HSBC Holdings has a $15 billion headache in China—a big stake in a local lender that it can’t easily sell and that could require a big write-down.

Long after most other Western banking giants have exited similar positions, HSBC has held on to its roughly 19% position in Bank of Communications, an investment that dates back to 2004. HSBC, Europe’s largest bank by market value, has said the stake is strategically important for its ambitions to grow in Asia.