Fama–MacBeth Regression
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Fama–MacBeth Regression
The Fama–MacBeth regression is a method used to estimate parameters for asset pricing models such as the capital asset pricing model (CAPM). The method estimates the betas and risk premia for any risk factors that are expected to determine asset prices. The method works with multiple assets across time (panel data). The parameters are estimated in two steps: # First regress each of ''n'' asset returns against ''m'' proposed risk factors to determine each asset's beta exposures.\begin R_ = \alpha_1 + \beta_F_ + \beta_F_ + \cdots + \beta_F_ + \epsilon_ \\ R_ = \alpha_2 + \beta_F_ + \beta_F_ + \cdots + \beta_F_ + \epsilon_ \\ \vdots \\ R_ = \alpha_ + \beta_F_ + \beta_F_ + \cdots + \beta_F_ + \epsilon_\end #Then regress all asset returns for each of ''T'' time periods against the previously estimated betas to determine the risk premium for each factor.\begin R_ = \gamma_ + \gamma_\hat_ + \gamma_\hat_ + \cdots + \gamma_\hat_ + \epsilon_ \\ R_ = \gamma_ + \gamma_\hat_ + \gamma_\hat_ + ...
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Capital Asset Pricing Model
In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. CAPM assumes a particular form of utility functions (in which only first and second moments matter, that is risk is measured by variance, for example a quadratic utility) or alternatively asset returns whose probability distributions are completely described by the first two moments (for example, the normal distribution) and zero transaction costs (necessary for diversification to get rid of all idiosyncratic risk). Under these conditions, CAPM shows that the cos ...
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Beta Coefficient
In finance, the beta (β or market beta or beta coefficient) is a measure of how an individual asset moves (on average) when the overall stock market increases or decreases. Thus, beta is a useful measure of the contribution of an individual asset to the risk of the market portfolio when it is added in small quantity. Thus, beta is referred to as an asset's non-diversifiable risk, its systematic risk, market risk, or hedge ratio. Beta is ''not'' a measure of idiosyncratic risk. Interpretation of values By definition, the value-weighted average of all market-betas of all investable assets with respect to the value-weighted market index is 1. If an asset has a beta above (below) 1, it indicates that its return moves more (less) than 1-to-1 with the return of the market-portfolio, on average. In practice, few stocks have negative betas (tending to go up when the market goes down). Most stocks have betas between 0 and 3. Treasury bills (like most fixed income instruments) ...
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Risk Premium
A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky return less the risk-free return, as demonstrated by the formula below. Risk \ premium = E(r) - r_f Where E(r) is the risky expected rate of return and r_f is the risk-free return. The inputs for each of these variables and the ultimate interpretation of the risk premium value differs depending on the application as explained in the following sections. Regardless of the application, the market premium can be volatile as both comprising variables can be impacted independent of each other by both cyclical and abrupt changes. This means that the market premium is dynamic in nature and ever-changing. Additionally, a general observation regardless of application is that the risk premium is larger during economic downturns and during periods of increased ...
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Risk Factor
In epidemiology, a risk factor or determinant is a variable associated with an increased risk of disease or infection. Due to a lack of harmonization across disciplines, determinant, in its more widely accepted scientific meaning, is often used as a synonym. The main difference lies in the realm of practice: medicine (clinical practice) versus public health. As an example from clinical practice, low ingestion of dietary sources of vitamin C is a known risk factor for developing scurvy. Specific to public health policy, a determinant is a health risk that is general, abstract, related to inequalities, and difficult for an individual to control. For example, poverty is known to be a determinant of an individual's standard of health. Correlation vs causation Risk factors or determinants are correlational and not necessarily causal, because correlation does not prove causation. For example, being young cannot be said to cause measles, but young people have a higher rate ...
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Panel Data
In statistics and econometrics, panel data and longitudinal data are both multi-dimensional data involving measurements over time. Panel data is a subset of longitudinal data where observations are for the same subjects each time. Time series and cross-sectional data can be thought of as special cases of panel data that are in one dimension only (one panel member or individual for the former, one time point for the latter). A study that uses panel data is called a longitudinal study or panel study. Example In the multiple response permutation procedure (MRPP) example above, two datasets with a panel structure are shown and the objective is to test whether there's a significant difference between people in the sample data. Individual characteristics (income, age, sex) are collected for different persons and different years. In the first dataset, two persons (1, 2) are observed every year for three years (2016, 2017, 2018). In the second dataset, three persons (1, 2, 3) are obse ...
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Eugene F
Eugene may refer to: People and fictional characters * Eugene (given name), including a list of people and fictional characters with the given name * Eugene (actress) (born 1981), Kim Yoo-jin, South Korean actress and former member of the singing group S.E.S. * Eugene (wrestler), professional wrestler Nick Dinsmore * Franklin Eugene (producer), American film producer * Gene Eugene, stage name of Canadian born actor, record producer, engineer, composer and musician Gene Andrusco (1961–2000) * Wendell Eugene (1923–2017), American jazz musician Places Canada * Mount Eugene, in Nunavut; the highest mountain of the United States Range on Ellesmere Island United States * Eugene, Oregon, a city ** Eugene, OR Metropolitan Statistical Area ** Eugene (Amtrak station) * Eugene Apartments, NRHP-listed apartment complex in Portland, Oregon * Eugene, Indiana, an unincorporated town * Eugene, Missouri, an unincorporated town Business * Eugene Green Energy Standard, an int ...
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Journal Of Political Economy
The ''Journal of Political Economy'' is a monthly peer-reviewed academic journal published by the University of Chicago Press. Established by James Laurence Laughlin in 1892, it covers both theoretical and empirical economics. In the past, the journal published quarterly from its introduction through 1905, ten issues per volume from 1906 through 1921, and bimonthly from 1922 through 2019. The editor-in-chief is Magne Mogstad ( University of Chicago). It is considered one of the top five journals in economics. Abstracting and indexing The journal is abstracted and indexed in EBSCO, ProQuest, EconLit , Research Papers in Economics, Current Contents/Social & Behavioral Sciences, and the Social Sciences Citation Index. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 9.103, ranking it 4/376 journals in the category "Economics". The journal is department-owned University of Chicago journal. Notable papers Among the most influential pa ...
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Standard Error
The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM). The sampling distribution of a mean is generated by repeated sampling from the same population and recording of the sample means obtained. This forms a distribution of different means, and this distribution has its own mean and variance. Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean. Therefore, the relationship between the standard error of the mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size. ...
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Review Of Financial Studies
''The Review of Financial Studies'' is a peer-reviewed academic journal covering the field of finance. It is published by Oxford University Press on behalf of the Society for Financial Studies. It was established following discussions at the 1986 Western Finance Association meetings, and the first issue was published in 1988. The current editor-in-chief is Itay Goldstein. It is considered to be one of the premier finance journals. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 5.814, ranking it 5/110 in the category "BUSINESS, FINANCE". Editors The following persons are or have been editors-in-chief: * Itay Goldstein (University of Pennsylvania, 2018–present) *Andrew Karolyi (Cornell University, 2014–2018) * David Hirshleifer (UC Irvine, 2011–2014) * Matthew Spiegel (Yale University, 2005–2011) * Maureen O'Hara (Cornell University, 2000–2005) * Ravi Jagannathan (Northwestern University, 1997–2000) * Franklin Allen (Universi ...
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Capital Asset Pricing Model
In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. CAPM assumes a particular form of utility functions (in which only first and second moments matter, that is risk is measured by variance, for example a quadratic utility) or alternatively asset returns whose probability distributions are completely described by the first two moments (for example, the normal distribution) and zero transaction costs (necessary for diversification to get rid of all idiosyncratic risk). Under these conditions, CAPM shows that the cos ...
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Ordinary Least Squares
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable. Geometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression surface—the smaller the differences, the better the model fits the data. The resulting estimator can be expressed by a simple formula, especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation. The OLS estimator is c ...
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Stata
Stata (, , alternatively , occasionally stylized as STATA) is a general-purpose statistical software package developed by StataCorp for data manipulation, visualization, statistics, and automated reporting. It is used by researchers in many fields, including biomedicine, epidemiology, sociology and science. Stata was initially developed by Computing Resource Center in California and the first version was released in 1985. In 1993, the company moved to College Station, TX and was renamed Stata Corporation, now known as StataCorp. A major release in 2003 included a new graphics system and dialog boxes for all commands. Since then, a new version has been released once every two years. The current version is Stata 17, released in April 2021. Technical overview and terminology User interface From its creation, Stata has always employed an integrated command-line interface. Starting with version 8.0, Stata has included a graphical user interface based on Qt framework which us ...
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