Jul 17

Expected Loan Return

by David Harper, CFA, FRM, CIPM

In FRM assigned Saunders (Credit Risk: Individual loan risk), he gives expected return as function of probability of repayment (p = probability of repay = 1 â€“ probability of default):

Where:

k = promised return (k)
p = probability of repayment (p)

Expected return, therefore, counts default risk. Put another way, expected losses (EL) are priced in the promised return. The implication of this: higher promised return is not always better. Higher promised return is associated with higher PD/lower (p). For example, below I assume that a promised return (k) of 8% is associated with 1% PD (p = 99%). Then each additional 1% of return increases the PD by 1.5% (extreme but just illustrative). Similarly, for promised returns less than 8% the PD tends toward zero. So the optimal promised return could be something like this: