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Co-moments of truth : is the pricing of higher-order co-moments robust across portfolio sorting methodologies?

Vikenes, Martin; Olstad, Viktor Johannes
Master thesis
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URI
http://hdl.handle.net/11250/2561715
Date
2018
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  • Master Thesis [4207]
Abstract
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.

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