Markowitz’s celebrated optimal portfolio theory generally fails to deliver out-of-sample diversification. In this paper, we propose a new portfolio construction strategy based on symmetry arguments only, leading to “eigenrisk parity” portfolios that achieve equal realized risk on all the principal components of the covariance matrix. This holds true for any other definition of uncorrelated factors. We then specialize our general formula to the most agnostic case, where the indicators of future returns are assumed to be uncorrelated and of equal variance. This “agnostic risk parity” (AGP) portfolio minimizes unknown-unknown risks generated by the over-optimistic hedging of different bets. AGP is shown to fare quite well when applied to standard technical strategies such as trend following.