So to pick up where we left off: how can one easily and reliably minimize volatility? The first chart above shows what happens when you weight the cities according to what would have produced the lowest volatility in the first 10 years and then watch what happens in the subsequent 10 years.
Answer: in the out-of-sample test, the formerly low volatility portfolio unexpectedly becomes even more volatile than the equal weighted portfolio.
Explanation: the portfolio weights were chosen via Excel Solver to minimize volatility during the first 10 years. This approach implicitly accounts for not only the volatility of each city, but the correlations amongst the cities. Sounds great, right, more is better? Not when the correlations are random. What happens, is the cities that were formerly non-correlated by chance are subsequently correlated in the out-of-sample test. Classic case of fitting the data to a theory or being fooled by randomness.
Just as aside, the weighted average volatility of the constituent cities selected by Solver was 4.4% during the first 10 years. This weighted average volatility was even higher than the 4.2% volatility of the equal weighted portfolio of cities, but nonetheless the selected portfolio exhibited an actual overall volatility of only 1.0% during the first 10 years because of how the movements of certain cities just so happened to offset the movements of other cities. When I subsequently conduct the out-of-sample test, the "just so happens" didn't happen anymore. Next I'll show a simple way to overcome the problem of persnickety correlations.
