I believe the FSA advises private investors that previous performance is no guide to future performance. Although one possible (very strict) interpretation of "no guide" is indeed "uncorrelated", I don't believe that's what they mean. They simply mean there are no guarantees. Moreover, they mean it to apply across the board. For instance, one fund may return +20% 3 years running and then -10% the next year, but might be attributable to the market (or market sector towards which this fund is biased) as a whole, yet our example fund may still be better than its best-equivalent competitors (which might have been returning +15% thrice followed by -20%).
The FSA warns private investors more against the stock market in general than against fund managers.
"Playing" the stockmarket isn't a pure gamble, though, and if what you're implying were true, then the whole idea of managed funds would be inherently daft, and the levying of charges inherently fraudulent, since it doesn't take highly-paid managers to pick shares at random (which according to you would be a strategy which on average (there's that let-out again) does no better nor worse than "actively"managed funds).
Fund managing would be an ideal job for persons addicted to gambling. Just imagine, you get to gamble to your heart's content, with other people putting up all the stake money, so you risk none of your own, these other people take all losses on the chin, with a smile, in return for which they take all the gains (but gamblers do it for the winning, not for the winnings), and best of all you get a guaranteed and generous salary for doing it!
Pull the other one, it can't really be like that.
That's just tautological and hence meaningless. The question is how the average unitised fund compares with the raw average of non-unitised performance in the same sector.