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I don't know what I'm talking about, but I would think the smart thing to do would be to sell off enough of your investment during the initial call-up hype to pay for the rest of your investment and have a free stake in a promising player.
I generally take the safe bet and end up selling well before they reach the majors. If their prices spike by roughly x2.5+ what I paid for them I'll sell. If it's a prospect who I really believe can make an impact at the major league level I'll hold and wait until it happens. Prices don't really increase by a significant amount once they reach the majors, however it may be significantly higher than what you originally paid if you began investing on the cheap. Significant spikes generally occur when they breakout at the minor league level, when they get ranked highly on top 100 lists, when they rake immediately after being promoted & when they first make an impact at the major league level (like hitting a bunch of home runs in a short period of time). Very rarely do I hold onto prospects after they complete their first major league season.
It's all about knowing when to buy and knowing when to sell. The longer you hold onto any given prospect the bigger the risk you take but the potential reward also increases (i.e. Trout, Judge, Kershaw)