How many stocks do need to have in a portfolio to maximize returns and still limit risk? OSAM’s Patrick O’Shaughnessy recently looked at that question, and his findings may surprise you.

“I set up portfolios which bought the absolute cheapest stocks trading in the U.S. (including ADRs),” O’Shaughnessy writes on his blog, Millennial Invest. “Portfolios ranged from 1 stock to 100 stocks, and stocks needed to have a minimum market cap of $200MM (inflation adjusted). Cheapness is defined as an equal weighted combination of a stock’s price/earnings, price/sales, EBITDA/EV, Free Cash Flow/EV and total (shareholder) yield. Each portfolio was rebalanced on a rolling annual basis (meaning 1/12 of the portfolio is rebalanced every month. Think of it like maintaining 12 separate, annually rebalanced portfolios). This means that the “one stock portfolio” will have more than one stock, because different stocks rise to the top through the months. This process removes any seasonal biases and makes the test more robust.”

The findings: O’Shaughnessy found that the best returns came from five-stock portfolio; the best risk-adjusted returns came from a 15-stock portfolio.

O’Shaughnessy says that he’s a “huge believer in high active share, and that to beat the market you mustdare to be great (that is, different). These results are further evidence support these beliefs.”