Randomly increasing the number of securities in a portoflio decreases risk (as measured in figure below with standard deviation) and enhances expected returns. This is seen in the figure shown below where on the left column it has been plotted the scatter plots in the standard deviation/return space of the securities in the portfolio, where the shading colors, in the range blue-red, represent weights in the max Sharpe portfolio. In the right column are a sample of feasible portfolios and the efficient frontier that show lowering of risk and enhancement of expected return the higher the number of securities in portfolio: it’s easy to notice that randomly increasing the number of securities in a portfolio lowers risk and enhances returns.
Data source: Eurostoxx 50 costituents, Yahoo!, daily returns June 2012 – June 2013.
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