SBD update: Current lower peg at 0.906$

Already yesterday I wrote about the broken SBD peg. Today a quick update and some math.

While the haircut, debt ratios and so on can be a bit hard to understand it is quite simple to derive the formula giving the current lower peg of SBD. Let us call s the total supply of steem tokens (284349022 at the moment of writing this post) and sbd the number of circulating SBD tokens (13427376) and p the price of steem in $ (0.385).

Then the debt ratio d is d=(sbd / (s⋅p+sbd))
The haircut activates when d > 0.1. In that case conversions are cut down by 0.1/d
Combining all we find that the lower peg puts sbd at 1$ if d < 0.1 or at (s ⋅ p / (9 ⋅ sbd))$ otherwise.
Entering the numbers above this gives a lower peg from conversions of 0.906$.

What it interesting to see in this equation is that the peg of sbd is proportional to the price of steem p once the haircut activates. This means that sbd has an exactly equal risk profile as steem. There is no stability left and it is wrong to think that sbd below 1$ is a good buy since it is bound to eventually return to 1$. If it returns to 1$ then because steem did increase in value and in that case it does not matter if you have sbd or steem.

It also shows nicely how conversions can help restore the peg. Each conversion that happens reduces the supply of sbd while increasing the supply of steem. That has a double positive effect on the peg! But for our ecosystem conversions at a low price are not good at all. The entire argument of SBD was that they help reduce steem inflation when they are redeemed at a higher value of steem than they were issued. Now the opposite is happening. Conversions are triggered at the lowest prices of steem and we should expect to see some steem inflation which will generate additional downwards pressure on steem (and therefore also on sbd!).

In black is the lower peg of sbd given current steem and sbd supply as a fucntion of steem price (shown on the bottom axis). All units are in $. We see that around 0.425$ a steem the 1$ peg is restored. The red curve takes into account the asymmetric opportunity cost for conversions that makes the peg weaker around the kink. The reason is that people buying to convert take an additional risk. When steem rises during the conversion they do not benefit proportionally as the peg is stabilising 1$. But when steem falls they pay for it. This line is just drawn by hand and not from a probabilistic computation! The green shaded areas are possible prices since sbd does not have an upper peg. There is no mechanism to push the price down so it could float up and stay there. Given the pessimistic sentiment I would not bet on it, but we have seen sbd at 6$ for extended periods in the past.