Diversification eliminates non-systematic risk, but at the cost of increasing the systematic risk. Diversification forces the portfolio manager to invest in assets without analyzing their fundamentals, solely for the benefit of eliminating the portfolio’s non-systematic risk (the CAPM assumes investment in all available assets). This artificially increased demand pushes up the price of assets that, when analyzed individually, would be of little fundamental value. The result is that the whole portfolio becomes more expensive and, as a result, the probability of a positive return decreases (i.e. the risk of the portfolio increases).
Empirical evidence for this is the price hike that stocks typically experience once they are included in major indices like the S&P 500.