The Efficient Market Hypothesis (EMH), is one of the most important hypotheses in the financial economy, which argues that yields have no memory (correlation), which implies that agents cannot have abnormal returns in the financial markets, base arbitration operations. This essay intends to investigate the efficiency, in its weak form, in the stock and bond markets of Portugal and EDP, in the period from December 31, 2019, to August 10, 2020. With the purpose of achieving such an analysis, whether: (i) with the evolution of the global pandemic (Covid-19) the Portuguese and EDP stock and bond markets show signs of (in) efficiency? (ii) Does the increased integration between the Portuguese and EDP stock and bond markets result in risk transmission? The model 𝐷𝐹𝐴 shows the existence of long memories in these markets, suggesting that they are not efficient, which validates the first research question. This situation has implications for investors, since some returns can be expected, creating opportunities for arbitrage and abnormal earnings. However, to confirm the inefficiency of these markets, based on our results, we must prove the existence of anomalous returns. In order to answer the second investigation question, we carried out the integration test that shows that these markets are mostly integrated. To validate whether financial integration results in risk transmission between the analyzed markets, we estimate the trendless cross-correlation coefficients (𝜆𝐷𝐶𝐶𝐴), which shows 4 pairs of markets showing risk transmission (4 out of 10 possible). In conclusion, the authors suggest that these results are of interest, among others, to international investors interested in expanding the geographical scope, regarding the implementation of portfolio diversification strategies.