*This blog post is part of a “Beyond the default rate” series, which investigates what the default rate actually means, how it affects you and why you should know more than simply the number you see on some report.*

If I told you there’s a loan group with 20% default rate. Would you be willing to invest into it? What if the rate was 10%? Or 5%?

In case you answered yes to any of these questions, then you will certainly benefit from reading this series of blog posts and should probably put yourself into the e-mail list to receive notifications of new posts in order to not miss them.

However, if you said no to any of them and it was not based entirely on some ethical reasons you might have, then you will also benefit and should do the same as mentioned above.

The correct answer would be that it depends. Depends on how the default rate was calculated, what the interest rates are, what’s your investment strategy etc. This is what the blog post series will be investigating.

The default rate number alone, would be as informative as a politician saying that he comes to work as often as he changes his socks. It seems that there’s enough information there to make a judgment, but that’s actually the context we ourselves add there. If you change socks daily, you might consider that he has a good work ethic. If for some reason in your world people change socks every few weeks only, then he would seem like a lazy bastard.

## What is the default rate?

So let’s start from beginning. What is “default rate”?

In short, it’s the proportion of loans that become 60+ (*or 120+ depending on context/platform*) days overdue. Whenever there is no recovery, you would consider this as the percentage of your investments that have been lost. However, in Bondora‘s case, the historical recovery rates have been great, so considering all as 100% lost, is definitely extremely pessimistic scenario.

There are several ways to calculate it and the methodology can also be somewhat different, depending whether you are calculating it on your investments or on the loan dataset. In the following blog posts we are considering calculations on the entire loan dataset.

The basic default rate formula is as follows:

Where:

D – default portion of the portfolio

LP – the loan portfolio

D% – default rate of the portfolio

## Count or sum of loans?

Although the formula is pretty simple and straightforward, there are several questions you need to answer first, before you can start calculating.

You need to think whether you want to calculate it based on the EUR amount that defaulted or the loan count (number of loans) that defaulted. It may not seem important at first glance, but this can give you radically different results in different situations.

In case of EUR amount, the D would be the amount of outstanding principal at the moment of default and in case of loan count, the D would be the number of loans that defaulted.

### Default, based on number of loans

For example, if you are a large investor who invests at the max 20% or 500 € limit, then calculating default rate based on the number of loans can give you results that have nothing to do with your real

exposure because the amounts invested into different loans are very different.

Let’s say you have 100 loans, 80 of them are 500 €, and 20 of them are 100 €. A 10% default rate could mean a 1000 € loss or 5000 € loss or anything in between. That is up to a 5x difference compared to reality.

However, if you invest 10 € per every loan, then the difference disappears and you might actually get a realistic result with the analyses.

I said you might, because in reality the story gets a bit more complicated than that.

In reality, most defaults happen sometime later in the process, meaning that you will receive a certain amount of repayments before the loan defaults. This means that if you invested 10 € and the loan

defaults a few months later, you may have received 3 € of principal repayments and 5 € of interest payments before it defaulted.

If you calculated the default rate based on the number of loans, then you’ll get too exaggerated results and might stop investing into segments that in reality are providing you decent profit and have a lot lower default rates than your calculations would assume.

**Example of default rates based on loan count:**

*Portfolio consists of 5 loans.*

*10,000 €*

*1,000 €*

*2,000 €*

*1,000 €*

*1,000 €*

*Totalling: 15,000 €*

*If the 10,000 € defaults, the default rate would be 20%.*

*For an investor who invested 10 € into each, the default rate would be 20% of loans.*

*For an investor who invested max limit into each, the default rate would be 20% of loans.*

*If the 1,000 € defaults, the default rate would be 20%.*

*For an investor who invested 10 € into each, the default rate would be 20% of loans.*

*For an investor who invested max limit into each, the default rate would be 20% of loans.*

Results stay the same irrespective of how many repayments were made prior or after the defaults or how much you actually invested into each of the loans.

### Default rates, based on EUR amount

Second option is to calculate the default rate based on EUR amounts. This means that the calculations will account for any repayments made on the loan. Your 3 € repayment on the 10 € loan would result in a 7 € default out of the 10 € investment.

In other words, the 10% default rate would in reality become more accurate 7% default rate. If you are investing at the max allowed limits, this would likely give you a more accurate default rate

calculation than looking at the number of loans, as your investment amounts also depend on the loan size (your investment amount is smaller for smaller loans because of the 20% ceiling).

However, because of loans that are above 5,000 €, the calculations can still skew your results either way.

For investor who invests smaller amounts, the results could be skewed even more due to the fact that a small loan that defaults will only affect the default rate very little whereas a large 10,000 € loan

affects the general default rates a lot. But with 10 € investments into each loan, they both have equal effect on your personal default rate.

**Example of default rate based on amount:**

*Portfolio consists of 5 loans.*

*10,000 €*

*1,000 €*

*2,000 €*

*1,000 €*

*1,000 €*

*Totalling: 15,000 €*

*If the 10,000 € defaults, the default rate would be 66.7%.*

*For an investor who invested 10 € into each, the actual default rate would be 20% of invested amount.*

*For an investor who invested max limit into each, the default rate would be 500/(500+3*200+400)= 33.3%.*

*If the 1,000 € defaults, the default rate would be 6.7%.*

*For an investor who invested 10 € into each, the actual default rate would be 20% of invested amount.*

*For an investor who invested max limit into each, the default rate would be 200/1500= 13.3% of the amount.*

**In case the loan defaults after repaying 20% of the loan:**

*If the 10,000 € loan defaults with 8,000 € outstanding principal, the default rate would be 53.3%.*

*For an investor who invested 10 € into each, the actual default rate would be 16% of invested amount.*

*For an investor who invested max limit into each, the default rate would be 400/(500+3*200+400)= 26.7%.*

*If the 1,000 € defaults with 800 € outstanding principal, the default rate would be 5,3%.*

*For an investor who invested 10 € into each, the actual default rate would be 16% of invested amount.*

*For an investor who invested max limit into each, the default rate would be 160/1500= 10.7% of the amount.*

As you can see, the differences based on your chosen method and your investment strategy can be quite large. However, in a large enough portfolio, the proportions might also even out or be skewed in the opposite direction than shown in the example.

In the loan dataset (on 30.Oct.2014) more than 60% of funded loans are below 3,000 € and majority of defaulted loans have made some payments before defaulting. This might indicate that calculating default rate based on the amount may likely be more accurate method in most cases.

## Combination of amount and number of loans

You can also opt for a combination of the both methods. This way you would look for the proportion of loans that default and you would adjust it based on the average exposure at default proportion.

For example, if based on count the default rate would be 20% and the average exposure at default would be 80%, then you’d get a default rate of 16%.

If you manage to get the proportion close enough to reality, you’ll have a pretty accurate result. However, in most cases this will not be worth the effort for unprofessional investors and simply

calculating based on amount would be close enough to make some estimations.

For a more conservative (pessimistic) estimate, you could also simply rely on using the count, if you use proper diversification and invest essentially equal amounts into every loan.

## Conclusion

Even though the formula for default rates is simple, there’s a lot more to it than meets the eye at first glance.

Today we have only scratched the surface and we are far from actually having covered enough of the topic to be able to jump into the dataset and start crunching the numbers.

However, hopefully this has given you sufficient food for thought for now. Make sure you understand why these different methods can result in entirely different results and which one is the best for your investment strategies.

The next post in the series will look more thoroughly at the LP part of the equation and the nuances related to this. To make sure you’ll catch it, feel free to subscribe to the updates by clicking the button below.

Also read the next post in the series:

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