Reading 2.8 Flashcards
Test statistic formula
(Estimated value - hypothesized value) / standard error
In Ordinary least squares (OLS) regression, what is beta, alpha and residual?
Beta = slope
Alpha = vertical intercept
Residual = distance from line to the actual value (data point)
What issues should an analyst be concerned about during regression analysis?
1) Outliers
2) Autocorrelation
3) Heteroskedasticity
What is heteroskedasticity?
Error term’s variance is correlated with an explanatory variable
OR
SD of a variable is not constant over time
What are leptokurtic distributions?
Fat - tailed distributions. = have more probability of extreme (rare) events
When does OLS generate unbiased estimates of A&B?
If error terms are:
1) normally distributed
2) uncorrelated
3) homoskedastic
What is homoskedasticity?
Error term / Variance of residual / SD
is constant
When is null rejected?
If p value < significance level (1/5/10%)
OR
T-test > critical value
When is null not rejected?
p value > significance level
OR
T test < critical value
What is P value?
Measure used to determine the likelihood that an observed outcome is the result of chance.
How is p value interpreted?
1) Measures presence of a relationship
2) the larger the t test the smaller the p value
3) reject null if p value less than significance level
How is t statistic interpreted
1) reject null if t test is larger than critical value
2) the larger the t test the smaller the p value
Main critical values (1,2,5,10%)
1% conf level = 2.575
2% сonf level = 2.33
5% conf level = 1.96
10% conf level = 1.645
What does OLS do?
Finds estimates of a&b that minimize sum of squared error terms (residuals)
9 sampling & testing problems
1) selection bias
2) self selection bias
3) survivorship bias
4) data mining
5) data dredging
6) backtesting
7) backfilling
8) cherry picking
9) chumming
Data mining
Trying to find patterns in very large data sets.
Usually just finds false patterns that are random.
Back testing
Retroactively testing your investment strategy using historical data and seeing if produces good returns. Prone to cherry picking because the analyst is already aware of the data.
Data dredging
Conducting multiple tests on same data and selecting only the results that show statistically significant findings
What p value indicates that the t test is statistically significant
The smallest one
OR
If its smaller than the significance level
Type 1 error in hypothesis testing?
False positive = false rejection of true null = the null should NOT be rejected because it true.
Alpha = probability of this type of error
Type 2 error in hypothesis testing?
False negative = test fails to reject a false null = null is false and SHOULD be rejected.
Beta is the probability of this error
How to treat HETEROSKEDASTICITY?
Use weighted least squares.
It weighs the data that has high error term volatility.
Luck in returns is defined as?
Ex ante alpha - ex post alpha
Steps in the statistical hypothesis test
1) state null and alternative
2) design statistical test for the hypothesis
3) perform test using sample data
4) reject/fail to reject hypothesis
Refers to the probability that null is rejected when true (type 1 error)
Statistical significance
1 - alpha is referred to as
Specificity of the test
Probability of type 2 error =
Beta.
1 - B in hypothesis testing =
Power of test
Which statistical issues incur during regression analysis that analyst SHOULD be worried about?
Many strategies produce extreme results
=>
Which has a large influence on regression estimates
Buying securities in a recently outperforming sector without considering broad sector metrics is an example of?
Cherrypicking
Jabir Wasem, an analyst at Betafund, is analyzing the exposure of a company’s stock to market return Auctuations using the ex-post single-factor CAPM-based regression equation. Which of the following is NOT likely to be part of this analysis?
A) The regression is run with an intercept.
B) The independent variable is the return on the market portfolio less the riskless rate of retumn.
C) Beta estimates the linear sensitivity of the stock return to changes in the market return.
D) The dependent variable is the return on the stock less the riskless rate of return.
C. Because in this example Beta measures the EXCESS return in EXCESS of market return. Not EXPECTED return.
Is difference of ex ante alpha of 0.0007% economically significant?
No
How can heteroskedasticity be detected?
Plot the residuals (E) against time
OR
Against independent variables
To see if a pattern emerges.
What does plotting the dependent variable against each independent variable do in relation to heteroskedasticity?
Results in the original scatter plot of returns does not help identify heteroskedasticity
What is a simple linear regression?
It describes the relationship of ONE dependent variable and ONE independent variable
Which measure explains the percentage of total variance in the dependent variable that can be explained by the regression model?
R squared
What does b represent in a simple linear regression?
B = change in (Ri - Rf) per unit change in (Rm - Rf)
Which type error is more serious?
Type 2 error
Analysis of Long term returns of HFs often results in flawed conclusions because?
Because of survivorship bias. Unsuccessful funds close down and stop reporting results, so successful funds are overrepresented
Beta drivers are? Example of beta invesmtments?
Capture risk premiums by bearing systematic risk (beta)
Ex: ETFs
Alpha drivers are? Examples of investments
Aim to outperform the market, use alternative invesments.
Ex: PE, HFs
Testing for null results in to 2 scenarious:
Rejected or NOT rejected.
Accepted and other terminology is not applicable
Issues with estimating RELIABLE alpha
1) non-normal returns
2) outliers
3) biased testing
- not random
- procedures are not specified before testing
Issues with estimating RELIABLE beta
1) true / false correlation
2) correlation / causality
How does expense ratio impact alpha?
Alpha is decreased by the amount of the expense ratio
What is the confidence interval in hypothesis testing?
Indication of a parameter’s true value
What is significance level of a hypothesis test?
Probability that the null is rejected when true
