"when starting with $10,000 or even $100,000 it is next to impossible to make it to a million when one uses diversification."
If you start with $100,000 then you can be almost guaranteed to make $1 million in 21 years if you have AIM manage a well-diversified set of stocks returning 12% per year. However I'd suggest that most AIMers can do better than 12% per year.
Starting with $10,000 will take a longer period of time. However I'd say it would be almost impossible to make it to $1 million (starting from $10,000) by not diversifying. The risks you'd have to take would be quite high, or the timeframe would have to be prohibitively long for the "safer" investments.
Of course, with $10,000, you'd have to start out without much (if any) diversification, because $10,000 doesn't allow you to properly diversify. However as your investment grows, you should then start to diversify.
At the individual stock level AIM manages your risk by moving you in and out of cash. At the portfolio level, properly diversifying manages your risk by reducing (or eliminating) non-market risk.
I don't think we can solely look at returns. Returns have to be looked at within the context of risk too.
Further to my previous post on diversification, I've also been looking at semivariance (a measure of downside risk). The Sharpe Ratio uses the standard deviation in its calculation. However StdDev doesn't differentiate between variances above the mean and variances below it.
Of course in investing, we don't mind huge variances above the expected return (i.e. no investor in his right mind would classify an abnormally high positive return as a risk, however most investors would classify a negative return as a risk).
Semivariance also works when returns aren't normally distributed, whereas StdDev doesn't.
I've been testing Semivariance-based diversification and it appears to provide much better results than StdDev-based diversification.
Interestingly enough, semivariance is a specific case of something called the Lower Partial Moment (LPM). Using general LPM investors can choose how risk-averse they want to be.