CAIA - CHAPTER 9 WITH COMPLETE SOLUTIONS.

Regression - a statistical analysis of the relationship that explains the values of a dependent variable as a function of the values of one or more independent variables based on a specified model. Independent Variable Are those explanatory variables that are inputs to the regression and are viewed as causing the observed values of the dependent variable. Simple linear regression A linear regression in which the model only has one independent variable. Dependent Variable is the variable supplied by the researcher that is the focus of the analysis and is determined at least in part by other (independent or explanatory) variables. Slope Coefficient A measure of the change in a dependent variable with respect to a change in an independent variable. Intercept Is the value of the dependent variable when all independent variables are zero. Residuals Residuals of the Regression, e,t, reflect the regression's estimate of the idiosyncratic portion of the asset is realized returns above or below its mean idiosyncratic return (i.e. the regression's estimates of the error term) Goodness of Fit of a regression - is the extent to which the model appears to explain the variation in the dependent variable. r-squared value of the regression - is also called the coefficient of determination, is often used to assess goodness of fit, especially when comparing models. t-test A statistical test that rejects or fails to reject a hypothesis by comparing a t-statistic to a critical value. t-statistic The t-statistic of a parameter is formed by taking the estimated absolute value of the parameter and dividing by its standard error. the result is compared to a critical value. - If t-statistic exceeds the critical value the parameter estimate is deemed to be significantly different from zero. Multiple Regression Model A regression model with more than one independent variable. Multicollinearity Is when two or more independent variables in a regression model have high correlation to each other. Stepwise Regression - is an iterative technique in which variables are added or deleted from the regression equation based on their statistical significance. Nonlinear Exposure - A nonlinear exposure of a position to a market factor is when the sensitivity of the position's value varies based on the magnitude of the level of change in the market factor's value. Conditional Correlation - is a correlation between two variables under specified circumstances. For Example: an analyst may estimate the correlation coefficient between a hedge fund's returns and the returns of an equity index during only those months in which the stock market rose by 1% or more. Nonstationary - that return volatilities and correlations vary through time. - Two approaches for modeling changing correlation: 1. Conditional correlation 2. Rolling window Negative Conditional Correlation When the correlation in the down sample is higher than the correlation in the up sample. Positive Conditional Correlation - of investment returns to market returns is: - when the correlation in the up sample is higher than the correlation in the down sample. Rolling Window Analysis - is a relatively advanced technique for analyzing statistical behavior over time, using overlapping subsamples that move evenly through time. Style Analysis - is the process of understanding an investment strategy, especially using a statistical approach, based on grouping funds by their investment strategies or styles. - KEY QUESTION: Do investment funds of the same stated investment style have returns that can be explained by the same underlying return factors. Principal Components Analysis - a statistical technique that groups the observations in a large data set into smaller sets of similar types based on commonalities in the data. - identifies subgroups of observations that tend to behave similarly.