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. P-963 Price if Yields Change Par Value (U.S. $) Treasury Security Market Value (U.S.$)
Current Price Up 100 Basis Points Down 100 Basis Points Modified Duration $48,000,000 2.375% due 2025 $48,667,680 101.391 99.245 103.595 2.15 50,000,000 4.75% due 2050 50,000,000 100.000 86.372 116.887 —
98,000,000 Total bond portfolio 98,667,680 — — — —

a. Calculate the modified duration of each of the following:
i. The 4.75% Treasury security due 2050.
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 years, the price sensitivity of the portfolio would be identical to that of a single, noncallable Treasury security that also has a duration of 5.25 years.”
In what circumstance would VanHusen’s remark be correct?