Resumen de Essays on multifactor models for stocks’ expected returns in european markets: a block-bootstrap validation proposal
José Manuel Cueto Muñoz
In this thesis we study the efficiency of multifactor models, based on statistical and financial factors, for the pan-European Equity market. The thesis consists of four chapters. Chapter 1 contains an approximation to the problem of study and the classical methodology used to solve it. Chapters 2 and 3 are the core of this thesis, where new factors and procedures to obtain and evaluate multi-factor models are proposed. Chapter 4 contains the main conclusions and some lines for further research.
In Chapter 1 we review the introduction of multifactor models for expected returns and give a brief description of portfolio construction. We start by introducing the CAPM model, the APT model and its natural extension to multifactor models, following the seminal paper by Fama and French (1992). Classical validation methodologies based on Time-series regression and Cross-sectional regression are presented. As an alternative, our first contribution is to drive all inferential results through a block-bootstrap procedure. This methodology is presented in Chapter 1 and applied along Chapters 2 and 3.
Chapter 2 is devoted to the analysis of factor-models based of three new factors, which are built from statistical measurements on stock prices. In particular, the factors under consideration are the coefficient of variation, skewness, and kurtosis. With the coefficient of variation, we aim to capture the stock volatility, while third and fourth order moments can be also strongly related to subsequent returns. The use of these factors in the construction of portfolios is our second contribution. The proposed models are evaluated on data coming from Reuters, corresponding to nearly 2000 EU companies and spanning from Jan-2008 to Feb-2018.
To test the validity of the models, we use classical methods based on Time-series regression, Cross-sectional regression, and the Fama-MacBeth procedure. As a methodological contribution, we propose a non-parametric resampling procedure that accounts for time dependency in order to test the validity of the model and the significance of the parameters involved. We compare our bootstrap-based inferential results with classical proposals (based on F-statistics).
The main findings of Chapter 2 are that the two factors that better complement the market (only factor at the CAPM) are the skewness and the coefficient of variation. This is consistent with previous studies both for the US and the European markets that have found the existence of risk premia for volatility and skewness. With regard to the Time-series regressions, the conclusions drawn from the newly proposed bootstrap inferential techniques are somehow coherent with the ones obtained from classical inference procedures. Indeed, since the used data does not fulfil all the classical distributional requirements, the bootstrap conclusions tend to be less strict with departures from then benchmark described at the null hypotheses. The Cross-section model built from the estimated coefficients presents some deficiency, since the coefficient of variation does not contribute significantly to it, while the market and skewness do. The underlying reason might be some multicollinearity problem. However, the performance of the model seems reasonably good in spite of the period analysed that comprises the European debt crisis.
In Chapter 3 we propose a procedure to obtain and test multifactor models based on statistical and financial factors. In particular, the factors considered are: Market Capitalization and Total Assets (measures of size), Price to Book ratio (measure of cheapness), Return on Assets and Return on Equity (measures of profitability), Momentum, and four statistical measures (mean, standard deviation, kurtosis and skewness). In order to select the factors to be included in the model, as well as the construction of the portfolios, we use a dimension-reduction technique designed to work with several groups of data called Common Principal Components (CPC). This is our third contribution. The underlying idea of this technique is to search for a common set of orthogonal axes that are able to capture the information of the factors under consideration measured along the same time period for 1230 companies. The resulting set of common axes are linear combinations of the factors, which remain equal for all the considered datasets (i.e., companies).
The multifactor model with four CPC-factors is able to explain 90% of the variability of the data. The first CPC-factor is a linear combination of mean and Momentum returns; the second and third CPC-factors are linear combinations of skewness and kurtosis returns and finally, the fourth CPC-factor is the standard deviation of the return. Next, portfolios are built by means of these CPCs using data from Reuters, corresponding to nearly 1250 EU companies, and spanning from October 2009 to October 2019.
As before, a block-bootstrap methodology is developed to assess the validity of the model and the significance of the parameters involved. 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 of Chapter 3 indicate that CAPM cannot explain by itself the return of the portfolios as β for Market is higher for portfolios with high standard deviation (CPC4) and α is higher (and positive) for portfolios with high Momentum and mean (CPC1). For these time-series models, R2 shows values not greater than 0.55, while despite the wide confirmation of the Market factor in the financial literature, it is not significant in our CAPM cross-section regression analysis, which leads us to conclude the need to control for other factors. When we incorporate additional factors, we notice that Momentum and mean (CPC1-factor), despite being correlated with the Market factor, and standard deviation (CPC4-factor) help explaining the cross-section of European stocks during the period considered. Now, Market β stabilize around 0.35, and CPC1 and CPC4 mainly capture the variability that the Market factor could not explain by itself in CAPM. For these models, we observed a substantial improvement in adjusted-R2, with a median value of 0.671. Apart from the calculation of βs and αs, which seem to be quite robust despite the relaxation of the assumptions of the model, GRS p-value is much higher for the bootstrap (which also occurs in CAPM). Finally, in the cross-section regression, two factors present risk premia different from zero, which are Market and the factor based on mean and Momentum (CPC1-factor). These findings lead us to conclude that the multifactor model based on CPC-factors is a good model with regard to the adjusted-R2, able to explain excess returns, although in the analysed time period only one of the CPC-factors presents positive risk premia.
Finally, in Chapter 4 we revisit the main conclusions of this thesis regarding factors, models, and tools. In particular, we summarize the main findings concerning models and give several key messages regarding tools. Some lines for further research are also sketched.
