The Beta Maths

5 Pages Posted: 13 Dec 2016 Last revised: 22 Jan 2022

Date Written: December 10, 2016


The two Nobel Prizes awarded in Economics in 1990 and 2013 define the boundaries of Modern Portfolio Theory (MPT). Size is the pillar for both the models. The 1990 winners assumed market to be driven by Market Capitalization (MCAP) size, while the 2013 winner explained that factors like ‘Small Size’ can explain portfolio performance better than ‘Big Size’. This conflict between the two ideas has bifurcated the industry into benchmark investing (MCAP) and everything else not MCAP (Smart Beta). The fact that benchmark investing and smart beta is expected to be 50% of the USD 100 trillion investment management industry in 2020 makes it imperative to seek a coherent argument and a conflict resolution.

This paper explains how a relative ranking on size could reframe the argument between big and small size as a debate around why the RGR (Rich Get Richer) and the PGR (Poor Get Richer), which are expressions of the statistical law of ‘Mean Reversion’ and its failure. The paper explains how benchmark investing and smart beta are not conflicting ideas and how a set of portfolio weights which allocate relatively shorter time (t) to big size companies and relatively longer time (T) to small size companies could have higher probability of offering more optimal set of portfolios among all the possible combinations involving different time periods and different sizes. The architecture could bring Finance closer to Physics and illustrate how assumptions of MPT may be irrelevant today.

Keywords: Market Capitalization, Size Factor, Modern Portfolio Theory, Beta, Smart Beta

Suggested Citation

Pal, Mukul, The Beta Maths (December 10, 2016). Available at SSRN: or

Mukul Pal (Contact Author)

AlphaBlock ( email )

Toronto, Ontario M8Z 2H6


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