How Accurate Is Mean Variance Optimization and Black-Litterman Model

[bootyman]

The current robo advisors use these 2 models for determining their allocation.  How accurate are they at forecasting long term returns?  Has 'backtesting' been done to see what these portfolio forecasting would have suggested back then and how they ultimately played out?

[pbkmaine]

Lo, these many years ago, I reviewed a MV optimizer for a financial planning publication. To make a long story short, you have to constrain asset classes for it to work. Left unconstrained, you get bizarre asset allocations like a real estate - emerging markets barbell. The human-applied constraints make the optimizers as much of an art as a science.

[MustacheAndaHalf]

The best prediction of future performance I know about is P/E ratio, and that's only a 0.40 correlation in the 10-20 year time frame.  It can't make any prediction about next year, or even 5 years from now.

MVO looks at past returns, and assume they exactly predict the future.  So you'll expect to see more allocation to emerging markets, even as China is struggling, and even as most people investing in Vanguard ETFs are pushing money into Vanguard Emerging Markets ETF.  Emerging markets is an interesting area to invest, but knowing how much should not be left to MVO.  To me, it's because emerging markets have positive expected returns (long term) and differs from US market enough to make a case for diversification.

I think of MVO's main use today is for marketing - to get money in the door at an advisor.  If you want to allocate based on past returns, know they do not predict future returns.  So while the SEC gives one message, fitting your portfolio seems to give the opposite message - that unpredictable future returns can be precisely predicted.

[dmn]

Mean-variance optimization is a nice idea but useless in practice. This study (link) explains the problem very nicely.

Basically, the paper finds that the equal-weight asset allocation rule (for which they quote the Babylonian Talmud) beats mean-variance optimization and all of its 14 modern variants which they studied, unless the modern models are calibrated to more than 250 years of market data. With less than 250 years of data, random statistical deviations will lead to a portfolio which is actually worse than the equal-weight portfolio. Since we do not have 250 years of market data, mean-variance optimization is therefore pointless for practical purposes.

Here is the original quote (abridged) from the paper:

In about the fourth century, Rabbi Issac bar Aha proposed the following rule for asset allocation: “One should always divide his wealth into three parts: a third in land, a third in merchandise, and a third ready to hand.” [source: Babylonian Talmud: Tractate Baba Mezi’a, folio 42a]

After a “brief” lull in the literature on asset allocation, there have been considerable advances starting with the pathbreaking work of Markowitz (1952). [...] Our objective in this paper is to understand the conditions under which mean-variance optimal portfolio models can be expected to perform well even in the presence of estimation risk. [...] Our first contribution is to show that of the 14 models evaluated, none is consistently better than the naive 1/N benchmark [...] Based on parameters calibrated to US stock-market data, we find that the critical length of the estimation window is 3000 months for a portfolio with only 25 assets, and more than 6000 months for a portfolio with 50 assets. The severity of estimation error is startling if we consider that, in practice, these portfolio models are typically estimated using only 60 or 120 months of data.

[Matumba]

Following

[Tyler]

Despite my interest in modern portfolio theory, I've generally never really cared for classical mean variance optimization (or at least how it's usually applied).  The idea of finding the ideal percentage of a set of assets is appealing, but the precision of the results implies a false sense of confidence and too often distracts people from the big picture.  Sure, 76.42% stocks and 23.58% bonds may be the "ideal" mix in the optimizer, but that number will be different based on the economic conditions of your lifetime and the greatest and most lasting improvements are generally not from shuffling a few percent here and there but from exploring diversification through completely different assets.  Layering on Black-Litterman predictions for the future only confuses people even more, and note that Wealthfront (and perhaps others) also introduces their own proprietary "risk tolerance metric" into the calculations. 

I have no doubt that the various robo-advisors are well researched, but make no mistake -- nobody can accurately forecast future returns.  IMHO, the healthier investing mindset is not to be constantly seeking the single best portfolio for the future based on your ever-changing asset preferences, but to identify a truly diverse option that can meet your needs in the safest way possible through a wide variety of economic conditions.  You'll never beat the single "ideal" portfolio in any given timeframe but it won't matter.  You'll sleep well knowing that your investment strategy is robust and well diversified and can handle anything the markets throw at it.  That confidence will help you stay the course, which is something that people obsessing over fractions of a percent rarely achieve.  As a result, you'll likely be a lot happier and wealthier in the long run. 

Importantly, I don't believe you need to pay an adviser (human or robot) to do that.  Try this.  It still can't predict the future, but maybe it can help you think about risk, returns, and diversification a little differently.