True or False?
There are two reasons why this statement is false. First, it pays to diversify one's holdings, so one should hold a wide range of assets regardless of the fact that the prices of the assets reflect all available information. Second, different assets and therefore different portfolios of assets have different degrees of non-diversifiable risk, again quite independently of the public availability of all information about them.
Diversification takes care of the diversifiable risk. That risk reflects that portion of the variability of the return from holding the asset that is uncorrelated with the returns from holding other assets in the economy. Including that asset in a portfolio of other assets can effectively eliminate this risk. The non-diversifiable risk reflects that portion of the variability of the return to the asset that is correlated with the returns to other assets in the economy. It cannot be diversified away because all asset returns are rising and falling at the same time.
Assets that show large fluctuations in return in association with fluctuations in the average return to all assets in the market tend to contribute a lot of variability to portfolios that contain them. They are therefore less desirable and have lower prices relative to earnings, and hence higher returns, than assets that fluctuate very little in association with general market fluctuations. Careful selection of assets in the portfolio can therefore lead to whatever degree of risk the owner of the portfolio is willing to bear. The greater the risk borne, the higher the return to the portfolio.