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Unformatted text preview: Homework 3 ECON 4721H: Money and Banking, Fall 2011 Due Monday, October 17, at the beginning of class Problem 1. Duration and Bank Immunization 5-years 1-year Y A The above gure describes the relationship between the log of price and the yield of some asset consisting of 1-year strip bonds and some another asset consisting of 5-years strip bonds. Here, 'log' always refers to the natural logarithm, and the yield in the above graph is in percentage. 1. Derive the durations of those two assets. (Remember that the durations of strip bonds don't depend on their face values) What do those durations correspond to in the gure? 2. Suppose that you are running a bank. You have assets consisting of 5-years strip bonds and debts consisting of 1-year strip bonds. Your assets and debts are balanced,' and denoted by 'A' in the above gure. The initial present value of the total assets and the total of debts is $50000. So, log(50000) is the value of y-axis at point A. Also, assume that the initial spot rate is 10%, and thus, the value of x-axis at point A is 10. (a) Suppose that the spot rate increases, and so, the yield changes from the initial value at point A to 12%. Then, will you get a gain or loss on your balance sheet? How much is it in dollar? (b) Suppose that the spot rate decreases, and so, the yield changes from the initial value at point A to 8%. Then, will you get a gain or loss on your balance sheet?...
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- Fall '11
- $10000, $50000, $10700, $8163