Today in “things I don’t understand about #finance”:
Loan rates are often specified as a combination of some base rate (“prime”, or the fed rate, or LIBOR or SOFR) plus some rate that captures credit risk. As an extreme example, if a bank thought there were only a fifty percent chance you’d pay back any of a one-year loan, they’d charge some base rate plus 100% in interest. If base were 0, half the time they’d get back $200 on a $100 loan; half the time nothing. Break even…
Marginally more realistic numbers: 5% base; 1/20 chance of default meaning a 5.26% credit rate. Nineteen times out of 20 a $100 loan returns $110.26; 1/20 nothing; return $104.747.
The fact that this is below the base rate isn’t what bothers me nearly as much as that /how much below/ is a function of the credit risk…and that *higher* risks are *less* lucrative for banks.
But okay; assume banks “price in” that premium, so high credit rates are nudged even higher. The whole point of the “base+credit” system is that credit is fixed while base (and total) float.
But in our first example, if base goes up to 20% the return is $110 (a $10 loss to base) and down to 5% it’s $102.5, a $2.50 loss.
Merely adding the two rates means that the bank really cares what happens to the base rate. And I thought the point was that they wanted to be indifferent to it?
The obviously “correct” thing is to set interest at 1-(1+base)(1+credit): base of 5%/10%/20% at credit of 100% (or 5.26%) gives rates of 110%/120%/140% (or 10.5%/15.8%/26.3%) which all return *exactly* the base rate on average.
It’s just very odd to me that even sophisticated borrowers can’t be sold on this not-very-complex formula instead of the naive add-the-rates approach.
Rob Shearer