You are assuming your conclusion, once again begging the question on this claim above re "we need relatively little data". You also contradict your own statements below. If 10-20 years is not enough for statistical knowledge on returns, it is also not enough for statistical knowledge of correlations. Ask LTCM.
I'm not assuming anything. This is just maths (and it's not my own maths, it's standard statistics). The variance of parameter estimates for correlation and volatility are much lower than they are for means and Sharpe Ratios. In plain english we need less data to be more confident about a correlation estimate than for a Sharpe Ratio estimate. You might find that surprising and inconsistent, many people do, but it is a fact.
That doesn't mean that correlations won't change over time, or become temporarily unhinged as in LTCM type crisis, or indeed in 2008 when the returns of CTA's like Cantab or Winton with equities went from mild positive correlation to massively negative correlation (and a good thing too).
All it means is that we have a better idea of what past correlations were historically than we do about past Sharpe ratios. It also means we have a better chance of forecasting future correlations than we do of forecasting future Sharpe Ratios.
GAT
