Chapter 9 - CAIA Flashcards - Regression, Multivariate, and Nonlinear Methods
CAPM
The best-known single-factor market model is the capital asset pricing model (CAPM), which states that the expected return and realized return of an asset are linearly related to its market beta.
Regression
A regression is 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.
Dependent Variable
The 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.
Independent Variable
Independent variables 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 simple linear regression is a linear regression in which the model has only one independent variable.
Slope Coefficient
The slope coefficient is a measure of the change in a dependent variable with respect to a change in an independent variable.
Intercept
The intercept is the value of the dependent variable when all independent variables are zero.
Ordinary Least Square Regression
Ordinary least squares regression, the most common regression procedure, selects the intercept and slope that minimize the sum of the squared values of the residuals (the values of eit).
Advantages of OLS
The use of ordinary least squares has several advantages: It is quick and easy, and the slope coefficient that results has an intuitive interpretation.
First Order Autocorrelation
First-order autocorrelation is a common phenomenon in alternative investments and is reasonably easy to address.
Goodness of Fit
The goodness of fit of a regression is the extent to which the model appears to explain the variation in the dependent variable.
R-Squared
The r-squared value of the regression, which is also called the coefficient of determination, is often used to assess goodness of fit, especially when comparing models.
T-Test
A t-test is a statistical test that rejects or fails to reject a hypothesis by comparing a t-statistic to a critical value.
Multiple Regression Model
A multiple regression model is a regression model with more than one independent variable.
Multicollinearity
Multicollinearity is when two or more independent variables in a regression model have high correlation to each other. A primary method of detecting multicollinearity is to examine the correlations between the independent variables.
Stepwise Regression
Stepwise regression is an iterative technique in which variables are added or deleted from the regression equation based on their statistical significance.
Non Linear 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.
Down Market Beta
The down market beta, bi,d, is the responsiveness of the fund’s return to the market return when the market return is less than the riskless rate (i.e., when the market’s excess return is negative, or down). The coefficient bi,diff is the difference between the sensitivities or betas of the fund’s return to up and down markets.
Up Market Beta
The up market beta, bi,u, is the responsiveness of the fund’s return to the market return when the excess market return is positive, and is estimated as the sum of bi,d and bi,diff.
Negative Conditional Correlation
When the correlation in the down sample is higher than the correlation in the up sample, it is termed negative conditional correlation.
Positive Conditional Correlation
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. Investors prefer investment strategies with positive conditional correlation, since the strategies offer higher participation in profits during bull markets and lower participation in losses during bear markets. The only indices exhibiting positive conditional correlation during this period were managed futures and equity market-neutral funds.
Rolling Window Analysis
Rolling window analysis is a relatively advanced technique for analyzing statistical behavior over time, using overlapping subsamples that move evenly through time.
Style Analysis
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.
Principal Component Analysis
Principal components analysis is a statistical technique that groups the observations in a large data set into smaller sets of similar types based on commonalities in the data.
Look Back Option
A look-back option has a payoff that is based on the value of the underlying asset over a reference period rather than simply the value of the underlying asset at the option’s expiration date.
