# 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.