4121hw5 S19B Sec 2 Duration and Repos PDF

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Duration and Repos...

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FINA 4121 Fall 2019B Homework #5 Due 4/24 Duration and Repos Questions 1-5 all involve Effective Annual Yields and Annual Coupons (use five decimal places for prices) 1. Calculate the Price, Macauley and modified duration of a one year zero coupon bond (Par Amount $100) selling for a YTM of 3.0%. 2. Calculate the Price, Macauley and modified duration of a twenty year zero coupon bond (Par Amount $100) selling for a YTM of 5.0%. 3. Calculate the Price, Macauley and modified duration of a five year 8% annual coupon bond (Par Amount $100) selling for a YTM of 4.5%. 4. Calculate the Price, Macauley and modified duration of a five year 2% annual coupon bond (Par Amount $100) selling for a YTM of 4.5%. 5. Calculate the Price, Macauley and modified duration of a five year 4.5% annual coupon bond (Par Amount $100) selling for a YTM of 4.5%. 6. Calculate weightings (% of Market Value invested in each bond) of the 1yr zero coupon bond in #1 above and the 20yr zero coupon bond in #2 above that would be required to create a $1,000,000 portfolio fully invested in these two bonds with a portfolio modified duration of 4.390 7. Two different mutual funds have approximate (effective) durations of 4.1. Fund A exhibits negative convexity due to a concentration in callable bonds while fund B has positive convexity. If all spot rates drop unexpectedly by 50 basis points tomorrow, which fund is likely outperform and why? 8. The one year repo rate is 3% and Five Year Bonds with a 5% annual coupon have an effective annual YTM of 5%. What is the carry on a one year repo of this bond? Assume a par value of $100,000. 9. If the haircut is 5% what is the maximum loan available in the repo market on the bond in question #8? 10. Assume you enter into a one year repo loan and simultaneously purchase the bond in #8. If the effective annual YTM on four year bonds is 6% at the end of next year, how much cash will you have if you sell the bond at the end of next year and you use the proceeds to repay your repo loan? (Assume no haircut.)...