I've been a researching minimum variance portfolios (from this link) and find that by building MVPs adding constraints on portfolio weights and a few other tweaks to the methods outlined I get generally positive returns over a six-month to one year time scale.
I am looking to build some portfolios that are low risk, but have good long term (yearly) expected returns. MVP (as in minimum variance NOT mean variance) seems promising from backtests but I don't have a good intuition for why this works.
I understand the optimization procedure is primarily looking to optimize for reducing variance, and I see that this works in the backtest (very low standard deviation of returns).
What I don't have an intuitive feel for is why optimizing variance alone (with no regards to optimizing returns, i.e. no mean in the optimization as in traditional mean-variance optimization) gives generally positive returns. Any explanations?