Download monthly prices for the Vanguard Total Stock Market ETF (Ticker: VTI) and Vanguard Total Bond Market ETF (Ticker: BND) from January 2013 to December 2017. [3.5 Points] a. Using the price information, calculate monthly returns from February 2013 to December 2017. [0.25 Points] b. Calculate expected returns for VTI and BND. [0.25 points] c. For each ticker, calculate the variance of returns by: [0.25 Points] i. Manually computing the average of the sum of squared deviations between the realized (ex-post) return and expected (ex-ante) returns. ii. Using the VARP function. d. For each ticker, calculate the standard deviation of returns by: [0.25 Points] i. Taking the square root of the average of sum of squared deviations between the realized and expected returns. ii. Using the STDEVP function.

3 e. You are considering investing $100 in each investment over the next 2 years (24 months). Using a Monte Carlo Simulation with 1,000 observations, for each investment, answer the following questions: [1.5 points] i. What is the average final wealth associated with each investment? ii. What is the standard deviation of wealth associated with each investment? iii. What is the 95% value at risk (i.e., the 5th percentile outcome) associated with each investment? iv. What is the probability of losing money with each investment? f. Plot the frequency distribution (with % of times as your Y-axis, and wealth as your X- axis) for each investment on the same graph. [0.5 points] g. Based on your answers to part e and f, do you believe one investment is better than the other? Explain why or why not? [0.5 points]