Efficient Asset Allocation for Individual Investors in the ETF World

1 Notes: The trading price observations of each ETF Is obtained from Bloomberg from June 2007 to December 2017. Out of approximately2200 funds. the 34 ETFs funds are used based on three screening criteria Including funds with the largest market capitalization, longest history, and within each category asset class. The ETFs are ranked from the largest size to smallest size in terms of total assets value expressed in billion dollars.

1 Notes: ETFs funds are ordered from the highest to lowest average monthly returns from August 2007 to December 2017, The monthly return is the percentage change In price of each ETF. Out of approximately 2,200 funds, the 34 ETFs funds are used based on three screening criteria Including funds with the largest market capitalization, longest history, and limiting ETFs from each category of asset classes. The ETFs are ranked from the highest to lowest returns. The average monthly return and standard deviation are expressed in percent.

1 Notes: The optimized portfolio return is calculated based on optimal allocation in each asset class using 7-month rolling period return and historical variance-covariance matrix. These performance was achieved using the last 60 months returns to find the optimal weights and applying these weights to the current month’s returns and repeating the process for the following month by adding the latest month and dropping the first month, and keeping 1he sample at 60 months. This process was repeated 65 times. 65 optimal returns are averaged for each portfolio and standard deviations are calculated and both annualized. Optimized portfolio returns are ordered from the lowest risk/lowest return (Portfolio 7) to the highest risk/highest returns (Portfolio 10). Returns on each individual ETFs are the average monthly returns of the same time period as optimized portfolio individual ETFs Performance are ordered from the highest to lowest returns. Sharpe ratio is the return on portfolio or ETFs, minus risk-free rate divided by their standard deviation, where 70-year Treasury rate of 2,18% is used as the risk-free rate, All returns and standard deviations are expressed In percent.

1 Notes: Portfolio optimization conducted for 65 times. Each of these optimization processes computes the optimal weights in each of these 34 ETFs for 10 model portfolios. In other words, each process produces a weight table with 34 rows and 10 columns. In most cases, the weights are zero. To summarize, we averaged weights by columns and rows. For example, the average weight of SHV (I-share’s 1-3-year Treasury bonds ETF) in portfolio 1 Is 0.997. This is the average weight of SHV in portfolio 1 for 65 estimations. It dominates portfolio 1 since this is a portfolio with minimum risk. It Is natural to see that low-risk Treasury bonds makes up the bulk of this minimum risk portfolio. Some ETFs have zero average weight across the spectrum of portfolios. Therefore, we did not Include these ETFs In the table since all the values are zero.

1 Notes: All the performances are calculated based on out-of-sample forecast and historical variance covariance matrix. Panel A uses historical 60 months observations on a 1-month rolling basis to determine the optimal weight for each month, while Panel B uses past 40-months observations. Panel C uses a cumulative sampling. The Initial sample starts with 60-months observations and the current month’s observation is added each month without removing the oldest observation. Unlike performances reported In Panels A, B, and C where portfolio composition Is changing once a month, the portfolio performance reported in Panel D using a proccess that reshuffles the portfolio annually.

1 Notes: This table presents the performance of optimized portfolios in the 65-month period starting from August 31,2012 to December 29, 2017. At the beginning of each month, the optimization process configured the most efficient allocation. The money is invested based on the best allocation and the performance is measured at the end of the month on the ex ante basis. The procedure Is repeated for the 65 months. In this optimization, the sample variance and covdridnce matrix is modified with a shrinkage technique. Risk Is measured as standard deviation. Return and risk are expressed in percent.

1 Notes: This table presents the performance of optimized portfolios In the 65-month period starting from August 31,2012 to December 29,2017. This performance is obtained with average optimal weights, Using the average of the optimal weights, 65 month returns are calculated. The average of these 65 returns and standard deviations are reported In this table.