Only by cycling in and out of haircut could that ever not be true.
Ok, finally, you start making sense.
You're assuming multiple cycles
No. You are assuming that we go into haircut once per cycle. But we can go into haircut multiple times in the same downtrend. For example, price goes down, we go into haircut, HBD trades at $0.5 (assuming supply of HBD nominally = 20% of hive marketcap now). HBD conversions happen when HBD trades below $0.5 and Hive printing begins.
After half the HBD supply is converted to hive, HBD goes back to $1. However, the HBD marketcap remains the same. It doesn't get halfed. Supply halfed, but price doubled. So marketcap of HBD is still 10% of hive.
What happens if HBD trades below $1 now? More conversions and more hive printing. It can easily excede 10% this way. In fact, with this particular example, the maximum is 15%.
HOWEVER, what happens if hive goes down again, right after the peg was restored?
HBD trades at $0.5 again, half the supply is converted to hive again, HBD is back at $1.
This can repeat infinitely many times. The total inflation in terms of US dollars is less than 10% of the original hive marketcap before the downtred, yes. But inflation in terms of hive is definitely higher than 10% at some point.
You can even see the Steem supply Data, the inflation rate was higher than 20% for 2019 or 2020, if I recall correctly.
Given the base rate is less than 8%, it means at least 12% inflation from HBD. There wasn't multiple cycles.
In your example, if half the HBD supply were converted during haircut, that would only be 5% inflation. If the price falls and half is converted again, that would be another 5%. I do agree this could result in aggregate of more than 10%, because it would be 5% every time the HIVE price falls in half and then half of the supply is converted. On the other hand, if some were converted before reaching 0.50 backing, which is likely (and historically consistent, as often conversions start happening before reaching even 1.00 backing), then the total would be less, and it wouldn't add another 5% each time.
Do you know where I could find the historical inflation data? I found a few posts but nothing very helpful. One was based on coinmarketcap which I don't trust and another had a graph but no source for the actual numbers. (I estimated about 18% peak rate from the graph November 2018 to November 2019, but this is very rough.)
BTW, the above situation (dropping 50% in value adding 5% inflation) is exactly the leverage effect. As the price goes down, your holdings are diluted a bit more. As the price goes up, your holdings (share of supply) increase through deflation.
This also illustrates why a 10% cap and a 1% cap, as we were discussing earlier, are NOT the same. With the 10% cap, every time the price drops by 50%, the supply expands by 5% (1.1x leverage as has been discussed for years). But with a 1% cap, every time the price drops by 50%, the supply expands by only 0.5% (1.01x leverage).
Also, as I noted earlier, the haircut means that the debt is self extinguishing, so the effect on your holdings is actually a bit less than true debt leverage at the same ratio (equity doesn't ever get wiped out, only progressively diluted, regardless of the drop).