No, you will not need to comply with SEC registration or exemption filings if you intend on investing your own money.
If you begin to invest others money on their behalf it changes the relationship and then you become a professional investor/trader. But you and your friend are free to pool your money and make trading decisions about how it is to be invested.
Obviously, there may be facts unknown here that might make a difference. If you believe there is some element to what you are doing that may be problematic you should ask a lawyer to review everything just to be sure.
Most of us here offer a free phone consult.
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It sounds like since both of you will (or should) own proportionate interests as officers of the LLC, you should be in good shape AS LONG as you do not solicit funds from others. One thing you should consider is having some documentation as to who will have authority to trade the funds. Having two people control a brokerage account like this is asking for trouble. Figure out who's doing what before you proceed.
The foregoing is not legal advice nor is it in any manner whatsoever meant to create or impute an attorney/client relationship.