Markowitz, and his optimization mathematics, are the undisputed king on wall street for finding an "efficient" portfolio given a few asset classes, their standard deviation, average return, and cross correlation. But it's not perfect... These optimization techniques fail in a number of ways:
- It assumes correlations are fixed - they're not.
- It doesn't paint the true picture of what the investor feels. Average returns are far too forgiving to losses, and standard deviation is not a perfect metric at defining risk. The average investor won't care about volatility in positive returns. They only care about how often they loss, and how bad did they lose. The Sortino ratio does a better job at defining risk using downside risk (RMS of losses). Most people, including Quantopian, incorrectly just compute the standard deviation of losses to be the denominator of the ratio - that is incorrect.
I wanted to use more performance/risk metrics than just average return and standard deviation of losses. So I used the following:
- Average return
- Annualized return
- Average 10 year return
- Worst 15 year return
- Standard deviation of returns
- Downside risk (RMS of losses, set gains to 0 - this weights frequency of losses and severity)
- Standard deviation of 10 year returns
- Maximum drawdown
But with all these metrics, I can't do a simple optimization routine. Instead I generated a few hundred thousand portfolio combinations and did a Z score weighting on each metric to find portfolio combinations that are efficient with all metrics. Then I simulated what actually would have happened, assuming annual rebalancing. This leads you down a path to alternative asset classes (like boring consumer staples sector, mid-cap value, countries etc.).
The data used, along with other asset classes, is available to download here. Most of it is available from the bogleheads forum, Simba's backtest spreadsheet. I was turned on to the countries after looking through the Credit Suisse Global Investment Returns Yearbook. I know making a country tilt is way out there (even though we're happy to do it here in the States, to Japan, to China etc.) but if you think about the resources that Sweden and South Africa have, geography, diversification benefit, etc. it starts to become an interesting proposition to make a small tilt there.
I've done some more in depth analysis on the asset classes on a blog I'm starting: engineeredportfolio. More posts are to follow with additional detail.