get the factor by which the probability of a late payment changes when the credit score changes one point, which in this case is 0.68.*

coef | exp(coef) | se(coef) | z | p | |
---|---|---|---|---|---|

Credit Score | -0.38 | 0.68 | 0.07 | -5.32 | 0.00 |

*This suggests that as the credit scores goes up one point, the predicted chance of a late payment in any given month changes by 0.68 - 1, or about -32%.*

*With a p-value smaller than 0.001, we can consider this effect statistically significant by conventional standards.*