Related papers: Statistical foundations for assessing the differen…
The Capital Asset Pricing Model (CAPM) is one of the original models in explaining risk-return relationship in the financial market. However, when applying the CAPM into reality, it demonstrates a lot of shortcomings. While improving the…
The CAPM regression is typically interpreted as if the market return contemporaneously \emph{causes} individual returns, motivating beta-neutral portfolios and factor attribution. For realized equity returns, however, this interpretation is…
The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on…
Beta is a widely used quantity in investment analysis. We review the common interpretations that are applied to beta in finance and show that the standard method of estimation - least squares regression - is inconsistent with these…
The simple linear model $$Y_i = \alpha + \beta \, x_i + \epsilon_i \qquad i=1,2, \ldots,N \geq 2$$ is considered, where the $x_i$'s are given constants and $\epsilon_1, \epsilon_2 , \ldots, \epsilon_N$ are iid with continuous distribution…
Gini-type correlation coefficients have become increasingly important in a variety of research areas, including economics, insurance and finance, where modelling with heavy-tailed distributions is of pivotal importance. In such situations,…
We find that the CAPM fails to explain the small firm effect even if its non-parametric form is used which allows time-varying risk and non-linearity in the pricing function. Furthermore, the linearity of the CAPM can be rejected, thus the…
We introduce a new system of stochastic differential equations which models dependence of market beta and unsystematic risk upon size, measured by market capitalization. We fit our model using size deciles data from Kenneth French's data…
This paper presents an empirical analysis of the capital asset pricing model using trading data for the Chinese A-share market from 2000 to 2019. Firstly, the standard CAPM is tested using a Fama-MacBetch regression and although the results…
We demonstrate that machine learning methods provide a powerful framework for modelling conditional asymmetric risk. Using a large cross-section of US stocks and a comprehensive set of firm characteristics, we show that allowing for…
Beta-sorted portfolios -- portfolios comprised of assets with similar covariation to selected risk factors -- are a popular tool in empirical finance to analyze models of (conditional) expected returns. Despite their widespread use, little…
The capital asset pricing model (CAPM) is readily used to capture a linear relationship between the daily returns of an asset and a market index. We extend this model to an intraday high-frequency setting by proposing a functional CAPM…
The risk premia of traded factors are the sum of factor means and a parameter vector we denote by {\phi} which is identified from the cross section regression of alpha of individual securities on the vector of factor loadings. If phi is…
We consider a linear regression model with regression parameter beta =(beta_1, ..., beta_p) and independent and identically N(0, sigma^2)distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified…
We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing…
The principal portfolios of the standard Capital Asset Pricing Model (CAPM) are analyzed and found to have remarkable hedging and leveraging properties. Principal portfolios implement a recasting of any correlated asset set of N risky…
We give an explicit formulaic algorithm and source code for building long-only benchmark portfolios and then using these benchmarks in long-only market outperformance strategies. The benchmarks (or the corresponding betas) do not involve…
Betas are possibly the most frequently applied tool to analyze how securities relate to the market. While in very widespread use, betas only express dynamics derived from second moment statistics. Financial returns data often deviate from…
The paper has 2 main goals: 1. We propose a variant of the CAPM based on coherent risk. 2. In addition to the real-world measure and the risk-neutral measure, we propose the third one: the extreme measure. The introduction of this measure…
Explaining empirically observed wealth and income distributions, featuring power-law tails alongside gamma or log-normal bulk shapes, challenges models that focus on either pairwise competition or individual investment mechanisms. This…