新西兰数学论文代写：CAPM中的有效边界
定义和描述CAPM中的有效边界。讨论关于有效投资组合和CAPM的命题1和3。列出模型的基本假设，主要结果和直觉
在风险收益空间中，可以绘制每种可能的资产组合，并且绘制的收益组合由该空间中的区域来定义。有效的边界是指沿着包括投资组合图的区域的上边缘的线。沿着这条线的所有组合被称为投资组合，排除那些无风险的替代方案。这些投资组合提供固定收益水平的风险最低。换句话说，可以说高效的边界为给定的风险水平提供了最好的回报（Jagannathan＆Wang，1996）。
在数学术语中，有效边界是通过具有代表一组投资组合的最小方差的投资组合的交集而获得的，该投资组合具有最大收益。
Var（rp）= w1 2 Var（r1）+ w2 2 Var（r2）+ 2w1w2 Cov（r1r2）
命题1
（1）式中的投资组合ω是独立的风险最优均值 – 方差有效率，其中n是有风险证券的回报向量R-r的预期超额回报率，n是有风险证券收益率之间的非奇异协方差矩阵Ω。当且仅当ω=Ω-1（R-r）/ [eTΩ-1（R-r）]时，均方差框架“
命题2
“在给定风险证券收益之间的期望收益率向量R-r和非奇异协方差矩阵Ω的情况下，当且仅当市场投资组合ωm=Ω-1（R-r）/ [eTΩ-1 R-R）]”
新西兰数学论文代写：CAPM中的有效边界
Define and describe the efficient frontier in CAPM. Discuss proposition 1 and 3 on efficient portfolios and CAPM. List basic assumptions, main results and intuitions of the model
In the risk-return space each possible combination of assets can be plotted and the collection of plotted portfolios is defined by the region in this space. Efficient frontier is referred to the line along upper edge of the region that includes plot of portfolios. All the combinations that lie along this line are known as portfolios that exclude those having risk free alternative. These portfolios offer lowest risk for a fixed level of return. In other words it can be said that efficient frontier offers best possible return for a given level of risk (Jagannathan & Wang, 1996).
In mathematical terms the efficient frontier is obtained by the intersection of set of portfolios having a minimum variance that represents a set of portfolio having maximum return.
Var(rp) = w1 2 Var(r1) + w2 2 Var(r2) + 2w1w2 Cov(r1r2)
Proposition 1
“Given the expected excess rate of return vector R–r on n risky securities and the non–singular covariance matrix Ω between n risky securities rate of returns, the portfolio ω in equation (1) is the unique risky optimal mean–variance efficient within the mean–variance framework if and only if ω = Ω–1(R–r)/[eTΩ–1(R–r)]”
Proposition 2
“Given the expected excess rate of return vector R–r and non–singular covariance matrix Ω between the risky securities returns, CAPM holds if and only if the market portfolio ωm = Ω–1(R–r)/[eTΩ–1(R–r)]”
