什么时候才适用market value-weighted duration呢？

NO.PZ2018120301000027 问题如下 Leinforms Molly thC ha single $500 million liability e in nine years, anshe wants SR to construa bonportfolio thearns a rate of return sufficient to poff the obligation. whichof the portfolios in Exhibit 1 best minimizes the structurrisk to asingle-liability immunization strategy A.Portfolio 1 B.Portfolio 3 C.Portfolio 4 CorreAnswer: is correct. Structurrisk to immunization arises from twists annon-parallel shifts in the yielcurve. Structurrisk is receminimizing the spersion of cash flows in the portfolio, whicaccomplisheminimizing the convexity for a given cash flow ration level. Because Portfolio 4 hthe lowest convexity comparewith the other two portfolios analso ha Macaulration close to the liability maturity of nine years, it minimizes structurrisk 老师，零息债券convexity最小，但是零息债券是barbell，barbell的convexity不是最大吗？我是哪里搞错了？

NO.PZ2018120301000027问题如下 Leinforms Molly thC ha single $500 million liability e in nine years, anshe wants SR to construa bonportfolio thearns a rate of return sufficient to poff the obligation. whichof the portfolios in Exhibit 1 best minimizes the structurrisk to asingle-liability immunization strategy A.Portfolio 1B.Portfolio 3C.Portfolio 4 CorreAnswer: is correct. Structurrisk to immunization arises from twists annon-parallel shifts in the yielcurve. Structurrisk is receminimizing the spersion of cash flows in the portfolio, whicaccomplisheminimizing the convexity for a given cash flow ration level. Because Portfolio 4 hthe lowest convexity comparewith the other two portfolios analso ha Macaulration close to the liability maturity of nine years, it minimizes structurrisk 题目中提到公司的liability e in nine years，portfolio 3正好是9年，为什么不对呢？感觉选择convexity最小的成了唯一标准。