Billionaire hedge-fund manager William Ackman is raising his bet that the migration of Americans to warmer, lower-tax cities is here to stay.

His Pershing Square Capital Management LP recently increased its stake in Howard Hughes Corp. to nearly 25%. The Houston-based developer is ramping up construction of multifamily housing in Texas, Maryland, Hawaii and Las Vegas.

“It’s not a Wall Street bet. It’s a generational bet,” said Mr. Ackman, who is also chairman of Howard Hughes’s board. The fund manager is widely known for his shareholder-activism campaigns and his bets on large companies such as Starbucks Corp. and J.C. Penney Co.

Pershing Square increased its stake in Howard Hughes by about 4.7% between June and January, according to public filings. The firm bought common stock, and some of its counterparties exercised options that compelled Pershing Square to buy additional shares, filings show.

Howard Hughes, a land owner and developer of master-planned communities, said it is starting construction on 1,475 new apartments across four cities that have experienced an influx of people over the past year.