Field Note #26. On "1 / N"

Source: Victor DeMiguel, Lorenzo Garlappi, Raman Uppal, "Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?" in Rev. of Fin. Studies vol. 22:2 (2009)

  • As explored in Field Note #22, complex decision environments don't necessitate complex solutions.  As it relates to investing (and crypto investing specifically), simple and robust heuristics may not be the "holy grail" answer for position sizing and portfolio construction, but perhaps they should, at a minimum, be the presumptive choice.
  • The 1 / N heuristic simply states that given N investable asset choices, one ought to simply divide one's risk capital equally across the N choices.  DiMiguel et al. found the following:
    (1) No optimization model tested consistently outperformed the 1/N allocation model.
    (2) Large time series of high integrity data is required to properly assess estimation error.
    (3) Simulations also show the need for very long estimation windows.
  • Accord. DeMiguel et al., the estimation windows needed to begin to optimize allocation for a 25 equity portfolio is 3,000 months (250 years), increasing to 6,000 months (500 years) for a 50 asset portfolio.
  • For comparison, as it relates to crypto, BTC genesis block originated Jan. 3, 2009 (~160 months, likely far less) and clearly later before there was sufficient trading liquidity and N > 1 (i.e., several liquid crypto assets, not just BTC) to begin to justify reliable price data worthy of analysis.
  • So, presumption lies with 1/N rule.  "[G]iven the inherent simplicity and the relatively low cost of implementing the 1/N naive-diversification rule, such a strategy should serve as a natural benchmark to assess the performance of more sophisticated asset-allocation rules.  This is an important hurdle both for academic research proposing new asset-allocation models and for 'active' portfolio-management strategies offered by the investment industry." (Id. at 1921)

There is also vital question as to what constitutes N such that the heuristic remains in tact.

I'd love to open a dialogue with those probing the "less sexy" topics in crypto concerning position sizing, attempted portfolio diversification, and allocation across illiquid and liquid crypto markets (crypto is uniquely hybrid in this regard).

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