根据分离定理，每个投资者都持有相同的风险资产组合M。如果某种证券在组合M中的比例为零，那么就没有人购买该证券，该证券的价格就会下降，从而使该证券的预期收益率上升，一直到在最终的切点处的风险资产组合M中该证券的比例非零为止。反之，如果投资者对某种证券的需要量超过其供给量，则该证券的价格将上升，导致其预期收益率下降，从而降低其吸引力，它在切点处的风险资产组合M中的比例也将下降，直至对其需要量等于其供给量为止。

Suppose in the tangent portfolio there are n assets, eash weight is wq_i, i=1,2,....n

Suppose there are m investors in the world and each investor's invests in the tangent portfolio is Dj, j=1,2,...m

for the ith asset the total investment value of all the investors is:

\[ D_1w_{q_i}+D_2w_{q_i}+...+D_mw_{q_i}=w_{q_i}\sum D_j  \]

for market portfolio, suppose the value of each asset is Vi, i=1,2,...n


the value weight of each asset i is:


\[ w_{m_i}=\frac{V_i}{\sum V_p}, p=1,2,3...n\]


it is easy to find that:


\[ V_i=w_{q_i}\sum_{j=1}^{m} D_j\]
and

\[ \sum V_i=\sum D_j\]
so

\[ w_{m_i}=\frac{V_i}{\sum V_p}=\frac{w_{q_i}\sum_{j=1}^{m} D_j}{\sum_{j=1}^{m} D_j}=w_{q_i} \]


so the market value weighted portfolio is the same as tangent portfolio

赞！正解