Stablecoins can lose their pegs, if there is a run on the coin or the algorithm fails. This has happened in the past with projects as big as Tether dropping as low as 0.51c on some exchanges. That means that these coins are not perfectly stable, and there is inherent risk in holding them. Furthermore, the centralised coins like Tether may not be holding the reserves that they claim, as they haven't been audited. This leaves the risk that the project could implode should investors feel that their funds are not backed up by assets. This would be a nuclear event for the cryptocurrency world.