Academic Research Insight: Diagonal Models versus 1/N Diversification

////Academic Research Insight: Diagonal Models versus 1/N Diversification

Academic Research Insight: Diagonal Models versus 1/N Diversification

By | 2017-11-22T07:33:06+00:00 August 7th, 2017|Academic Research Insight|3 Comments
  • Publication: THE FINANCIAL REVIEW,  2016 (version here)

What are the research questions?

In spite of several efforts by researchers to overcome the estimation-risk problem (the use of estimate inputs based on sample information as if they were representative of the true population) which produces the so-called “wacky weights”, DeMiguel, Garlappi and Uppal (2009) present striking evidence that favors a simple 1/N naıve portfolio strategy.

The authors challenge the results by DeMiguel et al. (2009) by studying the following research question:

  1. Are asset allocation models that use “diagonal” elements of the inverse covariance matrix superior to those using the “full” matrix, in addressing the “wacky weights” problem?
  2. Do “diagonal” models outperform the naive 1/N strategy?

What are the Academic Insights?

By using five different empirical datasets of disaggregate portfolio returns, simulated data, out of sample testing and the introduction of transaction costs, the authors find that:

  1. YES- Diagonal strategies naturally avoid short-sale positions and substantially mitigate the so-called “wacky weights” problem
  2. YES-Simple diagonal strategies based solely on estimates of total volatility, generally outperform the 1/N strategy.  The differences in the performance metrics are statistically significant in most cases

Why does it matter?

This study adds to prior literature focused on comparing “full-matrix” strategies to 1/N. In fact, it studies “diagonal only” solutions that consider limited information such as volatility or idiosyncratic volatility. It shows that they avoid short sale positions and limit the “wacky weights” issue. Additionally, they generally outperform 1/N. Asset allocation and its research development is not dead yet!

The Most Important Chart from the Paper

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About the Author:

Elisabetta Basilico, PhD, CFA

Dr. Elisabetta Basilico is a seasoned investment professional with an expertise in “turning academic insights into investment strategies.” Research is her life’s work and by combing her scientific grounding in quantitative investment management with a pragmatic approach to business challenges, she’s helped several institutional investor achieve stable returns from their global wealth portfolios. Her experise spans from asset allocation to active quantitative investment strategies. Holder of the Charter Financial Analyst since 2007 and a PhD from the University of St. Gallen in Switzerland, she has experience in teaching and research at various international universities and co-author of articles published in peer-reviewed journals. She and co-author Tommi Johnsen are currently writing a book on research backed investment ideas. You can find additional information at Academic Insights on Investing.


  1. Hannibal Smith August 7, 2017 at 12:40 pm

    Can we have an example of applying the “diagonal elements of the inverse correlation matrix” in layman English?

    • Elisabetta Basilico, PhD, CFA
      Elisabetta August 7, 2017 at 1:06 pm

      an example of the diagonal elements is “idiosyncratic volatility”. Sections 2 and 3 of the paper are a good reference to better understand these strategies. The main idea is to use “limited” information to reduce estimation risk but at the same to use “some information” compared to the case of 1/N.
      Hope this helps

  2. Noel Dunivant August 9, 2017 at 11:45 am

    Scanning the p-values shows that quite a few are nonsignificant, especially for some datasets (RTT) and some factors (Size, Industry). While the overall answer to Q2 is “Yes,” I’m not sure that wtg by inverse variances would be worth the effort or potential loss of robustness. Very simple is sometimes better than somewhat simple.

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