The Size Premium As a Lottery
38 Pages Posted: 9 Nov 2018 Last revised: 11 Jul 2019
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
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