There are other mechanisms that tend to push it toward $1 such as people choosing 50/50 HBD/HP or 100% HP for rewards, and speculation pushing it away from the bounds (makes more sense to sell HBD at 1.05 than to buy it, and likewise buy at 0.95 than sell).

I really hope you're right. I think it would tend to stay in the lower range of $0.95 more often than not as buying HBD at $1 would mean taking a certain time commitment to make up for the 5% fee. Around 3 months before ROI if the savings rate was 20% like currently.