You're using a different definition than the one I learned in school. The purpose of diversification, as opposed to simply picking the best asset, is to decreas

You're using a different definition than the one I learned in school. The purpose of diversification, as opposed to simply picking the best asset, is to decrease variance. Given a choice between two assets, or portfolios, one first maximizes expected value. Between two portfolios of equal expected value, you pick lower variance. That's the rational thing to do if you are managing a fund. The whole risk ratio thing arises only because so many investors are trying to build a well-diversified portfolio and bid up or down the price of assets accordingly. Price in turn affects expected return -- the expected value of the asset.