The CFO of Cirus Asset Management observes the current prices and characteristics of zero- coupon treasury bonds as summarized in the table below Zero Coupon Treasury Bonds Characteristics Bond Face Value Price ytm D* CV 1000 939.56 2.10% 2.94 11.51 1000 890.35 2.35% 4.89 ? 1000 841.27 2.50% 6.83 53.30 1000 773.62 2.60% ? 104.50 3 year 5 year 7 year 10 year a. Compute the 4 year forward interest rate 3 year in the future, namely $3,4. b. Compute the convexity of the 5 year zero coupon bond (hint: for pure discount bonds, the convexity is a function of only the maturity and the yield to maturity of the bond.) c. Cirus has a portfolio of liabilities with modified duration of 5.14. Cirus invests in bond portfolio to fund the liabilities. If Cirus invest 15% of the portfolio in the 3 year zero, what proportion of the portfolio should be invested in the 5 year zero and in the 7 year zero to provide Cirus with a good protection against the impact of a small parallel shift in the term structure of interest rates on both liabilities and assets (Hint: This is called "duration" matching)? d. If the 10-year yield shifts up by 0.2%, compute an estimated percentage change in the price of the 10 year zero using both modified duration and convexity of the 10 year zero. (Hint: first comupute the modified duration of the 10 year zero, then compute the percentage change in price)