Heuristics and Robustness in Asset Allocation: The 1/N Rule, “Hard” Constraints and Fractional Kelly Strategies
Introduction (Via Macroresilience )
Harry Markowitz received the Nobel Prize in Economics in 1990 for his work on mean-variance optimisation that provided the foundations for Modern Portfolio Theory (MPT). Yet as Gerd Gigerenzer notes, when it came to investing his own money, Markowitz relied on a simple heuristic, the “1/N Rule” which simply allocates equally across all N funds under consideration. At first glance, this may seem to be an incredibly irrational strategy. Yet, there is compelling empirical evidence backing even such a simple heuristic as the 1/N Rule. Gigerenzer points to a study conducted by DeMiguel, Garlappi and Uppal (DMU) which after comparing many asset-allocation strategies including Markowitz mean-variance optimisation concludes that “there is no single model that consistently delivers a Sharpe ratio or a CEQ return that is higher than that of the 1/ N portfolio, which also has a very low turnover.”
Before exploring exactly what the DMU study and Gigerenzer’s work implies, it is worth emphasizing what it does not imply. First, as both DMU and Gigerenzer stress, the purpose of this post is not to argue for the superiority of the 1/N Rule over all other asset-allocation strategies. The aim is just to illustrate how simple heuristics can outperform apparently complex optimisation strategies under certain circumstances. Second, the 1/N Rule does not apply when allocating across securities with excessive idiosyncratic risk e.g. single stocks. In the DMU study for example, the N assets are equity portfolios constructed on the basis of industry classification, countries, firm characteristics etc.