In this example, there are four asset classes, and the variance of the total portfolio is assumed to be 25%;这个是怎么得来的？谢谢

NO.PZ201803130100000107 问题如下 In the risk parity asset allocation approathMüller uses, the weight thMüller places on mestic bon shoulbe: A.less th25%. B.equto 25%. C.greater th25%. C is correct. A risk parity asset allocation is baseon the notion theaasset class shoulcontribute equally to the totrisk of the portfolio. Bon have the lowest risk level anmust contribute 25% of the portfolio’s totrisk, so bon must overweighte(greater th25%). The equcontribution of eaasset class is calculateas:wi* Cov(ri,rp)=1nδρ2 wherewi = weight of asset iCov(ri,rp) = covarianof asset i with the portfolion = number of assetsσ2= varianof the portfolioIn this example, there are four asset classes, anthe varianof the totportfolio is assumeto 25%; therefore, using a risk parity approach, the allocation to eaasset class is expecteto contribute (1/4 × 25%) = 6.25% of the totvariance. Because bon have the lowest covariance, they must have a higher relative weight to achieve the same contribution to risk the other asset classes. 为什么 varianof totportfolio = 25%？ 1/n * portfolio varian= w * covariance, 1/n * portfolio varian= actr, 那么 w * covarian= actr 么？如果是的话， 应该怎么理解这个公式呢？

NO.PZ201803130100000107 问题如下 In the risk parity asset allocation approathMüller uses, the weight thMüller places on mestic bon shoulbe: A.less th25%. B.equto 25%. C.greater th25%. C is correct. A risk parity asset allocation is baseon the notion theaasset class shoulcontribute equally to the totrisk of the portfolio. Bon have the lowest risk level anmust contribute 25% of the portfolio’s totrisk, so bon must overweighte(greater th25%). The equcontribution of eaasset class is calculateas:wi* Cov(ri,rp)=1nδρ2 wherewi = weight of asset iCov(ri,rp) = covarianof asset i with the portfolion = number of assetsσ2= varianof the portfolioIn this example, there are four asset classes, anthe varianof the totportfolio is assumeto 25%; therefore, using a risk parity approach, the allocation to eaasset class is expecteto contribute (1/4 × 25%) = 6.25% of the totvariance. Because bon have the lowest covariance, they must have a higher relative weight to achieve the same contribution to risk the other asset classes. 明白本题原理，对于文中提法有疑惑1.. The expectereturn of the mestic bonasset class is the lowest of the asset classes, 本句只说了mestic bonreturn最小，没有说risk最小，是据此退出的risk最小？2.anthe returns of the mestic bonasset class have the lowest covarianwith other asset class returns.mestic bon和其他资产的协方差最小，没有说公式里的和组合的协方差最小，怎么推出？

NO.PZ201803130100000107 问题如下 In the risk parity asset allocation approathMüller uses, the weight thMüller places on mestic bon shoulbe: A.less th25%. B.equto 25%. C.greater th25%. C is correct. A risk parity asset allocation is baseon the notion theaasset class shoulcontribute equally to the totrisk of the portfolio. Bon have the lowest risk level anmust contribute 25% of the portfolio’s totrisk, so bon must overweighte(greater th25%). The equcontribution of eaasset class is calculateas:wi* Cov(ri,rp)=1nδρ2 wherewi = weight of asset iCov(ri,rp) = covarianof asset i with the portfolion = number of assetsσ2= varianof the portfolioIn this example, there are four asset classes, anthe varianof the totportfolio is assumeto 25%; therefore, using a risk parity approach, the allocation to eaasset class is expecteto contribute (1/4 × 25%) = 6.25% of the totvariance. Because bon have the lowest covariance, they must have a higher relative weight to achieve the same contribution to risk the other asset classes. “the expectereturn of the mestic bonasset class is the lowest of the asset classes”这句话有什么用没有，好像在公式里不体现啊

NO.PZ201803130100000107 问题如下 In the risk parity asset allocation approathMüller uses, the weight thMüller places on mestic bon shoulbe: A.less th25%. B.equto 25%. C.greater th25%. C is correct. A risk parity asset allocation is baseon the notion theaasset class shoulcontribute equally to the totrisk of the portfolio. Bon have the lowest risk level anmust contribute 25% of the portfolio’s totrisk, so bon must overweighte(greater th25%). The equcontribution of eaasset class is calculateas:wi* Cov(ri,rp)=1nδρ2 wherewi = weight of asset iCov(ri,rp) = covarianof asset i with the portfolion = number of assetsσ2= varianof the portfolioIn this example, there are four asset classes, anthe varianof the totportfolio is assumeto 25%; therefore, using a risk parity approach, the allocation to eaasset class is expecteto contribute (1/4 × 25%) = 6.25% of the totvariance. Because bon have the lowest covariance, they must have a higher relative weight to achieve the same contribution to risk the other asset classes. 如题

NO.PZ201803130100000107 问题如下 MegBea anHanna Müller are senior analysts for a large, multi-visionmoney management firm. Bea supports the institutionportfolio managers, anMüller es the same for the private wealth portfolio managers.Bea reviews the asset allocation in Exhibit 1, rivefrom a mean–varianoptimization (MVO) mol for institutionclient, noting thtails of the MVO are lacking.Exhibit1 Asset Allocation anMarket Weights(in percent)The firm’s poliis to rebalana portfolio when the asset class weight falls outsi of a corrir arounthe target allocation. The wih of eacorrir is customizefor eaclient anproportionto the target allocation. Bea recommen wir corrir wihs for high-risk asset classes, narrower corrir wihs for less liquiasset classes, annarrower corrir wihs for taxable clients with high capitgains trates.One client sponsors a finebenefit pension plwhere the present value of the liabilities is $241 million anthe market value of plassets is $205 million. Bea expects interest rates to rise anboth the present value of plliabilities anthe market value of plassets to crease $25 million, changing the pension plan’s funng ratio.Bea uses a surplus optimization approato liability-relative asset allocation baseon the objective function Um =E (Rm) - 0.005λσm2where E(Rs,m) is the expectesurplus return for portfolio m, λ is the risk aversion coefficient, anσ2(Rs,m) is the varianof the surplus return. Bea establishes the expectesurplus return ansurplus varianfor three fferent asset allocations, shown in Exhibit 2. Given λ = 1.50, she chooses the optimasset mix.Exhibit 2 ExpecteSurplus Return anVolatility for Three PortfoliosClient Haunani Kealoha ha large fixeobligation e in 10 years. Bea assesses thKealoha hsubstantially more fun thare requireto meet the fixeobligation. The client wants to earn a competitive risk-austerate of return while maintaining a high level of certainty ththere will sufficient assets to meet the fixeobligation.In the private wealth arethe firm hsignefive sub-portfolios with ffering asset allocations thare useto funfferent client goals over a five-yehorizon. Exhibit 3 shows the expectereturns anvolatilities of the sub-portfolios anthe probabilities ththe sub-portfolios will exceeexpecteminimum return. Client Luis Roíguez wants to satisfy two goals. Go1 requires a conservative portfolio proving the highest possible minimum return thwill met least 95% of the time. Go2 requires a riskier portfolio thprovis the highest minimum return thwill exceeleast 85% of the time.Exhibit3 Characteristiof Sub-portfoliosMüller uses a risk parity asset allocation approawith a client’s four–asset class portfolio. The expectereturn of the mestic bonasset class is the lowest of the asset classes, anthe returns of the mestic bonasset class have the lowest covarianwith other asset class returns. Müller estimates the weight thshoulplaceon mestic bon.Müller ana client scuss other approaches to asset allocation thare not baseon optimization mols or goals-basemols. Müller makes the following comments to the client:Comment 1 aantage of the \"120 minus your age\" heuristic over the 60/40 stock/bonheuristic is thit incorporates age-basestock/bonallocation.Comment 2 The Yale mol emphasizes trationinvestments ana commitment to active management.Comment 3 A client’s asset allocation using the 1/N rule pen on the investment characteristiof eaasset class. In the risk parity asset allocation approathMüller uses, the weight thMüller places on mestic bon shoulbe: A.less th25%. B.equto 25%. C.greater th25%. C is correct. A risk parity asset allocation is baseon the notion theaasset class shoulcontribute equally to the totrisk of the portfolio. Bon have the lowest risk level anmust contribute 25% of the portfolio’s totrisk, so bon must overweighte(greater th25%). The equcontribution of eaasset class is calculateas:wi* Cov(ri,rp)=1nδρ2 wherewi = weight of asset iCov(ri,rp) = covarianof asset i with the portfolion = number of assetsσ2= varianof the portfolioIn this example, there are four asset classes, anthe varianof the totportfolio is assumeto 25%; therefore, using a risk parity approach, the allocation to eaasset class is expecteto contribute (1/4 × 25%) = 6.25% of the totvariance. Because bon have the lowest covariance, they must have a higher relative weight to achieve the same contribution to risk the other asset classes. 老师，看了答案和类似问题的回答，还是不太明白，怎么算出总的varian=25%，每个资产对于风险的贡献度一样，一共有4个资产，那是每个资产对于风险的贡献度=25%，不是总的variance=25%啊