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Equal Weighting vs. All Feasible Long-only Mean-variance Optimals

| | Posted in: Strategic Allocation

Is equal weighting (1/n) of portfolio components a good choice? In their November 2014 paper entitled “Is 1/n Really Better Than Optimal Mean-Variance Portfolio?”, Woo Chang Kim, Yongjae Lee and William Ziemba assess 1/n weighting by comparing its performance to the performances of all feasible mean-variance optimal portfolios for different asset universes. By “all feasible,” they mean many long-only mean-variance optimal portfolios generated by randomly picking the estimated future return-to-variance ratios for assets within a universe. They use Sharpe ratio to measure portfolio performance. They consider 10 asset universes: 10 U.S. equity sectors; 10 U.S. equity industries; eight country equity indexes; three U.S. equity factor portfolios; six U.S. equity styles; 25 U.S. equity styles; 100 U.S. equity styles; 250 large-capitalization U.S. stocks; 250 medium-capitalization U.S. stocks; and, 250 small-capitalization U.S. stocks.They apply mostly annual rebalancing but also consider semiannual and quarterly rebalancing for the three stock universes. They also test 1/n versus capitalization weighting for seven of the 10 universes. Using returns for specified assets at the tested rebalancing frequencies with sample start dates as early as July 1963 and end dates as late as June 2014, they find that:

  • When ranked against the randomly specified long-only mean-variance optimal portfolios, 1/n portfolios:
    • Rank above the middle for three of 10 asset universes.
    • Rank in the middle for seven of 10 asset universes.
  • Within available test periods, inception-to-date rankings of 1/n portfolios relative to randomly specified long-only mean-variance optimal portfolios fluctuate considerably.
  • 1/n portfolios perform about the same as corresponding capitalization-weighted portfolios.

In summary, evidence indicates that equal weighting of portfolio components mostly performs about the same as mean-variance optimal portfolios in the absence of portfolio manager ability to predict asset return statistics.

In other words, asset managers who can materially predict asset return statistics should on average beat 1/n.

Cautions regarding findings include:

  • As noted in the paper, results depend on the asset universes and sample periods used.
  • Reported results are gross, not net. Differences in portfolio rebalancing costs may be material, but the mostly annual rebalancing frequency mitigates this concern.
  • While the authors exclude shorting of assets, it is not clear whether they allow leveraged positions. Also, while precluding shorting implies a lower limit of zero for the expected asset return-to-variance ratio, it is not clear what upper limit they allow.
  • Sharpe ratio may not be the definitive performance metric for some investors.
  • The study does not address non-equity asset classes.
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