Modified Duration和Convexity如果是unequal weighted的话

NO.PZ202112010200000102 问题如下 The manager estimatesthaccelerateeconomic growth in Australia will increasethe levelofgovernment yiel-to-maturity 50 bps. Unr this scenario, whiof thethree portfolios experiences the smallest cline in market value? A.Bulletportfolio B.Barbell portfolio C.Equally weighteportfolio A is correct. Thechange in portfolio value e to a rise in Australigovernment rate levelsmcalculateusing Equation:%∆PVFull ≈ -(Mour ×ΔYiel + [½ × Convexity × (ΔYiel2],where Mour anonvexity refleportfolio ration anconvexity, respectively. Therefore,the bullet portfolio clines 2.093%, or -2.093% = (-4.241 × 0.005)+ [0.5 × 22.1 × (0.0052)],followea op of2.343% for the equally weighteportfolio, or -2.343% = (-4.779 ×0.005) + [0.5 × 37.4 × (0.0052)], ana op of 2.468%for the barbell portfolio, or -2.468% = (-5.049 ×0.005) + [0.5 × 45.05 × (0.0052)]. 这题答案还用公式算出了每个portfolio的prichange是多少. 我是直接看A的ration最小，就选了请问我的方法有什么问题么?谢谢。

NO.PZ202112010200000102 问题如下 A Syey-baseixeincome portfolio manager is consiring the following Commonwealthof Australia government bon traon the ASX (AustraliStoExchange): The manager isconsiring portfolio strategies baseupon various interest rate scenariosover the next 12 months. She is consiring three long-only governmentbonportfolioalternatives, follows:Bullet: Invest solely in 4.5-yegovernment bonBarbell: Invest equally in 2-yean9-yegovernment bonEquweights: Invest equally in 2-year, 4.5-year, an9-yebon The manager estimatesthaccelerateeconomic growth in Australia will increasethe levelofgovernment yiel-to-maturity 50 bps. Unr this scenario, whiof thethree portfolios experiences the smallest cline in market value? A.Bulletportfolio B.Barbell portfolio C.Equally weighteportfolio A is correct. Thechange in portfolio value e to a rise in Australigovernment rate levelsmcalculateusing Equation:%∆PVFull ≈ -(Mour ×ΔYiel + [½ × Convexity × (ΔYiel2],where Mour anonvexity refleportfolio ration anconvexity, respectively. Therefore,the bullet portfolio clines 2.093%, or -2.093% = (-4.241 × 0.005)+ [0.5 × 22.1 × (0.0052)],followea op of2.343% for the equally weighteportfolio, or -2.343% = (-4.779 ×0.005) + [0.5 × 37.4 × (0.0052)], ana op of 2.468%for the barbell portfolio, or -2.468% = (-5.049 ×0.005) + [0.5 × 45.05 × (0.0052)]. 我想问一下，从定性的角度，barbell的convexity是大于bullet 和laler portfoilo。所以interest rate 下降 50%，我们应该选择convexity最大的 barbell 组合才对，为什么计算出来的答案是bullet？什么和定量的理解矛盾？

NO.PZ202112010200000102 问题如下 The manager estimatesthaccelerateeconomic growth in Australia will increasethe levelofgovernment yiel-to-maturity 50 bps. Unr this scenario, whiof thethree portfolios experiences the smallest cline in market value? A.Bulletportfolio B.Barbell portfolio C.Equally weighteportfolio A is correct. Thechange in portfolio value e to a rise in Australigovernment rate levelsmcalculateusing Equation:%∆PVFull ≈ -(Mour ×ΔYiel + [½ × Convexity × (ΔYiel2],where Mour anonvexity refleportfolio ration anconvexity, respectively. Therefore,the bullet portfolio clines 2.093%, or -2.093% = (-4.241 × 0.005)+ [0.5 × 22.1 × (0.0052)],followea op of2.343% for the equally weighteportfolio, or -2.343% = (-4.779 ×0.005) + [0.5 × 37.4 × (0.0052)], ana op of 2.468%for the barbell portfolio, or -2.468% = (-5.049 ×0.005) + [0.5 × 45.05 × (0.0052)]. 请问这种equally weighteconvexity和M以直接加权平均吗？获得新的组合MConV. ,能一下原理吗？谢谢

NO.PZ202112010200000102 问题如下 A Syey-baseixeincome portfolio manager is consiring the following Commonwealthof Australia government bon traon the ASX (AustraliStoExchange): The manager isconsiring portfolio strategies baseupon various interest rate scenariosover the next 12 months. She is consiring three long-only governmentbonportfolioalternatives, follows:Bullet: Invest solely in 4.5-yegovernment bonBarbell: Invest equally in 2-yean9-yegovernment bonEquweights: Invest equally in 2-year, 4.5-year, an9-yebon The manager estimatesthaccelerateeconomic growth in Australia will increasethe levelofgovernment yiel-to-maturity 50 bps. Unr this scenario, whiof thethree portfolios experiences the smallest cline in market value? A.Bulletportfolio B.Barbell portfolio C.Equally weighteportfolio A is correct. Thechange in portfolio value e to a rise in Australigovernment rate levelsmcalculateusing Equation:%∆PVFull ≈ -(Mour ×ΔYiel + [½ × Convexity × (ΔYiel2],where Mour anonvexity refleportfolio ration anconvexity, respectively. Therefore,the bullet portfolio clines 2.093%, or -2.093% = (-4.241 × 0.005)+ [0.5 × 22.1 × (0.0052)],followea op of2.343% for the equally weighteportfolio, or -2.343% = (-4.779 ×0.005) + [0.5 × 37.4 × (0.0052)], ana op of 2.468%for the barbell portfolio, or -2.468% = (-5.049 ×0.005) + [0.5 × 45.05 × (0.0052)]. 老师好，想问下，这道题的答案中，是通过公式计算得出各个portfolio的变动后，再得到的答案。我在回答这个题的时候，是通过判断哪个portfolio的ration最低判断出的bullet portfolio，答案也是正确的。这样的思路是不是适合选择题？如果是主观题，是不是还得老老实实的按公式计算？

NO.PZ202112010200000102 问题如下 The manager estimatesthaccelerateeconomic growth in Australia will increasethe levelofgovernment yiel-to-maturity 50 bps. Unr this scenario, whiof thethree portfolios experiences the smallest cline in market value? A.Bulletportfolio B.Barbell portfolio C.Equally weighteportfolio A is correct. Thechange in portfolio value e to a rise in Australigovernment rate levelsmcalculateusing Equation:%∆PVFull ≈ -(Mour ×ΔYiel + [½ × Convexity × (ΔYiel2],where Mour anonvexity refleportfolio ration anconvexity, respectively. Therefore,the bullet portfolio clines 2.093%, or -2.093% = (-4.241 × 0.005)+ [0.5 × 22.1 × (0.0052)],followea op of2.343% for the equally weighteportfolio, or -2.343% = (-4.779 ×0.005) + [0.5 × 37.4 × (0.0052)], ana op of 2.468%for the barbell portfolio, or -2.468% = (-5.049 ×0.005) + [0.5 × 45.05 × (0.0052)]. 如题，barbells和equweighteconvexity是怎么算的，看答案好像是直接平均的，这样合理吗