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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?

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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}

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  • $\begingroup$ 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

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