Question 1 (5 points) ABC Bank issues a $150 million 3-year note at a xed annual coupon rate of 5% and uses the proceeds, along with $50 million in equity, to invest in a portfolio of 5-year, $200 million bonds with a fixed annual coupon rate of 6%. Immediately after these transactions were completed, all market interest rates decrease by 0.5% (50 basis points). Answer the following questions based on this information: a. What is the true market value of the bond portfolio and the note after the change in interest rates? b. What impact did these changes in market value have on the market value of the bank's equity? c. What was the duration of the bond portfolio and the note at the time of issuance? d. Use these duration values to calculate the expected change in the value of the bond portfolio and the note for the predicted decrease of 0.5 % in interest rates. e. What is the duration gap of ABC Bank after the issuance of the note and the investment in the bond portfolio? Question 2 (5 points) From the Treasury strip yield curve, the current required yields on one-, two-year Treasury strips are 4.5% and 5.0%, respectively. The current yield curve indicates that appropriate one-year discount bonds are yielding 6.5%, two-year bonds are yielding 7.5%. a. Calculate the one-year forward rate on the Treasuries and the corporate bond. b. Using the current and forward one-year rates, calculate the marginal probability of repayment on the corporate bond in years 1 and 2, respectively. c. Calculate the cumulative probability of default on the corporate bond over the next two years. Question 3(5 points) ABC Bank has a $2 million position in a ten-year, zero-coupon bond with a face value of $2,500,000. The bond is currently trading at a yield to maturity of 5.50 percent. The historical mean change in daily yields is 0.0 percent and the standard deviation is 8 basis pomts. a. What is the modified duration of the bond? b. What is the maximum adverse daily yield move given that we desire no more than a 1 percent chance that yield changes will be higher than this maximum? c. What is the price volatility of this bond? d. What is the daily earnings at risk for this bond