This project has two separate questions.
1. You got a job at MetLife pension department. Your supervisor needs your help with some of its liabilities and risk control. The pension fund has a series of liabilities to be paid to the pension plan beneficiaries:
In 6 months: $2,000,000,
In 1 year: $2,200,000,
In 1.5 years: $2,500,000,
In 2 years: $3,200,000,
In 2.5 years: $3,700,000,
In 3 years: $4,300,000,
In 3.5 years: $4,700,000,
In 4 years: $5,100,000.
Your company wishes to construct a portfolio of assets to cover this series of liabilities, such that it is immunized against interest rate risk right now. The company is considering investing in four different bonds: (1) a 1-year Treasury Bill with a face value of $1,000 and no coupon, (2) a 2-year Treasury note with a face value of $1,000 and an annual coupon rate of 1.5%, (3) a 3-year Treasury note with a face value of $1,000 and an annual coupon rate of 1.90%, and (4) a 5-year Treasury note with a face value of $1,000 and an annual coupon rate of 2.30%. All Treasury notes make 2 (semi-annual) coupon payments per year. Assume the current yield on all bonds is 1.85%. Your supervisor wants you to find out how many of each of these four treasury bonds the fund should buy to fully fund the liability and be immunized against interest rate risk right now?
2. This question’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 (1/1/2015 – 12/31-2019) on Yahoo finance and calculate its daily holding period returns.
(2) Generate a summary statistics report on its holding period returns.
(3) Create a Histogram chart on its holding period returns.
(4) Estimate its annualized volatility using all the holding period returns from (1).
(5) Use the S&P 500 holding period returns during the same period as market return, run a regression to estimate the beta of this stock. Y: stock return minus risk-free rate. X: market return minus risk-free rate. You can use 1.5% as risk-free rate.
(6) Once beta is estimated, calculate the expected return of this stock using CAPM. According to CAPM, Expected return = Rf + beta*(Rm-Rf). Note that Rf should be an annual return, Rm should also be an annualized 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. 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.)