Task: First Fidelity has asked you to bid for a zero coupon loan portfolio A with a term of 5 years. Their internal controls suggest it has a 90.00% chance of a paying $100.00 at maturity and a 10.00% chance of a paying $90.00. City Mutual recently sold a similar term loan portfolio B which you estimated as having a 60.00% chance of a paying $100.00 at maturity and a 40.00% chance of $90.00 for $71.46. If the 5 year risk free rate is 5% and your required risk premium p.a. is:
{(100* (Nominal – Expected value)) / Expected value}^1.3
Term
i) What is the maximum you would pay for portfolio A?
ii) If you think that the probability of the downside outcome is 10% higher for A what would you offer?
iii) Would a guarantee of First Fidelity's internal ratings be worth having at a cost of $0.50?
iv) Would you have paid more than the market for portfolio B?
A four-year par annual bond has a yield of 4.90%, a similar par 3-year bond yields 4.70%, while an annual par 2 year bond yields 4.60%.
i) What are the durations of the bonds?
ii) If the current one-year rate is 4.45% what are the expected one-year rates in years 2, 3 and 4?
iii) If we had a 0.20% parallel shift in the yield curve how would the price of the bonds change?
iv) Finally if year 1 rates increase by 0.40% with rates in years 2, 3 and 4 unchanged how would the prices change?