This is stressed over and again in my MV optimization course...
Suppose we have only 2 securities with high correlation.
Often one of them (AA) has a slightly higher Sharpe ratio than the other. The optimizer would go long a few hundred percent (say 300%) on it, and short 200% on the other (BB). These allocation weights add up to 100%.
If we tweak the historical mean return a bit so AA's Sharpe ratio becomes slightly below BB, then the optimizer would recommend go deep short AA and deep long BB.
This is a common illustration of the over-sensitivity and instability of MV allocation algorithm. In each case, the optimization goal is maximum Sharpe ratio of the portfolio. Why Sharpe? MV
