5. 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.

Price If Yields Change Par Value

(U.S. $)

Treasury Security Market Value

(U.S. $)

Current Price Up 100 Basis Points Down 100 Basis Points Effective Duration 48,000,000 2.375% due 2006 48,667,680 101.391 99.245 103.595 2.15 50,000,000 4.75% due 2031 50,000,000 100.000 86.372 116.887 —

98,000,000 Total Bond Portfolio 98,667,680 — — — —

a. Calculate the effective duration of each of the following:

i. The 4.75% Treasury security due 2031.

ii. The total bond portfolio.

b. VanHusen remarks to Kapple, “If 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 be correct?