Abstract
In this paper, we propose a procedure to obtain and test multifactor models based on statistical and financial factors. A major issue in the factor literature is to select the factors included in the model, as well as the construction of the portfolios. We deal with this matter using a dimensionality reduction technique designed to work with several groups of data called Common Principal Components. A block-bootstrap methodology is developed to assess the validity of the model and the significance of the parameters involved. Data come from Reuters, correspond to nearly 1250 EU companies, and span from October 2009 to October 2019. We also compare our bootstrap-based inferential results with those obtained via classical testing proposals. Methods under assessment are time-series regression and cross-sectional regression. The main findings indicate that the multifactor model proposed improves the Capital Asset Pricing Model with regard to the adjusted-R2 in the time-series regressions. Cross-section regression results reveal that Market and a factor related to Momentum and mean of stocks’ returns have positive risk premia for the analyzed period. Finally, we also observe that tests based on block-bootstrap statistics are more conservative with the null than classical procedures.
Highlights
IntroductionFinance theory has relied upon the risk-return relationship, i.e., the higher the risk (usually measured through the standard deviation of returns), the higher the return
Finance theory has relied upon the risk-return relationship, i.e., the higher the risk, the higher the return
The objectives of this paper are: (1) to propose a multifactor model based on statistical and financial factors using Common Principal Components (CPC) to reduce its number of dimensions, (2) to develop nonparametric resampling procedures that account for time dependency in order to test model validity and involved parameter significance, and (3) to compare the results obtained via bootstrap-based inferential procedures with those of the classical proposals
Summary
Finance theory has relied upon the risk-return relationship, i.e., the higher the risk (usually measured through the standard deviation of returns), the higher the return This concept is at the core of the Capital Asset Pricing Model (CAPM) (see Sharpe [1], Lintner [2], Mossin [3]), where the expected profitability of the i-th stock, E(Ri), is represented as follows: E(Ri) = r f + βi(E(rm) − r f ), where r f is the risk-free rate, E(rm) − r f is the Market Risk Premium, and βi the sensitivity of expected excess asset’s return associated with the i-th asset. Academia has pointed to the existence of several other factors that, beyond volatility, affect the returns of assets (basically, investors obtain a reward for bearing risks different from volatility) Some of these factors, relying on financial measures, are already considered as classical and have been tested in different Markets; see Fama and French [6].
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