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36 Cards in this Set
- Front
- Back
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Ordinary Least Squares Regression |
Generates unbias itemsif: 1) Normal distribution 2) Uncorrelated 3)homoskedatic The residual (i.e., error term) is the vertical distance between the regression line and an actual data point (not the intercept) minimizes the sum of the squared errors terms (not just the sum of the error terms). The result is best linear, unbiased estimators of the slope and intercept parameters |
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Homoskedatic |
Constant Variance |
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Auto correlated Returns |
-Have similar prices time period over time-period - Used in illiquid assets with appraised prices Many alts have appraised prices -Durbin Watson test used to test autocorrelation |
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Heteroskedasticity |
Variance varies over time In the presence of heteroscedastisity, the parameter estimates will not be unbiased; they will be unduly affected by the data associated with the largest variance in the error terms. |
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Regression |
set of statistical techniques used to investigate and model the dependence of the dependent variable on at least on independent variable |
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Goodness of Fit |
- Extent to how effective the regression model is at explaining the variation in the dependent variable -Use r squared |
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R-squared |
Square of the estimated correlation coefficient between the dependent and independent variables B/w 0-100% -Returns in x explain r squared number of variance of returns in y |
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Run a t-test |
-Run on an intercept by taking estimated vale/standard error -If greater than critical value than use bc it's identified as being "statistically different than 0" - |
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What is critical value at 5% significance level? |
5% |
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3 challenges of a regression? |
1) Outliers 2) Autocorrelation 3) Heteroskedasticity |
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Multicollinearity |
Independent variables are correlated with one another -Can be solved by using one independent variable in addition to a spread Leads to less accurate regression coefficients |
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Step wise regression |
-Process used to determine optimal amount of independent variables needed -Variables with greater t statistics are added or retained to the model - Involves removing variables with insignificant test statistics from the model one by one or adding variables with high test statistics |
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Dummy Variable Approach |
- Market timing -Formula implementing -Beta down -Beta Up -Beta Difference Market-timing skill is indicated by a positive bi,diff (i.e., the difference between up-market beta and down-market beta). |
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Separate Regressions |
If looking to regress different data sets or time horizons |
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Quadratic Appraoch |
Squaring market premium -U shaped profit-loss curve - Ex used for option straddles -Want beta to be as high as possible bc you are multiplying beta by the (Market premium)^2 |
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Conditional Correlation |
-Correlation of two variables in certain conditions -Negative- Higher correlation in down markets -Positive- Higher correlation in up markets |
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Rolling window analysis |
-Used selecting sub-period and running regression overlapping consecutive periods until the end of the data set -Used if there is style drift from the manager -This helps identify short term exposures by analyzing long term returns -Independent value is how many rolling time periods exist without overlap -time is in months # of regressions = T - m + 1 where T is total months and m is months in a single regression |
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Style Analysis |
Statistical Process that explains returns by grouping funds by their stated investment strategies/styles -Initially applied by Sharpe regressing mutual funds -Works well for mutual funds (i.e r squared of 90%) -Not as much for hedge funds (i.e 25%) |
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Principal Components Analysis (PCA) |
Groups Hedge fund data sets into similar types: 1) Opportunistic 2) Global Macro 3) Value 4) Trend-Following 5) Disressed 45 % of variation in returns can be explained by the above |
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significance level |
- Probability of rejecting a null hypothesis when it's true - Type 1 occurring false positive -error rate |
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p level |
-If p-level falls in red, reject null -p level less than significance reject -Cant fall within significance level |
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critical region |
defines how far away our sample statistic must be from the null hypothesis value before we can say it is unusual enough to reject the null hypothesis. |
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T-statistic |
Signal --------- Noise Higher the more significant more likely to reject null |
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Laszlo Paul |
It identifies factors based on how well they explain a particular hedge fund’s returns in order to replicate this hedge fund’s returns based on these factors. |
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Serial Correlation |
- measures correlation of returns between successive time periods |
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Concerns when running a regression analysis? |
1) Outliers 2) Heteroskedacity 3) Auto Correlation |
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down-market beta in the dummy variable |
how responsive a fund's return is to the market return when excess market return is negative (i.e., when Rm - Rf < 0) |
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Non-linear returns can be described using
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1) regression with dummy variables
2) separate regressions in different time periods 3) regressions using a quadratic (i.e., squared) term |
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Non-linear relations between returns and market factors are typically associated with
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alternative investments that have an option component (e.g., event risk funds, such as merger arbitrage and distressed investments) or engage in market timing (e.g., managed futures)
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simple linear regression
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Regression equations describe a relationship between a dependent variable and one or more independent variables. A simple linear regression has only one independent variable. |
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Characteristics of market-wide return factors in multi-factor models
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The factors can be determined empirically.
The factor exposures (i.e., the betas) can be determined empirically. The factors are tradable. |
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ex-post single-factor regression model
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the dependent variable is the excess stock return (i.e., stock return less riskless rate) and the independent variable is the excess market return (i.e., market return less riskless rate). Therefore, beta (i.e., the slope coefficient) estimates the linear sensitivity of the excess stock return to changes in the excess market return.
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R = a + bRm + e
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coefficient b represents the slope of the regression line
a represents the vertical intercept of the line e is the error/residual term |
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Spurious Correlation |
- False indication of two variables -Typically idiosyncratic and random -Unstable betas overtime dont always mean spurious correlation |
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Abnormal Returns |
-Always mean positive correlation good or bad |
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Rit = ai + bimRmt + eit , which of the following do the variables represent |
Rit is the dependent variable, Rmt is the independent variable, eit is the error term, and ai and bim are the regression coefficients. Rit is DEPENDENT ON RMT!!!! |
