How to calculate the probability of default on loans

Shivam Agarwal
2 min readFeb 23, 2021

The calculation of the probability of default is very important for banks. This can create a difference between a successful bank and an unsuccessful bank.

Photo by Micheile Henderson on Unsplash

Let us understand the basics of these calculations. Imagine you have 12,000$ dollars. One of your best asked to lend him 10,000$ dollars. This amount is too big to lend. So you asked him to keep give some collateral to you. You have given him the money. Now there are three possibilities:-

  1. He may return all the money borrowed
  2. He may return some of the money borrowed
  3. He may not return any of the money borrowed

As you have to manage your future expenses you should know how much you are expected to get back before lending it. Banks face this problem on daily basis and they have created a system. We will understand how do they do it.

The first question is whether he will return the money or not:-

We call this the probability of default (PD). Previously, you have blended money to four of your friends, and out of four only one has not returned your money. You can assume that in one out of four incidents your money will not be returned to you. So we can say that the probability of default is 1/4.

In case of default, how much money will not be returned:-

At the time of default, he may already have returned some of the money. Assume he has returned 6000$ and only 4000$ is left to return. This is what we call exposure at default.

how much we can not recover from assets:-

Remember, we are having collateral. We can sell the collateral to recover some of our losses. But the value of the collateral may not be sufficient to recover all our losses. Suppose we got only 4000$ by selling the collateral. Still, we have to recover 1000$. This is what we call LGD (Loss given default)

Now you have to decide whether to lend money to your friend or not. Your decision is based on your future requirement of cash. If you need more than 1000$ in the future, you can not lend money to your friend. As there are chances that you will not 1000$ out of 10,000$



Shivam Agarwal

Shivam is an accomplished analytics professional and algo trader, sharing expertise in algo trading, data science, and AI through insightful publications.