Co-moments of truth : is the pricing of higher-order co-moments robust across portfolio sorting methodologies?
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- Master Thesis 
The discovery rate of pricing factors has increased substantially in the last decades. Whereas the number of factors discovered was about one per annum in the period 1980 – 1991, it has risen to about 18 per year in the last decade (Harvey, Liu, & Zhu, 2016). This thesis investigates whether the proposed factors co-skewness and co-kurtosis are in fact priced in equity markets, and how sensitive the pricing of these factors are to the portfolio sorting methodology. Just as the market beta represents an asset´s co-variance with the market, relative to the variance of the market, the higher-order co-moments, co-skewness and cokurtosis, are analogous to non-linear variations of the market beta. Given the esoteric nature of these concepts, we also include a more ad-hoc measure of skewness, FMAX, which is a proxy for lottery demand. We review the pricing of higher-order co-moments with new methods of portfolio sorting. Intuitively, the choice of test assets should not matter, as a pricing model should price all assets, not just subsets of assets. However, Daniel and Titman (2012) show that sorting on a single factor (HML in their case) effectively eliminates most of the variation independent of that factor. Furthermore, we apply the latest adjustments to the CRSP data supported in the asset pricing literature. More specifically, we use univariate, triple-sorted and industry portfolios in our analysis. To illustrate the effect of the portfolio sorting, we also include the more widely known factors SMB (size), HML (value) and the excess market return in our analysis. We utilise a Fama-MacBeth regression methodology to find the risk premia for the market, SMB, HML, co-skewness, co-kurtosis and FMAX, in the different portfolio settings. Moreover, we follow up on the study by Chung, Johnson and Schill (2006) and check whether co-skewness and co-kurtosis proxy for the SMB and HML factors. Our results indicate that all the aforementioned factors are sensitive to the portfolio sorting methodology. Co-skewness and co-kurtosis does seem to add some explanatory power (adjusted R-squared) to the Fama-French model and CAPM, but do not appear to be priced factors. Moreover, we find limited evidence of the SMB and FMAX factors being priced. The only factor that exhibits some consistency across sorting methodologies is the HML (value) factor.