This project analyzes 5 years of closing price data for six Exchange Traded Funds (ETFs) that track diversified financial indexes from various markets around the world. The analysis identifies trends in the price data and distinguishes between diversifiable and non-diversifiable risk. The ETFs are treated as samples of larger distributions, and descriptive univariate statistics are calculated to infer characteristics about the distribution of their prices. The Gaussian form is assumed for the distributions of the prices, and estimation errors are computed and analyzed.
The project also calculates a measure of risk-adjusted return (Sharpe ratio) for each ETF and uses intensive computer-assisted resampling methods to calculate standard errors of measurement and confidence intervals. Pairwise scatterplots, covariance and correlation matrices are used to understand interactions between the ETFs, and VaR is computed at different risk levels and time horizons. The project also tests the assumption of covariance stationarity and calculates global minimum variance, tangency, and target return-equivalent portfolios. Finally, the project considers portfolios that may be used in 401(k) plans and emphasizes the importance of good underlying assets and the impact of the restriction on short selling on portfolio construction.