A broad set of bond exchange-traded funds are trading out of sync with their underlying assets, testing investors’ faith in a fast-growing part of the investment world.

Bond ETFs of BlackRock Inc., Vanguard Group and others traded at historic discounts to the net asset value of their underlying bonds in recent days. BlackRock’s iShares iBoxx USD Investment Grade Corporate Bond ETF closed down at a discount of over 5% late last week, a record since 2008. The $28 billion bond fund, with the ticker LQD, typically trades within...