The short answer: probably not.
I’ll lay out the pros and cons, but let’s address the technicalities first
There is nothing explicitly stopping someone from doing this, but the standard rules still apply; you can only contribute a maximum of $6,000 to IRA accounts in a given year. That includes any Roth IRA(s), Traditional IRA(s), or any combination thereof. That is to say, if you wanted to equitably fund 6,000 IRAs in 2020, you could only put $1 into each. I shouldn’t have to tell you not to do that.
Coming back to the original question (and moving on from my absurd 6,000 IRAs scenario), I could see some appeal to this. You could use different IRAs to manage different portfolios (e.g. one for a broad market ETF, one for a few niche ETFs, and one for your own stock picks). It would be interesting (and easier) to track the performance of these individual portfolios if they were separate. You could also try out accounts with different brokerages and see which interface you liked best. But…
You can kinda do all that stuff (save for testing out different accounts) without opening a new account every year or using different IRAs for different portfolios. Plus, there are some major cons to the “many accounts” approach.
What are the downsides?
For starters, it’s a lot to track and manage (can you imagine logging in to 20 different accounts anytime you wanted to make a withdrawal?). If you ever work with a financial planner, they’re going to be pissed at you because it’ll be a big paper-work headache for them to get access. Plus, as you approach retirement, it’ll make risk reduction and diversification a gigantic headache.
Having different accounts for different investments isn’t uncommon, but there’s no sense in going overboard (as mentioned, you could put something like 60% into an account for 1 broad market ETF, 30% into a different account for sector/style specific ETFs, and 10% is reserved for individual stocks that you’re interested in). That said, this approach to investing is still pretty manageable from one account.
All things considered opening a new account each year isn't a savvy move.
The hassle of linking all those accounts to a single account-tracking tool makes me cringe (we recommend some of these apps below!).
Ultimately it is great to have visibility into ALL of your accounts
And if it’s not clear by now, I do not mean 6,000 IRAs. More like one place to see your IRA, 401k, High Yield Savings Account, checking account, etc. For those interested in doing this sorta thing, we have a few recommendations below (I’ve used all three — none are “sponsored” — and think they’re all pretty good).
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Have a great day!