If you mean repeated draws from the same urn, then they’d all have the same orientation. If you mean draws from different unrelated urns, then you’d need to add dimensions. It wouldn’t converge the way I think you’re suggesting.
The ratio of risk to return goes down with many independent draws (variances add, but standard deviations don’t). It’s one of the reasons investors are keen to diversify over uncorrelated investments (though again, risk-avoidance is enough to explain that behaviour in Bayesian framework).
If you mean repeated draws from the same urn, then they’d all have the same orientation. If you mean draws from different unrelated urns, then you’d need to add dimensions. It wouldn’t converge the way I think you’re suggesting.
The ratio of risk to return goes down with many independent draws (variances add, but standard deviations don’t). It’s one of the reasons investors are keen to diversify over uncorrelated investments (though again, risk-avoidance is enough to explain that behaviour in Bayesian framework).