Assuming you and your family always get along and everyone is happy with the situation...
Should you become ill, die, or go on government benefits for some catastrophe, the government will look at all those funds as YOURS, and now your wonderful family is hurt by the estate tax and/or expectations of how much of the bill you handle before support kicks in.
Additionally, should you ever reach a point where you are married and then facing divorce (even if no fault of your own), all that investment is now up for grabs in equitable distribution. So your family's entire investment fund is at risk.