To address the instability problem, the analyst may constrain the portfolio weights e.g., prohibit short-selling so that all portfolio weights are positive… and Avoid “re-balancing” until significant events occur in the efficient frontier what do these mean?

My understanding… Instability comes from small chances in the inputs for minimum variance calculation (variance, covariance, expected returns) having large changes on the resulting minimum variance frontier and the the efficient frontier. One reason this happens is because if you’re forecasting from the past, different time periods can give different inputs. These small input changes may have large frontier changes, causing optimal portfolio weights to be excessively negative (i.e. unrealistically large amount of short selling) or causing re balancing of the portfolio to occur too frequently. Basically, the small statistically/economically insignificant changes in inputs can cause the frontier to distort, messing up your asset allocation process. To solve for this, we constrain portfolio weights to >0 (positive, so no shorting) and may use a kind of “confidence interval” for changes in the efficient frontier to determine when it has changed enough to warrant a rebalance. Someone please correct if I’m off, but I’m fairly confident about this one.

I think, this is perfect explanation.