Following modern portfolio theory, this lack of correlation builds the robustness of the portfolio, reducing portfolio volatility and risk, without significant negative impacts on return.
Some regard the standard deviation of the historical returns or average returns of a specific investment as providing some historical measure of risk; see modern portfolio theory.
Generally risk premia are returns (above the risk-free interest rate) as compensation for taking systematic risks (risks which in the context of modern portfolio theory can not be diversified away).
The need to answer all these questions has led to the development of more sophisticated performance measures, many of which originate in modern portfolio theory.
