LOS ANGELES The final reading for HSBC’s closely watched China manufacturing Purchasing Managers’ Index came in slightly stronger than the preliminary reading, printing at 50.5 on Monday from an initial 50.4. The data confirmed the index’s rise above the 50 level — which divides expansion from contraction — for the first time in 13 months. The HSBC China PMI’s final October reading was 49.5. Over the weekend, the government-sponsored version of the China manufacturing PMI for November came in at 50.6, up from 50.2 in October and just shy of economists’ expectation for a 50.8 reading. Mainland China’s benchmark Shanghai Composite Index swung to a gain of 0.2% after the data from a 0.2% loss at the open, while Hong Kong stock indexes extended their opening gains.