1. Tutorial. Measuring Credit Risk (Individual Loan)
The return of a loan
Revision of probability theory

2. Contents
A quick review
Some exercises

3. The return of a loan If the default risk is not taken into account
The annual gross return (effective yield), k, per dollar lent on a loan is given by

4. The return of a loan Loan rate (per annum) = BR + m
where BR is the base lending rate and m is the credit risk premium or margin.
Other charges = D×of
where D is the contractual loan amount, of is the loan origination fee.
Actual amount borrowed = D×(1–b) + D×b×RR = D×(1 – b (1 - RR))
where b is the compensating balance and RR is the reserve requirement.

5. 𝑘= 𝐵𝑅+𝑚+𝑜𝑓 1−𝑏(1−𝑅𝑅) The return of a loan
when neglecting the present value effect;
𝑘= (𝐵𝑅+𝑚) 1 1+𝑑 +𝑜𝑓 1−𝑏(1−𝑅𝑅)
when considering the present value effect

6. The return of a loan If the default risk is taken into account
The annual gross return, r, per actual dollar lent of the loan is a random variable. r is less than k.
E(r) is defined as the annual expected return per actual dollar lent of the loan.

7. The return of a loan
The effective amount of loan receive at the end of the year (random) = D* × (1 + r).
Denote q as the probability that no default in one year. When default doesn’t occur, the annual gross return is k; when default occurs, the lender can recover R (0 ≤ R ≤ 1) of D*.
Thus, E(D* ×(1+r))=q×D* ×(1+k)+(1-q)×D*×R
E(r) = q × k - (1-q)×(1-R)

8. Thanks! Q&A