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

<ul>
<li>In scenario 1, payoff is <span class="math-container">$-L+(1+0.05)L=0.05L$</span> (giving out <span class="math-container">$L$</span> and getting back the principal plus interest)</li>
<li>In scenario 2, payoff is <span class="math-container">$-L$</span> (giving out <span class="math-container">$L$</span> and getting nothing back)</li>
</ul>

<p>The expected payoff from making the loan would be 
<span class="math-container">\begin{equation}
EV=p(0.05)L+(1-p)(-L)=1.05pL-L.
\end{equation}</span></p>

CC BY-SA 4.0
2019-10-23T15:58:08.130Z
But in scenario 2 you are asuming that we are making no loss?
jennifer ruurs
CC BY-SA 4.0
2019-10-23T18:23:50.417Z
@jenniferruurs: You're right. I've edited the answer.
Herr K.
CC BY-SA 4.0
2019-10-22T18:27:48.470Z
2019-10-23T18:23:23.743Z
2019-10-23T18:23:23.743Z
Herr K.
<p>Banks are providing loans. </p>

<p>While granting a loan two scenarios can take place</p>

<ol>
<li>The Loan is repaid</li>
<li>The Loan is not-repaid</li>
</ol>

<p>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)</p>

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

<banking><trading>
Banks providing loans
jennifer ruurs
# Banks providing loans

(Asked by: username_0 on 2019-10-22)

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?

**Tags:** banking, trading


---

## 1 answers

### Answer by username_1 on 2019-10-22. Score: 2 | Accepted answer

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}

> **Comments:**
> **username_0**: But in scenario 2 you are asuming that we are making no loss?  
> **username_1**: @username_0: You're right. I've edited the answer.  

---

