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Think MPT Doesn’t Work? Clearing Up Some Misconceptions

June 25, 2015

A note to readers: I have posted some interesting material the last few weeks on Blue Sky Asset Management (BSAM) that may be of interest.  This includes our monthly commentaries on current market observations and also a  whitepaper series on Dynamic Asset Allocation that is definitely worth reading. I also recently posted a new blog article on the site as well: Defense is the Best Offense   Readers should keep  an eye out on the website as we plan to roll out some “geekier” research papers and interesting  current market analytics in the future.  

I have spent  many years toiling with creating different asset allocation methodologies including the application of traditional and non-traditional portfolio optimization. Given the recent flare of articles on this topic in the blogosphere, I felt it was worthwhile to share my two cents. Applying optimization to a tactical approach is a topic that readers may already be familiar with, I recently posted an article on the subject on my LinkedIn :  Think MPT Doesn’t Work? You Are Probably Using it the Wrong Way .  Wouter Keller of Flex Capital, Adam Butler of BPG,  and Ilya Kipnis of Quantstratrader wrote a great paper that was referenced in the post that readers are encouraged to take a look at; Momentum and Markowitz; A Golden Combination. They show that using the MPT algorithm in a dynamic context with shorter-term data helps to capture the momentum effect as well as producing diversified portfolios with good risk-adjusted returns. This paper is in many ways a very important contribution to a stream of research and practitioner debate that is at times imbalanced and one-sided— and without good logical reasons. MPT happens to be widely and roundly criticized in the industry for perceived algorithm-specific flaws and research that shows poor out-of-sample performance.  Of course, this is primarily because it is used the wrong way–at intermediate or longer time horizons that are ill-suited to the approach. It is also important to keep in mind that industry heavyweights such as AQR and Goldman Sachs have used variants of a dynamic MPT approach to build sophisticated portfolios that have performed very well for decades.

Some other related articles on the same topic that are quite interesting include The Universal Investment Strategy by Frank Grossman of Logical Invest, and Momentum and Diversification by Andrew Gogerty of Newfound Research – 3rd Place winner of the prestigious NAAIM Wagner Award. The methodology in these two articles for optimization is nearly identical. They both find maximum Sharpe  portfolios by using brute force to combine equity curves with a constrained set of choices into a portfolio instead of using MPT. It is important to understand that both MPT and these approaches are essentially interchangeable for the most part (MPT finds the brute force optimal solution mathematically). Grossman uses a variant on the objective function with a risk-aversion parameter. Newfound introduces the twist of allowing for different rebalancing windows in the lookback window which is more similar to a dynamic programming approach. In both cases, I wanted to clarify to readers that finding the sharpe ratio by combining equity curves (assuming daily rebalance) is identical to using the calculated correlation/volatility and return to compute sharpe optimal portfolios- so there is no escaping “estimation error” it is just implicit as opposed to explicit.

Wes Gray of Alpha Architect is always a good source of research and demonstrates the more traditional use of MPT (not the tactical) in asset allocation in his post; Beware of Geeks Bearing Formulas. Unfortunately, this post is not comparing apples to apples since the MPT lookback parameters are longer-term than the simple tactical benchmarks being compared. As a consequence this post happens to be biased against the use of MPT in a dynamic format which is common within the industry and in my opinion a bit unfair since there is more good to work with than bad.  It just happens to be the case that using MPT in a tactical format comes with a set of unique complexities that do not plague simpler methods- these include higher turnover, concentrated portfolios and greater sensitivity to estimation error. The higher level of estimation error occurs for several reasons. One is greater dimensionality since there are many more inputs to estimate. The other is that in MPT the magnitude of returns dictate weights as well as the ranks of returns—in contrast a basic momentum approach only pays attention to rank. This puts greater pressure on return estimation in MPT versus  a simple momentum approach. Another issue is the integration of noisy/random correlations which interfere with errors in return estimates. Adding correlations is important for stressing diversification but only to the extent that they are not highly error-prone.  Using MPT for allocating across investment strategies rather than asset allocation is even more challenging since strategies have far more complex inputs to estimate, and some inputs cannot be estimated quantitatively.  On the positive side,  using MPT in a tactical approach carries much less room for data mining bias than building a simple tactical system using rules. This is especially true if the system builder is free to vary multiple parameters and may also choose their investment universe through repeated testing. Using one algorithm that is mathematically compact like MPT with one lookback parameter is far less subject to these insidious data mining problems.

I think the most important takeaway from the debate in the industry is that many algorithms, trading methods, or indicators are often unfairly discarded through improper or unsuitable analysis (or use) rather than for true deficiencies. The skilled cook can take a few mediocre or exotic ingredients and create a masterpiece while less knowledgeable cooks can find the same box of ingredients to be wholly deficient for creating a suitable meal. There are plenty of examples of people that have been successful even with the ultimate black-box machine-learning approach–it is a hazardous path much like climbing Mount Everest but apparently there are some good climbers out there (see Renaissance Technologies). Of course in good quantitative system design as in cooking, using great simple ingredients makes it easy to create a great meal without a lot of manipulation or effort. Pushing the edges by exploring the more exotic applications creates greater risk of  failure but also greater opportunity- and that is a risk worth taking in highly competitive markets. You just need to have a good understanding of where to draw the line. To that extent, I  guess the decision to incorporate MPT within tactical asset allocation is ironically a matter concerning utility curves……..

 

7 Comments leave one →
  1. JAK78 permalink
    June 25, 2015 8:18 pm

    Don’t the errors of MPT get magnified because they are multiplicative with respect to each other? Also, why would you want other assets in your portfolio when the trend in stocks is positive, since stocks have nearly twice the long run return of bonds and you can use trend following to reduce the risk of stocks?

    • June 25, 2015 9:36 pm

      That’s not historically true, actually. For the 21st century, bonds have kept up with stocks due to the two crashes. In the 19th century, this was also the case. The 20th century may very well be an anomaly in and of itself.

      • Jak78 permalink
        June 26, 2015 1:57 pm

        Ilya- In his book, Stocks for the Long Run, Jeremy Siegel shows the annual real return of stocks from 1802 through 2012 (19th, 20th and 21st centuries) as 6.6%, while the annual real return from bonds was 3.6%

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