There is no guarantee HBD will stay at $1.310 throughout the conversion, in fact it is almost guaranteed it won't. It may go up resulting in a higher yield or go down reducing the yield. As long as the median stays above $1.05 it is a profitable operation and provides a direct benefit to all stake holders.

You don't get paid out HBD at the end of the conversion. You get paid back hive and the amount is calulated according to hive's median price and HBD at $1.05.

So it doesn't matter how the price of HBD varies.