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COVER PAGE

EE590 Project Proposal

Term:Spring 2023

Date:1/9/2023

Title of Project: Optimizing a stock portfolio using mean-variance portfolio theory

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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, willtry 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 andour 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

2. 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 assetsand and are the amount of money we invested in asset at the beginning of the j-th period. The required rate of return is andis the return of stock in period j, and And let where is the weights of stock during period j, which means .

Since we have $100,000 in total, then we have . The return of each stock at the end of first month is therefore the total return of the portfolio is .The total asset we have at the end of first month would be

In Markowitz’s theory, the risk of an asset is evaluated by its variance. Let denote the covariance matrix and where represents the covariance of stock j and stock k during i-thperiod. We will use the following formula to calculate

Therefore, the variance of the portfolio can be defined as . Since our goal is to maximize the return with a constrained level of risk V, we would formulate the problem of the first month as follows:

Find a vector w so that is minimized

with constraints  (At the beginning of the first month, we have $100,000)

(The return should be greater than the required return)

.(The total weights should be 1)

Second month would be :

Find a vector w so that is minimized

With constraints (At the beginning of second period, we have 100,000 + which is 100,000 plus the return we get in first period.)

(The return should be greater than the required return)

.(The total weights should be 1)

Third month would be:

Find a vector w so that is minimized

With constraints (At the beginning of second period, we have 100,000 +  which is 100,000 plus the return we get in first and secondperiod.)

(The return should be greater than the required return)

.(The total weights should be 1)

After formulating the problem mathematically, we would like to gather data since right now we don’t have the statistics of the stocks in our portfolio. For each period, we will use the daily closing price from the previous two months to estimate the mean, variance, and covariance matrix of the candidate stocks. For example, if we are calculating for February, we will use the data from January and December. The data we use will be from the Webull app [1]. After collecting all the historic data into an excel file, we will estimate the statistics of these stocks and find the optimal solution in a python notebook fileusing scipi and linprog package python or cplex package of AMPL.

3. Deliverables and Expected Outcome (1/2 page min)  

The deliverables will include a final report in a Microsoft word file (.doc), a python notebook file (.ipynb) with optimization steps(or an AMPL mod file along with a doc file documenting the commands we used in solving the optimization problem), an Excel file with collected historical data of the stocks[1], a Microsoft word file that contains the fundamental analysis of stock we choose, . The results can be used by the public.

4. References

[1] https://app.webull.com/watch

[2] https://en.wikipedia.org/wiki/Markowitz_model

Check List for Proposal and Final Report

Check that you addressed each item and initial it to the right

1. Structure of document: fond, spaces, minimum number of required pages. Font should be 11. Space should be single or 1.15. Margins should be 1in all around   _________BL_______________

2. All abbreviations are defined when first appeared______________________

3. All figures and tables are labeled with numbers and captions. Figure captions go under the plots and table captions above tables. Make sure you indicate units. _________BL______________

4. Figures, tables, diagrams, pictures taken from the web or papers should include the source otherwise it is plagiarism_________BL_____________________

5. No text should be copied and paste from anywhere as it is plagiarism. If you quote someone you should put it under “….”  and identify the source as a reference but it should not be more than a couple of lines._______BL______________

6. All listed references should be mentioned in text. Use format [1], [2] ___________BL____________________

7. Grammar and English should be carefully checked .No report with typos and grammatical errors will be accepted. Check the tenses. Some students tend to use parts of the proposal that uses the words ‘I will’ , ‘I plan’ etc. The final report should state what you did not plan to do. _________BL________________

PLIAGIARISM: Any identified form of plagiarism will be reported to the University and in addition to receiving no credit for EE590 the graduation of the student may be affected. All past reports are kept and a software program is used to identify overlaps with past reports and literature. If you use figures or tables or diagrams from a website or papers you need to indicate that and include the reference..

I confirm that my proposal/report abides with the above guidelines and no material was copied from any source that is not indicated in the report and referenced accordingly.

Name _________BinxuanLi_____________________________

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