Quantitative Methods

Question 1

What are the two formulas for R Squared?

Answer 1

R sq = Correlation Squared

R sq = RSS / SST

Question 2

What is the formula to calculate the t-stat for the correlation coefficient?

Answer 2

t = (r√n-2) / (1-r2)

Question 3

What does R Squared represent?

Answer 3

R squared represents the amount of variation in the dependent variables accounted for by an independent variable.

Question 4

Does regression analysis assume that:

a) The independent variable is uncorrelated with the residuals.
b) The dependent variable is uncorrelated with the residuals.

Answer 4

It only assumes that the Independent Variable is uncorrelated with the residuals.

Question 5

For a single-factor regression model, how many degrees of freedom does the critical T for calculation of a confidence interval for:

a) A parameter estimate.
b) A “Y-Value” estimate.

Answer 5

2 degrees of freedom for both.

Question 6

What are the formulas for Mean Squared Regression and Mean Squared Error?

Answer 6

MSR = RSS/ df

MSE = SSE/ df

Question 7

What is the formula for Standard Error of the Estimate?

Answer 7

SEE = √MSE

Question 8

What is the formula for F-Stat?

Answer 8

F-Stat = MSR/MSE

Question 9

What is the formula for calculating a confidence interval?

Answer 9

Confidence Interval = Coefficient Estimate +/- (Critical T)(Standard Error)

Question 10

What is the formula for calculating t-stat for a parameter?

Answer 10

T-Stat = (Coefficient Estimate - Value to Compare) / Standard Error

Question 11

What is spurious correlation?

Answer 11

Spurious correlation is when there there appears to be a statistical correlation between variables, but no actual relationship exists.

Question 12

How many degrees of freedom does the regression have?

Answer 12

k degrees of freedom.

Question 13

How many degrees of freedom does the error have?

Answer 13

n - k - 1 degrees of freedom.

Question 14

How should the upper and lower Durbin-Watson values be used to determine whether to accept or reject the null hypothesis.

Answer 14

0 - Lower = Reject H0; Positive serial correlation exists

Lower - Higher = Inconclusive

> Higher = Do not reject H0

Question 15

Would failing to include a variable that affects the dependent variable lead to misspecification?

Answer 15

Yes.

Question 16

Would using actual inflation as a proxy for expected inflation lead to misspecification?

Answer 16

Yes.

Question 17

Would using a lagged variable lead to misspecification?

Answer 17

Yes.

Question 18

How will be the coefficients be when a model is misspecified?

Answer 18

Biased and inconsistent.

Question 19

What is the solution to serial correlation?

Answer 19

Use Hansen method to adjust the standard errors.

Question 20

What should all qualitative variables be tested for?

Answer 20

Heteroskedasticity, Serial Correlation and Multi-Collinearity.

Question 21

What is a potential solution when a time series has a unit root?

Answer 21

Model the first differences, as these usually do not exhibit a unit root.

Question 22

What is a trend model?

Answer 22

A model in which the independent variable is time (t).

Question 23

When is a loglinear model used?

Answer 23

When a time series grows at a constant rate.

Question 24

What does covariance stationary mean?

Answer 24

That the time series will be mean-reverting.

Question 25

How is annual seasonal lag of quarterly returns? a) By adding a t-4 parameter b) By adding a t-12 paramater c) By adding both

Answer 25

By adding a t-4 parameter.

Question 26

How do you know if a time series is a random walk?

Answer 26

It has a unit root.

Question 27

What is the null hypothesis of the Dickey-Fuller/ Engle-Granger test?

Answer 27

That the time series has a unit root/ is nonstationary.

Question 28

Does the Dickey-Fuller test use conventional or adjusted: a) t-statistics b) Criticial t-values

Answer 28

The Dickey-Fuller test uses a conventional t-statistic but compares it to adjusted critical t-values.

Question 29

What does a 4th autocorrelation need to differ significantly from for a model to exhibit seasonality?

Answer 29

Zero.

Question 30

What is Autoregressive Conditional Heteroskedasticity (ARCH).

Answer 30

When an error is correlated with a lagged error.

Question 31

What will the R2 and coefficient t-stats be if multicollinearity is present?

Answer 31

High R2 and insignificant t-stats.

Question 32

How does historical simulation estimate VaR?

Answer 32

It uses actual returns and takes the 5th percentile.

Question 33

What is the formula for VaR?

Answer 33

VaR = Mean Return - (Critical T * Standard Deviation)

Question 34

How do you adjust annual standard deviation (volatility) in VaR to calculate daily standard deviation?

Answer 34

Daily SD = Annual SD / √No. Of Days Note the square root of days, not the no. of days.

Question 35

What is maximum drawdown?

Answer 35

The worst drop in performance from peak to trough, or the worst historical performance in a period.

Question 36

How many degrees of freedom are there when determing the critical t-stat?

Answer 36

N - K - 1 degrees of freedom.

Question 37

What is the general limit for a t-stat to be significant?

Answer 37

Greater than 2.

Question 38

What is serial correlation?

Answer 38

When there is correlation between regression errors.

Question 39

What is heteroskedasticity?

Answer 39

When the variance of errors is not constant, and is related to the independent variables.

Question 40

What is reverse stress testing?

Answer 40

Creating a hypothetical event that would affect a company's top exposure at the same time.

Question 41

What is the test for heteroskedasticity and what part of the regression does it test?

Answer 41

The Breusch-Pagan Chi Squared test is carried out on the R-Squared

Question 42

What part of the regression does the Hansen method adjust?

Answer 42

The standard errors.

Question 43

What are the two steps to test for ARCH?

Answer 43

1. Square the residuals. | 2. Regress the squared residuals against squared residuals from previous periods.

Question 44

What is the formula for the standard error of the autocorrelation?

Answer 44

1 / √n

Question 45

If a regression covers periods that should have their own regressions, what type of misspecification is this?

Answer 45

Functional form misspecification.

Question 46

What do unbiased and consistent mean?

Answer 46

Unbiased means the sample is representative of the population. Consistent means that as the sample size increases, the estimate gets closer to the population.