It is possible that proof-of-burn cryptocurrencies can be more stable in terms of price than proof-of-work and proof-of-stake currencies, for the following reason:

• When price goes up, it is more expensive to burn coins. So people will be burn less than normal.
• When price goes down, it is less expensive and people will burn more.

Now, block rewards - and the "normal" money supply increase - are normally the same in times of high and low prices*. So when more coins are burnt, the money supply decreases, and vice versa.

So a proof-of-burn currency probably gets more scarce in times of low prices. That should reduce sell orders on exchanges, and price can return to previous levels fast when (buy) demand goes up again.

The same applies in price bubbles, when prices go up excessively, less coins are burnt and supply is greater than normal. There will be more sell orders and price can correct fast without overheating too much.

So PoB currencies should be more "elastic" respect to supply/demand variations and therefore they may be more stable. As price stability is a unsolved problem in Bitcoin and other cryptocurrencies, that could be an important advantage of SLM and other PoB coins.

Obviously, a cryptocurrency must reach a certain maturity before such mechanisms can apply. So the actual Slimcoin price performance (less than 2 months after the start, with bug-caused problems and with very low trade volume) still cannot be analyzed this way. But it will be interesting how price behaves if Slimcoin establishes itself as a stable cryptocurrency.

*In Slimcoin with its difficulty-dependant PoW block reward there may be reward variations caused by price volatility. But I think the concept can still be applied to it.