Assuming that I have means of determining and calculating the following metrics:
- Risk (i.e. probability*) of a default to a particular borrower as P
- Profit margin of X%
The profit margin is taken to mean that "irrespective of defaults that might occur, in the long run, I expect to make X% for lending to this particular (class of) borrower.
Thinking it through (from first principles):
Expectation[given loans to borrower with P% of default at a rate of R%] = X%
For the sake of simplicity, lets assume that a default implies the entire lent out capital is lost, so then:
( (100 - P)/100 ) * (1+R) = X
We then trivially, solve for R.
Somehow, I think I've missed something. Can anyone shed some light on if this is a good (correct?) way to solve for R the interest rate to charge the borrower.
Note: I am aware that I'm using a slightly different definition of risk premium from that used in textbooks.
I'm using the frequentist interpretation of probability, where P denotes the number of occurrences (defaults) in a sequence of 100 "runs".