Slowing U.S. inflation has sparked hopes of a big turnaround for hard-hit parts of the $10.6 trillion U.S. corporate bond market.

Bonds issued by America’s most valuable companies, from Apple Inc. AAPL to Amazon.com AMZN to Microsoft Corp. MSFT to Johnson & Johnson, JNJ have been trading at some of their lowest prices in nearly two decades, a casualty of the Federal Reserve’s interest rate hikes in the past 18 months.

Prices…