In this dissertation, we investigate the impact of measurement horizon on the empirical appraisal of asset pricing models. This is important because researchers can estimate financial parameters using returns measured over various horizons, including daily, monthly, quarterly, annual or others. Our three essays demonstrate that the estimation of co-skewness and the pricing role of higher-order comoments and common risk factors are sensitive to the length of measurement horizon, respectively.
In our first essay, we examine the theoretical and empirical relationship between measurement horizon and return co-skewness. An asset that displays positive co-skewness in one horizon may have negative co-skewness in another. This phenomenon is particularly evident for small-capitalization and illiquid stocks. We propose a theoretical model to estimate long-horizon co-skewness using daily data. This model emphasizes the role of price adjustment delays in pricing market-wide information among securities. Moreover, in the absence of intertemporal cross-correlation, we show that co-skewness remains horizon dependent, resulting in a “scaling law". Our findings are robust and have strong implications for investors and researchers. For example, a risk-averse investor who prefers high and positive co-skewness should be very careful in choosing his or her horizon in measuring returns.
Our second essay studies the pricing sensitivity of the five Fama and French (2015) factors to variation in the return horizon. Adding profitability and investment factors in pricing assets outperforms the Fama and French (1993) three-factor model over all horizons. However, the new profitability and investment factors are only found to be priced significantly in short horizons. This finding is consistent with evidence in the existing literature where monthly returns are used. The use of monthly returns is thus appropriate for these factors. Fama and French (2015) find that the value factor becomes redundant for describing average returns after adding the two new factors. Interestingly, we find this empirical phenomenon only exists when short-horizon returns are used, while HML remains significant if 2-and 3-year returns are used.
In our third essay, we further investigate the pricing roles of higher-order comoment risk factors across measurement horizons. Employing both portfolio returns based on preranking betas and Fama and MacBeth (1973) cross-sectional regressions, we report consistent evidence. Specifically, in the 3-moment CAPM and 4-moment CAPM frameworks, co-skewness is found to be priced over short horizons, while co-kurtosis is priced over intermediate horizons. Our results are also robust to the use of daily or weekly data and in using different proxies for the market index. Our findings suggest that short-term investors are more likely to be concerned with co-skewness shocks. In contrast, long-run investors can reap the risk premia associated with co-skewness and co-kurtosis and bear fewer of these risks, given these two higher-order comoments are not significantly priced in the long-run perspective.
Overall, our findings highlight the importance of measurement horizon in asset pricing and determining systematic risk premia. Any study based on only one horizon without discussion of the choice of horizon may result in potential ambiguity in pricing and selecting assets.