问题如下图：
implied return 的计算不是已知权重，相关系数，方差，得出它，跟CAPM有什么关系？请老师回答一下
Shimin_CPA税法主讲、CFA教研 · 2020年03月18日
嗨，努力学习的PZer你好：
这道题来源于原版书R13课后第15题，在经典题中也讲过，建议听一下，对应有答案版讲义24-25页。
reverse optimization代入的最优权重是各个资产的市值权重，相当于每个资产在index中的占比， 这个index可以看成是market portfolio。在CAPM中，假设所有投资者都有相同的预期，相同的观点，所以每一种资产的expected return与市场观点（也就是每个投资者的观点）一致，所以CAPM求出来的return就是每个资产在最优权重下的implied return。
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NO.PZ201803130100000402 问题如下 Contrast, using the information proviabove, the results of a reverse optimization approawith thof the MVO approafor eaof the following: ii. The values of the expectereturns for US equities anglobbon. Justify your response. The values of the expectereturns for US equities anglobbon■ For the reverse optimization approach, the expectereturns of asset classes are the outputs of optimization with the market capitalization weights, covariances, anthe risk aversion coefficient useinputs.■ In contrast, for the MVO approach, the expectereturns of asset classes are inputs to the optimization, with the expectereturns generally estimateusing historicta.■ The computevalues for the expectereturns for globbon anUS equities using the reverse optimization methoare 5.3% an9.7%, respectively.■ In contrast, the expectereturn estimates usein the MVO approafrom Exhibit 1 for globbon anUS equities are 4.7% an8.6%, respectively.The output of the reverse optimization methoare optimizereturns whiare vieweunobserveequilibrium or imputereturns. The equilibrium returns are essentially long-run capitmarket returns provieaasset class anare strongly linketo CAPM. In contrast, the expectereturns in the MVO approaare generally forecastebaseon historicta anare useinputs along with covariances anthe risk aversion coefficient in the optimization. The reverse-optimizereturns are calculateusing a CAPM approach. The return on asset class using the CAPM approais calculatefollows:Return on Asset Class = Risk-Free Rate + (Bet(Market Risk Premium)Therefore, the impliereturns for globbon anUS equities are calculatefollows:Return on GlobBon = 2.0% + (0.6) (5.5%) = 5.3%Return on US Equities = 2.0% + (1.4) (5.5%) = 9.7%The implieequilibrium returns for globbon anUS equities are 5.3% an9.7%, respectively. These impliereturns are above the forecastereturns baseon historicta (from Exhibit 1) useinputs in the MVO approafor globbon anUS equities of 4.7% an8.6%, respectively.
NO.PZ201803130100000402 问题如下 Contrast, using the information proviabove, the results of a reverse optimization approawith thof the MVO approafor eaof the following: ii. The values of the expectereturns for US equities anglobbon. Justify your response. The values of the expectereturns for US equities anglobbon■ For the reverse optimization approach, the expectereturns of asset classes are the outputs of optimization with the market capitalization weights, covariances, anthe risk aversion coefficient useinputs.■ In contrast, for the MVO approach, the expectereturns of asset classes are inputs to the optimization, with the expectereturns generally estimateusing historicta.■ The computevalues for the expectereturns for globbon anUS equities using the reverse optimization methoare 5.3% an9.7%, respectively.■ In contrast, the expectereturn estimates usein the MVO approafrom Exhibit 1 for globbon anUS equities are 4.7% an8.6%, respectively.The output of the reverse optimization methoare optimizereturns whiare vieweunobserveequilibrium or imputereturns. The equilibrium returns are essentially long-run capitmarket returns provieaasset class anare strongly linketo CAPM. In contrast, the expectereturns in the MVO approaare generally forecastebaseon historicta anare useinputs along with covariances anthe risk aversion coefficient in the optimization. The reverse-optimizereturns are calculateusing a CAPM approach. The return on asset class using the CAPM approais calculatefollows:Return on Asset Class = Risk-Free Rate + (Bet(Market Risk Premium)Therefore, the impliereturns for globbon anUS equities are calculatefollows:Return on GlobBon = 2.0% + (0.6) (5.5%) = 5.3%Return on US Equities = 2.0% + (1.4) (5.5%) = 9.7%The implieequilibrium returns for globbon anUS equities are 5.3% an9.7%, respectively. These impliereturns are above the forecastereturns baseon historicta (from Exhibit 1) useinputs in the MVO approafor globbon anUS equities of 4.7% an8.6%, respectively. 老师，我理解的是，mvo方法下，根据历史数据得到E（R），方差等数据，根据E（R）来算出各类资产的weight；reverse下，是根据各类资产的市值先算出weight，再根据weight算出E（R），后面如果是BL的话，再在这个E（R）中加入主观判断，调整E（R），在用调整的E(R)计算weight。但是本题中用了capm模型，是说reverse方法下，根据weight算出E（R）的这个过程其实是用CAPM算出来的吗？不太清楚是怎么根据weight算出E（R）的，为什么又用CAPM了？
NO.PZ201803130100000402问题如下 Contrast, using the information proviabove, the results of a reverse optimization approawith thof the MVO approafor eaof the following: ii. The values of the expectereturns for US equities anglobbon. Justify your response. The values of the expectereturns for US equities anglobbon■ For the reverse optimization approach, the expectereturns of asset classes are the outputs of optimization with the market capitalization weights, covariances, anthe risk aversion coefficient useinputs.■ In contrast, for the MVO approach, the expectereturns of asset classes are inputs to the optimization, with the expectereturns generally estimateusing historicta.■ The computevalues for the expectereturns for globbon anUS equities using the reverse optimization methoare 5.3% an9.7%, respectively.■ In contrast, the expectereturn estimates usein the MVO approafrom Exhibit 1 for globbon anUS equities are 4.7% an8.6%, respectively.The output of the reverse optimization methoare optimizereturns whiare vieweunobserveequilibrium or imputereturns. The equilibrium returns are essentially long-run capitmarket returns provieaasset class anare strongly linketo CAPM. In contrast, the expectereturns in the MVO approaare generally forecastebaseon historicta anare useinputs along with covariances anthe risk aversion coefficient in the optimization. The reverse-optimizereturns are calculateusing a CAPM approach. The return on asset class using the CAPM approais calculatefollows:Return on Asset Class = Risk-Free Rate + (Bet(Market Risk Premium)Therefore, the impliereturns for globbon anUS equities are calculatefollows:Return on GlobBon = 2.0% + (0.6) (5.5%) = 5.3%Return on US Equities = 2.0% + (1.4) (5.5%) = 9.7%The implieequilibrium returns for globbon anUS equities are 5.3% an9.7%, respectively. These impliereturns are above the forecastereturns baseon historicta (from Exhibit 1) useinputs in the MVO approafor globbon anUS equities of 4.7% an8.6%, respectively. 本文给出例题中，有四个点，分别是一句描述。四个点之后又是一大段文字。考试答题，只答四个点？还是后面一大段文字也都需要？
NO.PZ201803130100000402 问题如下 Contrast, using the information proviabove, the results of a reverse optimization approawith thof the MVO approafor eaof the following: ii. The values of the expectereturns for US equities anglobbon. Justify your response. The values of the expectereturns for US equities anglobbon■ For the reverse optimization approach, the expectereturns of asset classes are the outputs of optimization with the market capitalization weights, covariances, anthe risk aversion coefficient useinputs.■ In contrast, for the MVO approach, the expectereturns of asset classes are inputs to the optimization, with the expectereturns generally estimateusing historicta.■ The computevalues for the expectereturns for globbon anUS equities using the reverse optimization methoare 5.3% an9.7%, respectively.■ In contrast, the expectereturn estimates usein the MVO approafrom Exhibit 1 for globbon anUS equities are 4.7% an8.6%, respectively.The output of the reverse optimization methoare optimizereturns whiare vieweunobserveequilibrium or imputereturns. The equilibrium returns are essentially long-run capitmarket returns provieaasset class anare strongly linketo CAPM. In contrast, the expectereturns in the MVO approaare generally forecastebaseon historicta anare useinputs along with covariances anthe risk aversion coefficient in the optimization. The reverse-optimizereturns are calculateusing a CAPM approach. The return on asset class using the CAPM approais calculatefollows:Return on Asset Class = Risk-Free Rate + (Bet(Market Risk Premium)Therefore, the impliereturns for globbon anUS equities are calculatefollows:Return on GlobBon = 2.0% + (0.6) (5.5%) = 5.3%Return on US Equities = 2.0% + (1.4) (5.5%) = 9.7%The implieequilibrium returns for globbon anUS equities are 5.3% an9.7%, respectively. These impliereturns are above the forecastereturns baseon historicta (from Exhibit 1) useinputs in the MVO approafor globbon anUS equities of 4.7% an8.6%, respectively. 如题
NO.PZ201803130100000402 问题如下 Contrast, using the information proviabove, the results of a reverse optimization approawith thof the MVO approafor eaof the following: ii. The values of the expectereturns for US equities anglobbon. Justify your response. The values of the expectereturns for US equities anglobbon■ For the reverse optimization approach, the expectereturns of asset classes are the outputs of optimization with the market capitalization weights, covariances, anthe risk aversion coefficient useinputs.■ In contrast, for the MVO approach, the expectereturns of asset classes are inputs to the optimization, with the expectereturns generally estimateusing historicta.■ The computevalues for the expectereturns for globbon anUS equities using the reverse optimization methoare 5.3% an9.7%, respectively.■ In contrast, the expectereturn estimates usein the MVO approafrom Exhibit 1 for globbon anUS equities are 4.7% an8.6%, respectively.The output of the reverse optimization methoare optimizereturns whiare vieweunobserveequilibrium or imputereturns. The equilibrium returns are essentially long-run capitmarket returns provieaasset class anare strongly linketo CAPM. In contrast, the expectereturns in the MVO approaare generally forecastebaseon historicta anare useinputs along with covariances anthe risk aversion coefficient in the optimization. The reverse-optimizereturns are calculateusing a CAPM approach. The return on asset class using the CAPM approais calculatefollows:Return on Asset Class = Risk-Free Rate + (Bet(Market Risk Premium)Therefore, the impliereturns for globbon anUS equities are calculatefollows:Return on GlobBon = 2.0% + (0.6) (5.5%) = 5.3%Return on US Equities = 2.0% + (1.4) (5.5%) = 9.7%The implieequilibrium returns for globbon anUS equities are 5.3% an9.7%, respectively. These impliereturns are above the forecastereturns baseon historicta (from Exhibit 1) useinputs in the MVO approafor globbon anUS equities of 4.7% an8.6%, respectively. 老师好！看了之前同学的提问，总结了一下，不知道以下理解是否正确1.如果是计算asset class的return，就用答案中的公式 Return on Asset Class = Risk-Free Rate + (Bet(Market Risk Premium)2.如果计算单个资产，则用Return = Risk-Free Rate + (Bet(Market Risk Premium-Risk-Free Rate)谢谢！