1. Today is May 15, 2000, and the current, semi-annually compounded yield curve is in the table below Compute the Macaulay and modied duration for the following securities: (1.5 Points) (a) 3-year zero coupon bond (b) 3 1/4-year coupon bond paying 6% semiannually (c) l-year coupon bond paying 4% quarterly Maturity Yield Maturity Yield Maturity Yield 0.25 6.33% 2.75 6.86% 5.25 6.39% 0.50 6.49% 3.00 6.83% 5.50 6.31% 0.75 6.62% 3.25 6.80% 5.75 6.24% 1.00 6.71% 3.50 6.76% 6.00 6.15% 1.25 6.79% 3.75 6.72% 6.25 6.05% 1.50 6.84% 4.00 6.67% 6.50 5.94% 1.75 6.87% 4.25 6.62% 6.75 5.81% 2.00 6.88% 4.50 6.57% 7.00 5.67% 2.25 6.89% 4.75 6.51% 7.25 5.50% 2.50 6.88% 5.00 6.45% 7.50 5.31% Notes: Yields are calculated based on data from CRSP (Daily Treasuries). 2. Using the parametric form of a 2-year coupon bond with coupon rate C and face value F, prove the following facts: (Do not use numbers, just parameters!) (2 points) 2.1. The Duration is decreasing in coupon rate (The higher is the coupon rate, the lower is the Duration). 2.2. The Duration is decreasing in yield (The higher is the yield, the lower is the Duration). 3. Using the yield curve in questions 1, compute the dollar duration for the following securities: (1.5 Points) (a) Long a 5-year coupon bond paying 4% semiannually (b) Short a 7-year zero coupon bond (c) Long a 3 1/2-year coupon bond paying 7% quarterly