美国波士顿学院论文代写：股票收益
美国波士顿学院论文代写：股票收益
有效边界的计算已在Excel中完成。每个股票的预期收益（年化）已计算出的股票的平均回报率。此外，标准偏差计算使用Excel表中给出的回报。标准偏差也按年计算。在每个股票回报率，投资组合的回报范围是从0.11到0.19。对于每一个预期的平均求解器用于获得最小标准偏差。
为了得到有效的前沿，可以预期的回报最大化或标准偏差可以最小化。在这里，我们尽量减少标准偏差。有效边界可以限制或不受限制。在无限制的有效前沿，卖空是允许的，因此不会对资产的权重有任何约束。在有限效率边界中，个人资产的权重将被限制在0到1之间。除此之外，还会有一个约束，即所有资产的权重总和应为1。因此，将有共同的约束权重总结到1的有效前沿，并在有限的有效前沿将有额外的约束个人资产的权重（默顿，1972）
有不同的原因，投资者可能不使用该模型。第一个原因是投资者可能没有风险中性。投资者可规避风险或承担风险。对于他们的均值方差优化不成立。他们可以选择具有最高风险和回报的股票或风险最小的股票。
投资者可能不会购买部分股票，因此就不可能实现模型给出的精确输出。
它考虑到历史的回报和标准偏差。历史未必是对未来的正确表述。投资者预期收益可能与历史回报不同。投资者可能会认为，与过去相比，该股有望获得更好的回报。这可能是因为公司有了新项目。因此，可以与模型不考虑的投资者的信息。
美国波士顿学院论文代写：股票收益
The calculations for the efficient frontier has been done in excel. The expected return for each stock (annualized) has been calculated by taking the average of the returns of the stocks. Also the standard deviation is calculated using the returns given in the excel sheet. The standard deviation is also annualized. Looking at the each stock return, the portfolio returns range is taken from the 0.11 to 0.19. For each expected mean the solver is used to get the minimum standard deviation.
To get the efficient frontier either the expected return can be maximized or the standard deviation can be minimized. Here we have minimized the standard deviation. Efficient frontier can be restricted or unrestricted. In an unrestricted efficient frontier, short selling is allowed hence there will be no constraint on the weights of the assets. In the restricted efficient frontier the weights of individual asset will be restricted between 0 and 1. In addition to this there will be one more constraint, i.e. the sum of weights of all the assets should sum up to 1. Hence there will be common constraint of weights summing to 1 in both the efficient frontiers, and in restricted efficient frontier there will be additional constraints on the individual asset weights (Merton, 1972)
There are different reasons why investor may not use the model. First reason is that the investor may not be risk neutral. Investor may be risk averse or risk taking. For them the mean variance optimization does not hold true. They may go for stock which has the highest risk and return or the stock with least risk.
Investors may not be to buy partial stocks and hence it becomes impossible to implement the exact output given by the model.
It takes into account the historical return and standard deviation. History may not be correct representation of the future. Also the investor expected return may differ from the historical return. The investor may have the opinion that the stock is expected to give better returns as compared to the past. This can be due to the fact that the firm has got new projects. Thus there can be information with the investor which the model is not taking into account.
