NO.PZ2020011303000222
问题如下：
An investor has a bond position worth USD 20,000 with a duration of seven. Suppose that the bond position has a convexity of 33. Two bonds are available for hedging. One has a duration of ten and a convexity of 80.The other has a duration of six and a convexity of 25. How can a duration plus convexity hedge be set up?
选项：
解释：
To make both duration and convexity equal to zero, we must solve
10P1+ 6P2+ 20,000×7= 0
80P1+ 25P2+ 20,000×33= 0
This gives P1 = −2,000 and P2 = −20,000, indicating that a short position of USD 2000 in
the first bond and a short position of USD 20,000 in the second bond is required.
题目问：一个投资者投资了USD20000，duration为7的债券。假设这个债券的convexity是33。现在可以用两个债券来进行对冲，债券1的duration=10，convexity=80，债券2的duration，convexity=25。如何用这两个债券一起来进行对冲？
目标是使得组合的duration以及convexity=0：
10*bond1+6*bond2+20000*7=0
80*bond1+25*bond2+20000*33=0
解得bond1=-2000
bond2=-20000
需要shortUSD2000的bond1，shortUSD20000的bond2。
duration 是 利率变动 1% 价格的变动率。 (delta P/P)/deltaY = 7 delta Y = 0.01，deltaP = 7*0.01 *20000，我是这样理解的，不对是在哪里
