## 这是一篇来自美国的关于利用均值-方差投资组合理论优化股票投资组合的作业代写，以下是作业具体内容：

Proposed Work

1. Problem Statement

There are two types of investment strategies in stock investing: value investing and growth investing. Value investors tend to look for stocks that are undervalued while growth investors seek companies that have the potential to outperform the overall market. In this paper, we will be value investors, will try to develop a stock portfolio, and try to optimize this portfolio. A portfolio is a collection of different types of assets, such as bonds, stocks, derivatives, etc. A stock portfolio is just a portfolio in that every asset is a stock. Ideally, a portfolio will consist of different kinds of assets to avoid systematic risk, but in this paper, we will only focus on the stock market.  We will pick 10~20 stocks from S&P 500 based on fundamental analysis, which means we will analyze the overall economy, the industry that the company is in, and the performance of the company itself to find out which stocks are worth investing in. Since there is always a trade-off between risk and return, we want to find the optimal point where we get as much return as possible but also the risk is tolerable. After picking up stocks, we would like to assign weights to those stocks and optimize our portfolio. By optimizing a portfolio, we are referring to the process of making a better portfolio based on several criteria, such as maximizing the return, minimizing the risk, maximizing the return with a target risk, etc. In this paper, we want to minimize the risk while achieving the required rate of return, i.e. reach the efficient frontier of chosen stocks. We assume that we have \$1 million to invest fully in stocks and our goal is to construct a such portfolio, hold it for three months, each month count as one period and see how much return we can get with a target risk level. In the end, we will also compare the rate of return of our portfolio with the S&P 500 to evaluate the performance of our portfolio. Noticing here the goal is investing instead of trading, which implies that short-term buying and selling is not in the scope of discussion of this paper.

I believe the process is meaningful. First, through fundamental analysis, we get to analyze how to pick a stock with potential, which is an essential skill for financial managers to help clients to manage their wealth. Also, since models are a simplified version of reality, putting them in the real market can show us how much our model deviate from reality and test its feasibility

1. Approach

The first step would be picking stocks. We will use the bottom-up style fundamental analysis, which means we will compare different aspects of companies in the same industry such as price-to-earning ratio, quick ratio, credit rating, annual reports, patents that the company holds, etc. We also want the stocks to be as diverse as possible to avoid systematic risk.

After done with picking the stocks, the general outline for solving this problem would be: (1) Build a mathematical model of the problem (2) Analyze available data to use in this model (3) Use numerical data to solve the model (4) Turn the solution of the model into actual decisions.

The model we will use is Markowitz’s mean-variance model [2]. In this model, we have several assumptions. We assume investors are risk averse, which means that given two assets with the same rate of return, investors will always choose the one with lower risk and we also assume investors want the high reward. We would also assume that there is no transaction cost or taxes, investors have access to the same information and they make their decisions based on expected return and variance.

Since we will hold the stocks for three months, each month can be regarded as a period. Assume in a portfolio there are  assets and and  are the amount of money we invested in asset  at the beginning of the j-th period. The required rate of return is  and  is the return of stock  in period j

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