请问他sell一个bond然后long一个option 是如何保持ptf的duration不变的呢？

NO.PZ2018120301000038 问题如下： Zhang is a junior fixed-income analyst in a securities firm. He believes that the yield curve will remain stable over the next 12 months. Zhang recommends his client ABC pension fund to sell the 15-year bonds in the portfolio and purchase the short-term at-the-money options on long-term bond futures. The portfolio’s duration remains unchanged before and after this strategy. The chairman of ABC pension fund wants to know how would this strategy affect the portfolio’s return given the stable yield curve forecast over the next 12 months? 想问个题外话，他如何保持duration不变呢？没太想明白 谢谢