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In this paper, we studied the influence of book value financial leverage in the pricing of euro area equities from 1989 to 2019. To do so, we used the Fama and French three-factor model (1993) as a framework, adding our leverage factor to the three original ones. We also tried to answer these questions: Are the expected common stock returns negatively related to the financial leverage? Does the Fama and French three-factor model already capture financial risk in its factors? Is the importance of financial leverage dependent on the business cycle as a risk factor? We found that a factor model including financial leverage is a better proxy for common risk factors in returns than the original Fama and French three-factor model. However, we have evidence that the value factor (HML) and the financial leverage factor (LMU) have elements in common in their stock explanatory power. Despite these similarities, neither of them should be discarded to preserve the performance of our model. We also observed that expected common stock returns are negatively related to financial leverage, which supports George and Hwang (2010) claim that when we account for market frictions in capital structure optimisations models, firms with high distress costs select low leverage and have the greatest exposure to systematic risk. This effect dominates the strengthening effect of financial leverage on equity risk. Moreover, we tested the robustness of our model over time. We estimated our four-factor model using rolling windows. We found that, although the performance of the model changes over time, it is always a good proxy for common risk factors in returns. Nevertheless, we did not find any statistically significant relationship between the performance of the model and any variable related to the economic situation.

Fama --- French --- leverage --- three-factor model --- asset pricing --- equity --- regression --- eurozone --- debt-to-equity --- multi-factor model --- GRS --- Sciences économiques & de gestion > Finance

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Mathematical finance plays a vital role in many fields within finance and provides the theories and tools that have been widely used in all areas of finance. Knowledge of mathematics, probability, and statistics is essential to develop finance theories and test their validity through the analysis of empirical, real-world data. For example, mathematics, probability, and statistics could help to develop pricing models for financial assets such as equities, bonds, currencies, and derivative securities.

Coins, banknotes, medals, seals (numismatics) --- cluster analysis --- equity index networks --- machine learning --- copulas --- dependence structures --- quotient of random variables --- density functions --- distribution functions --- multi-factor model --- risk factors --- OLS and ridge regression model --- python --- chi-square test --- quantile --- VaR --- quadrangle --- CVaR --- conditional value-at-risk --- expected shortfall --- ES --- superquantile --- deviation --- risk --- error --- regret --- minimization --- CVaR estimation --- regression --- linear regression --- linear programming --- portfolio safeguard --- PSG --- equity option pricing --- factor models --- stochastic volatility --- jumps --- mathematics --- probability --- statistics --- finance --- applications --- investment home bias (IHB) --- bivariate first-degree stochastic dominance (BFSD) --- keeping up with the Joneses (KUJ) --- correlation loving (CL) --- return spillover --- volatility spillover --- optimal weights --- hedge ratios --- US financial crisis --- Chinese stock market crash --- stock price prediction --- auto-regressive integrated moving average --- artificial neural network --- stochastic process-geometric Brownian motion --- financial models --- firm performance --- causality tests --- leverage --- long-term debt --- capital structure --- shock spillover

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Mathematical finance plays a vital role in many fields within finance and provides the theories and tools that have been widely used in all areas of finance. Knowledge of mathematics, probability, and statistics is essential to develop finance theories and test their validity through the analysis of empirical, real-world data. For example, mathematics, probability, and statistics could help to develop pricing models for financial assets such as equities, bonds, currencies, and derivative securities.

cluster analysis --- equity index networks --- machine learning --- copulas --- dependence structures --- quotient of random variables --- density functions --- distribution functions --- multi-factor model --- risk factors --- OLS and ridge regression model --- python --- chi-square test --- quantile --- VaR --- quadrangle --- CVaR --- conditional value-at-risk --- expected shortfall --- ES --- superquantile --- deviation --- risk --- error --- regret --- minimization --- CVaR estimation --- regression --- linear regression --- linear programming --- portfolio safeguard --- PSG --- equity option pricing --- factor models --- stochastic volatility --- jumps --- mathematics --- probability --- statistics --- finance --- applications --- investment home bias (IHB) --- bivariate first-degree stochastic dominance (BFSD) --- keeping up with the Joneses (KUJ) --- correlation loving (CL) --- return spillover --- volatility spillover --- optimal weights --- hedge ratios --- US financial crisis --- Chinese stock market crash --- stock price prediction --- auto-regressive integrated moving average --- artificial neural network --- stochastic process-geometric Brownian motion --- financial models --- firm performance --- causality tests --- leverage --- long-term debt --- capital structure --- shock spillover