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The CFO of Star Asset Management observes the current prices and characteristics of zero-coupon treasury bonds as summarized in the following table.
a. Compute the 4 year forward interest rate 3 years in the future, namely
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. Star has a portfolio of liabilities with a modified duration of 5.14. Star invests in a bond portfolio to fund the liabilities. If Star invests 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 Star with 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 the estimated percentage change in the price of the 10 year zero using both modified duration and convexity of the 10 year zero. (Hint: first compute the modified duration of the 10 year zero, then compute the percentage change in price)
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