P = 88 * exp (-0.04 * 5) = 72.05 million.

问题如下：

A portfolio manager controls USD 88 million par value of zero-coupon bonds maturing in 5 years and yielding 4%. The portfolio manager expects that interest rates will increase. To hedge the exposure, the portfolio manager wants to sell part of the 5-year bond position and use the proceeds from the sale to purchase zero-coupon bonds maturing in 1.5 years and yielding 3%. What is the market value of the 1.5-year bonds that the portfolio manager should purchase to reduce the duration on the combined position to 3 years? (Practice Exam)

选项：

A.

USD 41.17 million

B.

USD 43.06 million

C.

USD 43.28 million

D.

USD 50.28 million

解释：

In order to find the proper amount, we first need to calculate the current market value of the portfolio (P), which is:

P = 88 * exp (-0.04 * 5) = 72.05 million.

The desired portfolio duration (after the sale of the 5-year bond and purchase of the 1.5 year bond) can be expressed as:

[5 * (P-X) + 1.5* X]/P = 3 where X represents the market value of the zero-coupon bond with a maturity of 1.5 years.

This equation holds true when X = (4/7) * P, or 41.17 million.