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It shouldn't make a difference - a Steem Dollar is designed to be always worth a dollar. Whoever holds a Steem Dollar can (at anytime) convert it for 1 dollars worth of Steem using their wallet. It's designed to offer holders protection against crypto volatility should they wish it.

However in the open market people are not necessarily rational. All coins are getting pumped, included Steem Dollars. This means holders of Steem Dollars can sell at a premium.

But if the price of STEEM goes up, the steem dollar will still be worth one dollar, while the STEEM would be really valuable, no?

Correct....and if STEEM goes down the Steem dollar will still be worth a dollar.

As per the whitepaper

Steem Dollars were designed as an attempt to bring stability to the world of cryptocurrency and to the individuals who use the Steem network.

The idea is that people can choose to trade in (or hold) Steem dollars with a greater certainty of what it will be worth over time.