NO.PZ2021120102000004
问题如下：
An investment manager is considering decreasing portfolio duration versus a benchmark index given her expectations of an upward parallel shift in the yield curve.
If she has a choice between a callable, putable, or option-free bond with otherwise comparable characteristics, the most profitable position would be to:
选项：
A.
own
the callable bond.
B.
own the putable bond.
C.
own the option-free bond.
解释：
B is correct. The value of a bond with an embedded option is equal to the sum of the value of an option-free bond plus the value to the embedded option.
With a putable bond, the embedded put option is
owned by the bond investor, who can exercise the
option if yields-to-maturity increase, as in this scenario.
Under A, the embedded call option is owned by
the bond issuer, who is more likely to exercise if
yields-to-maturity decrease (that is, the bond investor is short the call
option).
As for C, the option-free bond underperforms the putable bond given the rise in value of the embedded put option.
如果这个题目问利率平行上行（下行）的时候，相同久期的子弹，哑铃和等权重组合，哪一个收益最大呢？咋一想应该是哑铃？因为凸性比较大。还是说要结合题目数据自行计算？谢谢！
