Three portfolio managers are discussing a strategy for immunizing a portfolio so as to achieve a target yield. Manager A, whose portfolio consists of Treasury securities and option-free corporates, stated that the duration of the portfolio should be constructed so that the Macaulay duration of the portfolio is equal to the number of years until the liability must be paid. Manager B, with the same types of securities in his portfolio as Manager A, feels that Manager A is wrong because the portfolio should be constructed so that the modified duration of the portfolio is equal to the modified duration of the liabilities. Manager C believes Manager B is correct. However, unlike the portfolios of Managers A and B, Manager C invests in mortgage-backed securities and callable corporate bonds.

Discuss the position taken by each manager and explain why they are correct.