# How to calculate expected return on a loan while having probability of default

I have data on loans including: initial loan taken by each borrower, their probability of default. Is there a way to calculate VaR that would show potential loss of that asset?

First what I need is the expected return on the investment. I have total loan amount and probability that this borrower defaults in 12 months. The loan period is for instance 10 years, therefore, I can't just say that my expected return equals to (1-probability of default)*loan amount. Is there a way to solve this problem?

• Two important points. 1 Do you mark the loans to market, i.e. to a fair value that you'd get if you sold them in an orderly secondary market? If yes, then this fair value changes if the credit quality changes, and possibly if the risk-free interest rates change, and the VaR also measures how much this fair value can change. If no, i.e. you have a "banking book" and every loan is marked to its face value, until or unless it either defaults or is paid off, then the only change comes from the defaults. 2 do you assume that when a loan defaults, Sep 18, 2023 at 12:02
• (cont) its value jumps to exactly zero, or do you assume the possibility of some recovery? In reality, many defaulted loans recover sometimes as little as 10%, sometimes as much as 90%. Once the possibillity of default is real enough, thinking what the defaulted loan might be worth in recovery is a good practice. Sep 18, 2023 at 12:07
• and 3, what do you assume about the correlations? E.g. if you loan to two coal minets, are you more likely to have two defaults than if you loaned to one coal miner and one social media company? Do the defaults become more likely if the risk-free interest rates go up? Sep 18, 2023 at 12:12
• Thank you for your answer. 1) I assume a banking book scenario. 2) I would assume that a fraction of the loan would be repaid, but in my eyes that would be just a fixed percentage. 3) I do not take into account correlations between borrowers
– Jone
Sep 18, 2023 at 13:08
• Additionally just to be clear borrower default probably is recalculated every quarter. So I have new default probabilities every quarter showing how likely the borrower default on a loan
– Jone
Sep 18, 2023 at 13:11