Similarly, to get the same about of return with much less volatility is just as difficult. It's why people were so willing to put money into Bernie Madoff's ponzi scheme, and why his years of steady returns with very little volatility turned out to be too good to be true.
Lack of correlation can be very valuable even if the returns are mediocre to poor.
I don't remember or understand how it works, but I think I read once about how a fund manager claimed to be able to take more risk with the "long" part of a portfolio because of the uncorrelated "short" part, even though the returns of it were unimpressive.
So, if you have two different assets with the same expected value and same variance, but with zero correlation, then all mixtures of the two will have the same expected returns, but a 50/50 basket of the two assets will have 0.707 (1/sqrt(2)) times the variance of either of the two assets alone.
More generally, for a basket of non-correlated assets, a basket that maximizes expected returns divided by standard deviation of returns will never be 100% one asset. Returns are a linear function of the individual weights, but std. deviation of returns are a non-linear function. (This is true, regardless of statistical distribution of the random variables, as long as std. deviation is well-defined... no assumptions about normal distribution are involved.)
1) Portfolio size, 2) low market correlation, 3) above market performance.
Choose two. You cannot have all three.