'Pick a random slate of 20-30 companies with good statistical properties.'

As you and others have shown, this is a very good investment approach. The top stocks as ranked by the given criteria have high returns, and the returns of the deciles as ranked by the given criteria fall smoothly in line. I uploaded a graph of the returns by decile for the Magic Formula to the Motley Fool Berkshire board to illustrate this point. As I understand it, criteria that work well include profitability (e.g., one-year or five year average ROA and ROE), growth (revenue per share or earnings per share) and valuation (earnings yield or free cash flow yield). The graph illustrates the importance of selecting the top few percent of stocks as ranked by the chosen criteria.

Could you please give us an estimate of the turnover in the example you chose, top one-year ROE and 5-year sales growth, reconstituted semi-annually? I have a bias for low turnover. Thank you, mungofitch.