Corporate Fins
Autor: Eileen Zhou • August 14, 2015 • Coursework • 3,787 Words (16 Pages) • 896 Views
Week 3 Lecture:
Grading rule:
To get the full 1-mark credit for problem set 3, you would need to attempt all two past exam questions and the end-of-chapter Chapter 10, Q30 and Chapter 11, Q15.
To get the half credit for problem set 3, you would need to attempt Chapter 10, Q30 and any one of the other three compulsory questions mentioned above.
Past exam questions:
1. There are two pure-discount bonds (i.e., zero-coupon bonds) issued by the same firm, one with one year to maturity, and the other one with two years to maturity. Two bonds have the same seniority in terms of payments (i.e., they have same levels of credit risk). If the issuer defaults, both bonds are expected to lose all the claims on principal and interests. The yield to maturity for the 2-year bond is 10% per annum. The 1-year risk free spot rate is 4%, and the risk-free forward rate in the 2nd year is 4.7% according to the current term structure of interest rates. What is the expected probability of default of the 2-year bond over its 2-year life according to term structure model of credit risk?
Answer:
2-year gross return of the bond = 1+k = (1+10%)^2 = 1.21
2-year gross risk-free rate = 1+ i = (1+4%)*(1+4.7%) = 1.08888
Under the term-structure model of credit risk, expected returns should be equal:
(1+k)*p + (1+k)*γ*(1-p) = (1+k)*p = 1 + i
Where p is the probability of payment (i.e., no default), γ is the recovery rate upon default, and the second equality holds because γ = 0.
So p = 1.08888/1.21 ~= 0.90
So the probability of default = 1- p = 10%.
2. Suppose that an FI holds two loans with the following characteristics.
Loan | Weight | Loan Spread | Annual Fee | LGD | EDF |
1 | 0.45 | 5.50% | 2.25% | 30% | 3.50% |
2 | 0.55 | 3.50% | 1.75% | 20% | 1% |
The correlation of return between the two loans is ρ12 = -0.20
Loan spread is the annual spread between loan rate and FI’s cost of funds.
Calculate of the return and risk on the two-asset portfolio using Moody’s Analytics Portfolio Manager model.
Answer:
The return and risk on loan 1 are:
R1 = (.055 + .0225) - [.035*0.30] = 0.0670 or 6.70%
σ1 = [.035(.965)]^(1/2)*0.30 = .05513 or 5.513%
The return and risk on loan 2 are:
R2 = (.035 + .0175) - [.01*0.20] = 0.0505 or 5.05%
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