how to calculate the number $15

问题如下：

The bank’s proprietary fixed-income portfolio is structured as a barbell portfolio: About half of the portfolio is invested in zero-coupon Treasuries with maturities in the 3- to 5-year range (Portfolio P1), and the remainder is invested in zero-coupon Treasuries with maturities in the 10- to 15-year range (Portfolio P2). Georges Montes, the portfolio manager, has discretion to allocate between 40% and 60% of the assets to each maturity “bucket” He must remain fully invested at all times. Exhibit 1 shows details of this portfolio.

If Montes is expecting a 50 bp increase in yields at all points along the yield curve, which of the following trades is he most likely to execute to minimize his risk?

选项：

A.

Sell $35 million of P2 and reinvest the proceeds in three-year bonds

B.

Sell $15 million of P2 and reinvest the proceeds in three-year bonds.

C.

Reduce the duration of P2 to 10 years and reduce the duration of P1 to 3 years

解释：

Duration is a measure of interest rate risk. To reduce risk in anticipation of an increase in interest rates, Montes would seek to shorten the portfolio’s duration. He is limited, however, in the amount he can shift from P2 to P1. Selling $15 million of P2 reduces that portfolio to the lower end of the permitted 40% to 60% range. By reinvesting the proceeds at the shortest maturities allowed, Montes substantially reduces the portfolio duration.