- You graduated from Univarsty and 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. The current yield on all bonds is 1.45%. 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?
- Pick a stock (It can be any stock, as long as it is a common stock traded in NYSE/Nasdaq/Amex).
(1) Obtain its 5-year historical daily prices (1/1/2013 – 12/31-2017) 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 go online and use the 1-year Treasury bill yield 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) Pick another 3 stocks, and repeat (1)-(7) for these 3 stocks. If your group has less than 4 members, you may pick another 2 stocks instead of 3 stocks for this part.(9) Form a portfolio with all 4 (or 3) stocks above. Estimate the correlation coefficients among all stock returns.(10) Set a target portfolio return, use Solver to estimate the optimal weights for all stocks 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 all your stocks have expected returns around 10% based on CAPM, setting a target portfolio return of 20% will probably not work.)
| Q1: Use timeline to calculate PV of liabilities | 1 pt |
|---|---|
| Q1: Use timeline to calculate Duration of liabilities | 1 pt |
| Q1: Use timeline to calculate PV of assets | 1 pt |
| Q1: Use timeline to calculate Duration of liabilities | 1 pt |
| Q1: Use solver to calculate # of bonds to buy | 1 pt |
| Q1: Overall model setup, format, flexibility | 0.5 pt |
| Q2: Obtain prices and calculate HPRs | 2 pts (0.5 pt per stock) |
| Q2: Generate summary statistics using “Data Analysis†tool | 2 pts (0.5 pt per stock) |
| Q2: Generate Histogram chart using the bin range you created | 2 pts (0.5 pt per stock) |
| Q2: Calculate annualized volatility using any method | 2 pts (0.5 pt per stock) |
| Q2: Create Y and X to run a regression, generate regression output | 2 pts (0.5 pt per stock) |
| Q2: Calculate stock expected return using CAPM | 2 pts (0.5 pt per stock) |
| Q2: Stock price simulation for 252 days assuming stock prices follow Geometric Brownian | 2 pts (0.5 pt per stock) |
| Q2: Create correlation matrix | 2 pts |
| Q2: Calculate portfolio variance | 1 pt |
| Q2: Use Solver to solve optimal weights of the portfolio | 1 pt |
| Q2: Overall model setup, format, flexibility, coherence. | 1.5 pts |
| Total | 25 pts |
Jermaine Byrant
Nicole Johnson
OVER
RATING
YEARS
