Voting and non-voting shares of ten German companies are analyzed for fractional cointegration. It turns out that seven pairs of price series are fractionally cointegrated, which means that for each pair there is a linear combination of the two series that is a long-memory process. If two stocks are fractionally cointegrated, future returns of at least one of the stocks can be predicted by past prices. This contradicts the weak form of the efficient market hypothesis. A simple trading strategy is proposed and analyzed; it leads to considerable excess returns in two out-of-sample evaluations.