The Size Premium As a Lottery

38 Pages Posted: 9 Nov 2018 Last revised: 11 Jul 2019

See all articles by Richard McGee

Richard McGee

Smurfit Business School

Jose Olmo

Universidad de Zaragoza; University of Southampton

Date Written: November 6, 2018


We investigate empirically the dependence of the size effect on the top performing stocks in a cross-section of risky assets separated by industry. We propose a test for a lottery-style factor payoff based on a stochastic utility model for an under-diversified investor. The associated conditional logit model is used to rank different investment portfolios based on size and we assess the robustness of the ranking to the inclusion/exclusion of the best performing stocks in the cross-section. Our results show that the size effect has a lottery-style payoff and is spurious for most industries once we remove the single best returning stock in an industry from the sample each month. Analysis in an asset pricing framework shows that standard asset pricing models fail to correctly specify the size premium on risky assets when industry winners are excluded from the construction of the size factor. Our findings have implications for stock picking, investment management and risk factor analysis.

Keywords: size effect, lottery, asset pricing, industry momentum, monotonicity tests, risk factors, ranked sorted portfolios

JEL Classification: G11, G12

Suggested Citation

McGee, Richard and Olmo, Jose, The Size Premium As a Lottery (November 6, 2018). Available at SSRN: or

Richard McGee (Contact Author)

Smurfit Business School ( email )

Blackrock, Co. Dublin

Jose Olmo

Universidad de Zaragoza ( email )

Gran Via, 2
50005 Zaragoza, Zaragoza 50005

University of Southampton ( email )

United Kingdom

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