HBD may rise briefly but since you can convert $1.05 worth of HIVE into HBD, it is more likely that high demand for HBD translates into a lot of HIVE being destroyed to create more HBD. This likely drives HIVE much higher while HBD only experiences a short bump moderately above $1. The last time there was a surge in demand for HBD it peaked briefly at about $1.20 and quickly returned to $1 while millions of HIVE were destroyed and the price of HIVE went way up.

The stabilizer budget is much higher now than during that least surge as well, so it is possible HBD will remain even more stable (while still resulting in a lot of HIVE being bought and destroyed). That would be a good thing for the long term utility of HBD, since it aims to provide stability.