Statistical Analysis in Finance Class

A statistical model that pools data across different groups (e.g., firms, countries) to estimate a single set of coefficients. This assumes the underlying relationship is the same across groups.

A model that accounts for differences across groups by including dummy variables representing each group. This assumes the relationship varies by group.

A statistical model that accounts for unobserved heterogeneity across groups, assuming it's random. It is a combination of fixed effects and the pooled OLS estimations.

Adjusting the standard errors of regression coefficients to account for correlations in the data, such as clustered or time-series data.

Using panel data to analyze asset returns. This approach involves estimating the coefficients of a regression model that includes cross-sectional variation.

A procedure for estimating asset pricing models using panel data. It involves calculating time-series regressions for each asset and then averaging the results.

A model that explains asset returns based on factors such as size (SMB) and value (HML), using time-series and cross-sectional regression analysis.

A statistical model where the errors are assumed to be normally distributed. This allows for hypothesis testing and deriving confidence intervals for coefficients.

A statistical measure used to estimate the standard deviation of abnormal returns in an event study.

A test statistic used to evaluate the significance of the average abnormal return (AAR) in an event study. It follows a t-distribution with N-1 degrees of freedom.

A statistical concept that states that for a large enough sample size, the distribution of the sample mean will approximate a normal distribution. This even holds true if the original data is not normally distributed.

Instead of relying on the t-distribution, the standard normal distribution can be used to assess the significance of the average abnormal return in event studies if the sample size is large enough.

The chosen level of significance for a statistical test, which determines the probability of falsely rejecting the null hypothesis.

The values that define the boundaries of the rejection region in a statistical test. These values are determined by the chosen significance level.

The cumulative abnormal return (CAR) measures the total abnormal performance of event firms over an extended period, typically encompassing several event periods.

A situation where multiple events occur within the same calendar period, leading to correlation between their abnormal returns, invalidating the t-test.

The degree to which abnormal returns from different events are related. Positive correlation means returns move in the same direction.

A technique used to adjust the standard error of average abnormal returns in cases of cross-sectional dependence, addressing the underestimation caused by event clustering.

A statistical test used to compare the means of two groups, but it is not valid when there is significant cross-sectional correlation, such as in event clustering cases.

The average return of a portfolio formed by combining the returns of events occurring on the same calendar day, used as an alternative to the t-test when dealing with event clustering.

The difference in return between a portfolio of small firms and a portfolio of large firms.

The difference in return between a portfolio of firms with a high book-to-market ratio (value firms) and a portfolio of firms with a low book-to-market ratio (growth firms).

A model that extends the market model with the returns on a "size" portfolio (SMB) and a "value" portfolio (HML) to better explain stock returns.

The return that a firm is expected to earn based on the Fama-French Three Factor Model.

The difference between a firm's actual return and its expected normal return according to the Fama-French Three Factor Model.

An approach to calculating normal returns that uses the return of a company or group of companies with similar size and book-to-market characteristics instead of a linear regression model.

A study of the financial performance of a firm during a specific period following a major event, such as an IPO or SEO, to assess the event's impact on the firm's stock performance.

Measurement errors in explanatory variables can introduce bias in OLS estimates.

When we observe a noisy version of an explanatory variable instead of its true value, we call it measurement error.

Measurement error occurs when the observed variable deviates from its true value.

The errors-in-variables problem arises when explanatory variables are measured with error.

The observed explanatory variable (x̃t) is equal to the true value (xt) plus a random noise term (νt).

The composite error term (ut − β2 νt) in the regression model is correlated with the observed explanatory variable (x̃t) due to the presence of νt. This correlation leads to inconsistent parameter estimates.

The OLS estimate of β2 becomes biased due to the correlation between the error term and the observed variable, leading to an inaccurate representation of the true relationship.

When explaining the variability of yt with x̃t, the correlation between the error term and the observed variable causes the OLS estimate of β2 to be inconsistent, meaning it won't converge to the true value even with an infinite amount of data.

A statistical method used to measure abnormal performance of a portfolio strategy (e.g., IPO timing) by comparing its returns to a benchmark model (e.g., Fama-French three-factor model).

The intercept (αp) of the regression of event portfolio returns on Fama-French factors captures the abnormal performance of the strategy. It measures how much the strategy's returns exceed the benchmark model after adjusting for market and risk factors.

A type of data that includes both time series and cross-sectional dimensions, meaning the same group of individuals, firms, or assets are observed across multiple time periods. For example, observing the stock returns of a set of companies over several years.

A panel data estimation method that allows for heterogeneity in the intercept term (αi), meaning the intercept can vary across different individual units (i) in the data. Frequently used in corporate finance and banking.

A popular panel data estimation method in asset pricing that permits both the intercept (αt) and slope coefficients (βt) to vary over time (t). This variation allows for the study of dynamic relationships between variables.

A method used to adjust for omitted variable bias in panel data by using a time-invariant variable specific to each unit (e.g., firm size). It essentially removes time-invariant differences across units.

An approach that allows for heterogeneity in the intercept term (αi) and slope coefficients (βi) to vary across individual units. It is commonly used in panel data analysis to accommodate differences in underlying relationships across individuals.