Banks are providing loans.

While granting a loan two scenarios can take place

  1. The Loan is repaid
  2. The Loan is not-repaid

The benefit from a re-payed loan is small profit. (Let's say 5% in general) The loss from a not re-payed loan is huge loss. (you lost all your investments)

Are there formulas that can calculate the ratio of loss of (based on pseudo-numbers for example) or other theories related to this issue?


If you have an estimate of the probabilities of each scenario, say with probability $p\in[0,1]$ the loan is repaid (assuming no other scenario exists), then you can calculate the expected value of making the loan of size $L$:

  • In scenario 1, payoff is $-L+(1+0.05)L=0.05L$ (giving out $L$ and getting back the principal plus interest)
  • In scenario 2, payoff is $-L$ (giving out $L$ and getting nothing back)

The expected payoff from making the loan would be \begin{equation} EV=p(0.05)L+(1-p)(-L)=1.05pL-L. \end{equation}

  • $\begingroup$ But in scenario 2 you are asuming that we are making no loss? $\endgroup$ – jennifer ruurs Oct 23 '19 at 15:58
  • $\begingroup$ @jenniferruurs: You're right. I've edited the answer. $\endgroup$ – Herr K. Oct 23 '19 at 18:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.