# 9. Regression, Multivariate, and Nonlinear Methods Flashcards

## Practice questions

- What are the two distinguishing characteristics that make a regression a simple linear regression?

- One independent variable

* The relationship between the dependent and independent variable is liner

- In a linear regression analysis of realized fund returns based on the single factor market model, what parameters or variables of the regression would be associated with a fund’s estimated ex ante alpha, a fund’s estimated beta and a fund’s estimated idiosyncratic returns?

- Ex ante alpha is the intercept of the regression (relative to the riskless rate)
- A fund’s estimated beta is the slope coefficient of the regression
- A fund’s estimated idiosyncratic returns is the residuals (estimated error terms).

- List the three primary assumptions used in a least squares regression to justify that the estimated parameters are unbiased and most likely.

➢ The model’s error terms are assume to be:

• Normally distributed

• Uncorrelated

• Homoskedastic (i.e., have the same finite variance)

- Why is multicollinearity an issue in a multiple regression model but not a single regression model?

• There is only one independent variable in a single regression model, but two or more independent variables are needed to have multicollinearity. A multiple regression model is 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.

- The excess returns of a fund are being analyzed using a quadratic regression approach with an intercept and one independent variable: the squared value of the excess return of the overall market. What would be the likely interpretations of a result in which both the intercept and the slope coefficient are significantly positive?

- A positive slope coefficient indicates that a manager has been able to successfully time the market.
- A positive intercept indicates superior security selection.

- In the context of a dummy variable approach to dynamic risk exposures, what is a “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”).

- A fund specializing in market timing of listed equities is estimated to have exhibited negative conditional correlation with the returns of a major equity market index. The fund alternates between net short positions and net long positions. What is primary interpretation of this finding?

• The manager is mis-timing the market by having higher risk exposure (higher betas or, more net long) when the market falls having less exposure when the market rises.

- Why would an analyst use a rolling window analysis of the systematic risk exposures of an investment strategy rather than a single analysis based on the entire dataset?

• The analyst is concerned about style drift (specifically, systematic risk exposures that change through time). By using a short-term analysis that moves through time the analyst can get estimates of the change in risk exposures through time.

- Consider a style analysis of fund returns based on Sharpe’s seminal approach. Based on past observations, how would you expect the goodness of fit of a regression to change based on whether the fund returns were from traditional mutual funds or from hedge funds?

• Traditional mutual fund returns are well explained by the returns of the asset classes that the funds hold but the same is not true for hedge funds. Empirical evidence indicates that the returns on most hedge funds are not well explained by passive return indices of their underlying assets. This is because hedge funds are more likely to have quickly and/or substantially changing risk exposures.

- What are two major shortcoming of an empirical study that examines performance persistence of funds by comparing the correlation of returns in an earlier period with returns in a subsequent period when returns are based on appraised values?

- The results could be driven by serial correlation in returns that does not reflect true performance correlations
- The returns are not risk-adjusted

conditional correlation

is a correlation between two

variables under specified circumstances.

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.

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).

goodness of fit

of a regression is the extent to which the

model appears to explain the variation in the dependent

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.