This blog post explores a comprehensive statistical analysis project conducted on a dataset comprising weekly returns of 95 ETFs over a span of 454 weeks from May 2006 to May 2015. The analysis delves into data quality, empirical distribution, and performance metrics of selected ETFs, leveraging statistical methods to examine their average returns, variance, and covariances. Additionally, it explores portfolio optimization techniques to maximize returns while managing risk, providing insights into effective investment strategies.

Data description

The dataset encapsulates weekly returns from 95 different ETFs, recorded over 454 weeks, with no missing data points, ensuring high data quality. The analysis focuses on four specific ETFs - AGG, VAW, IWN, and SPY, examining their empirical distributions, sample means, variances, standard deviations, and quartiles to derive insights into their performance.

Methods

The study employs various statistical methods, including plotting empirical density and box plots for understanding distributions, computing covariance matrices to analyze relationships between ETFs, and applying portfolio optimization techniques. The analysis also incorporates hypothesis testing to compare the average weekly returns against a baseline, and confidence interval estimation for average returns and variance.

Results

The results reveal distinct characteristics of the ETFs, with varying levels of return and volatility. Portfolio optimization highlighted specific allocation strategies that could potentially enhance investment returns. Hypothesis testing suggested significant differences in the performance of the ETFs compared to a no-investment scenario.

Conclusion

The analysis underscores the importance of statistical methods in understanding financial data and guiding investment decisions. It demonstrates how different ETFs exhibit unique risk-return profiles, necessitating tailored portfolio strategies to maximize gains. The project illustrates the critical role of empirical distribution analysis, covariance assessment, and portfolio optimization in financial analytics, offering valuable insights for investors seeking to optimize their investment portfolios.