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

Contents A quick review Some exercises

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

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.

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

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.

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)

Thanks! Q&A