FRANKFURT—German carmaker Porsche and sportswear maker Puma will join the nation’s premier DAX stock index, as it expands to 40 from 30 companies in the biggest overhaul of its 33-year history, the exchange operator Deutsche Boerse said on Friday. The expansion, contemplated for years, got a push in reaction to the collapse of German payments company Wirecard, which dramatically fell from grace in 2020, just two years after promotion to the benchmark index. A bigger index means greater diversification and potentially more stability for investors. The move promotes an array of companies to an index previously reserved for German corporate titans like Volkswagen and Siemens. Other new entrants include the plane manufacturer Airbus and the online fashion retailer Zalando. The changes are effective on Monday, Sept. 20. Wirecard’s demise embarrassed the German government and stained the nation’s reputation as a safe haven investment, accelerating the reform imitative backed by Deutsche …