Part A: [15 points] What is the current value of a $100 4% government bond that matures in 5 years and 2 months from today if the yield to maturity is 3% p.a. (compounding semi- annually)? Part B: [5 points) A one-year $100 zero-coupon bond is currently trading at $97. A two-year zero-coupon bond is currently trading at $94. What rate of interest could you lock in today for a loan that starts one year from now and finishes two years from now? Assume that all of these instruments have the same counterparty, so are of equivalent risk. Part C: [5 points] Consider a collateralised debt obligation based on a reference set of 100 corporate bonds. Assume that all of the bonds are equally weighted and that the recovery rate is set to 40%. You are considering a product that loses all of its value once 4.8% of the capital is subject to a credit event. What is the probability of a total loss of value if we assume that credit events are independent across bonds and over time, such that each bond has a 3% probability of experiencing a credit event during the life of the product you are considering? How does that probability change if we assume that there is a 50/50 chance of the default probability being 0% or 6% over the relevant period? Part A: [15 points] What is the current value of a $100 4% government bond that matures in 5 years and 2 months from today if the yield to maturity is 3% p.a. (compounding semi- annually)? Part B: [5 points) A one-year $100 zero-coupon bond is currently trading at $97. A two-year zero-coupon bond is currently trading at $94. What rate of interest could you lock in today for a loan that starts one year from now and finishes two years from now? Assume that all of these instruments have the same counterparty, so are of equivalent risk. Part C: [5 points] Consider a collateralised debt obligation based on a reference set of 100 corporate bonds. Assume that all of the bonds are equally weighted and that the recovery rate is set to 40%. You are considering a product that loses all of its value once 4.8% of the capital is subject to a credit event. What is the probability of a total loss of value if we assume that credit events are independent across bonds and over time, such that each bond has a 3% probability of experiencing a credit event during the life of the product you are considering? How does that probability change if we assume that there is a 50/50 chance of the default probability being 0% or 6% over the relevant period
