Sandra Kapple presents Maria VanHusen with a description, given in the following table, of the bond portfolio held by the Star Hospital Pension Plan. All securities in the bond portfolio are noncallable U.S. Treasury securities.

a. Calculate the effective duration of each of the following:
i. The 4.75% Treasury security due 2036.
ii. The total bond portfolio.
b. VanHusen remarks to Kapple, €œIf you changed the maturity structure of the bond portfolio to result in a portfolio duration of 5.25, the price sensitivity of that portfolio would be identical to the price sensitivity of a single, noncallable Treasury security that has a duration of 5.25.€ In what circumstance would VanHusen€™s remark becorrect?

Price If Yields Change Market Value (U.S. S) Up 100 Down Current Bsis 100 Basis Effective Par Value (U.S. $) 48,000,000 2.375% due 2011 48,667,680 101.391 99.245 103.595 2.15 50,000,000 4.75% due 2036 50,000,000 100.000 86.372 116.887 98,000,000 Total Bond Portfolio 98,667,680 _ Treasury Security Price Points Points Duration