Need it done by 11pm Eastern Standard Time
This project's purpose is to form a portfolio with 2 risky assets (2 common stocks) and 1 risk-free asset (1-year Treasury Bills), and calculate the optimal portfolio weights among these assets.
Pick 2 stocks you are interested in investing (They can be any stock, as long as they are common stocks listed on NYSE/Nasdaq/Amex). For each of the stock, do the following:
(1) Obtain its 5-year historical daily prices (1/1/2017 – 12/31-2021) on Yahoo finance and calculate its daily holding period returns.
(2) Generate a summary statistics report on its holding period returns, using Data Analysis tool.
(3) Create a Histogram chart on its holding period returns, using Data Analysis tool. Bin range needs to be created by you, not automatically by Excel.
(4) Estimate its annualized volatility using all the holding period returns from (1).
(5) Download the historical data for market index during the same sample period and calculate its holding period returns. Since ^GSPC is not available to download directly on yahoo finance, you can use ^SPY instead, which is an ETF for S&P 500 index. Use SPY's holding period returns as market returns, run a regression to estimate the beta of this stock. Y: stock returns . X: market returns.
(6) Once beta is estimated, calculate the expected return of this stock using CAPM. According to CAPM, Expected return = Rf + beta*(Rm-Rf). In this equation, Rf is risk-free rate, you can use 1% as Rf. Rm is historical annualized market return, which can be calculated using average of daily S&P 500 returns in part (5) multiplied by 252.
(7) Use the expected return and annualized volatility you estimated in part (4) and (6), simulate daily stock prices for the next 252 days, assuming stock prices follow Geometric Brownian Motion.
(8) Form a portfolio with both stocks and risk-free asset. To set up the portfolio, stock's mean should be CAPM return from part (6), stock's SD should be annualized volatility from part (4). Risk-free rate is 1%. Estimate the correlation coefficients between two stocks. Use this formula =CORREL(HPRs of stock1, HPRs of stock 2)
(9) Set a target portfolio return, use Solver to estimate the optimal weights for all assets in your portfolio. (Tip: If your solver is unable to give you a solution, consider changing your target portfolio return to a more realistic number, for example, if both your stocks have expected returns around 10% based on CAPM, setting a target portfolio return of 20% will probably not work.)