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CFA Level 2 > Quantitative Finance (Facts) > Flashcards

Quantitative Finance (Facts) Flashcards

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1
Q

What are Outliers?

A

Extreme values in a sample. Can result in errors indicated a relationship where none exists

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2
Q

What is a Spurious Correlation?

A

Appearance of a casual linear relationship where none exists (correlations need an economic reason)

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3
Q

What is a Simple Linear Regression?

A

Analysis that explains the variation in a dependent variable due to variation in the independent. Yi = b0 + b1 Xi + E

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4
Q

What are the 6 assumptions of Linear Regression?

A

1) Linear Relationship exists between dependent and independent variables 2) Independent variable is uncorrelated with residuals 3) Exp Value of Residuals is 0 4) Variance of residual is constant for all observations 5) Residuals are independently distributed (not correlated with each other) 6) Residuals are normally distributed

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5
Q

What is Sum of Square Errors?

A

SSE - Sum of Squared distance (vertical) between Est. and actual y-values

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6
Q

What is Standard Error of Estimate?

A

A measure of the degree of variability of actual to estimated Y values. It is the Std Dev. of the error terms in a regression.

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7
Q

What is Regression Sum of Squares?

A

The explained variation between Est. and actual y-values

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8
Q

What is Total Sum of Squares?

A

TSS = SSE and RSS

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9
Q

What is the Coefficient of Determination?

A

R squared - Percentage of total variation in the dependent explained by the independent

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10
Q

What is Adjusted R squared?

A

An adjusted measure of R squared that allows for the increase in value of R squared due to higher independent variables.

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11
Q

What is a Regression Coefficient Confidence Interval?

A

An interval used to test statistical significance and determine if a regression’s coefficients fall within the confidence interval.

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12
Q

What is the P-Value?

A

Smallest level of significance for which the null hypothesis can be rejected. If p-value > sig level null cannot be rejected If p-value < sig level null is rejected

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13
Q

What is the F-stat?

A

A measure of how well a set of independents explain the variation in the dependent as a group.

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14
Q

What is Heteroskedasticity?

A

Is when the variance of the residuals is not constant across all observations in the sample. There are two types: Unconditional and Conditional.

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15
Q

What is Unconditional Heteroskedasticity?

A

Level of heteroskedasticity is not related to the level of independents. I.e. it does not vary with a change in the level of independents.

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16
Q

What is Conditional Heteroskedasticity?

A

Level of heteroskedasticity is related to the level of independents. It exists if residuals increase as the value of independents increase.

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17
Q

What effect does Heteroskedasticity have on regression analysis?

A

1) Std Errors are usually unreliable 2) Coefficient estimates (b1) are not affected 3) t-stats are too small or large and statistical significance is unreliable 4) F-test is unreliable

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18
Q

How to detect Heteroskedasticity?

A

1) Via a scatter plot examination 2) Breusch Pagan test (regress squared residuals on the independents. If present independents will significantly contribute to the explanation of squared residuals). Uses BP chi-sq test = n x Rsq residual

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19
Q

How to correct for Heteroskedasticity?

A

1) Robust Standard errors (corrects the std errors of the linear regression model’s est. coefficients to account for heteroskedasticity). 2) Generalized Least Squares (modifies the original equation in an attempt to eliminate heteroskedasticity). CFA recommends using Robust Std Errors

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20
Q

What is Serial Correlation?

A

When the residual terms of a regression are correlated. There are two types: Positive and Negative

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21
Q

What is Positive Serial Correlation?

A

When a positive regression error in one period increases probability of observing a positive in the next

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22
Q

What is Negative Serial Correlation?

A

When a negative regression error in one period increases the probability of observing the opposite (positive value) in the next (and vice versa).

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23
Q

What effect does Positive Serial Correlation have on regression analysis?

A

1) Coefficient errors are too small
2) T-stats are then likely to be too large
3) Type I errors occur 4) Unreliable F-test

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24
Q

What effect does Negative Serial Correlation have on regression analysis?

A

1) Coefficient std errors are too large
2) T-stats are then likely to be too small
3) Type II errors occur

25
Q

How to detect Serial Correlation?

A

1) Via a scatter plot examination 2) Durbin-Watson test If DW = 2 there is no serial correlation. If < 2 then it is positively and > 2 is negatively serially correlated.

26
Q

How to correct for Serial Correlation?

A

1) Adjust the coefficient standard errors using Hansen method. 2) Adjust the specification of the model CFA recommends use of the Hansen method (which also corrects for conditional heteroskedasticity).

27
Q

What is Multicollinearity?

A

A condition which occurs when two or more independent variables in a multiple regression are highly correlated with each other.

28
Q

What effect does Multicollinearity have on regression analysis?

A

1) Distorts standard errors of estimates and coefficient standard errors 2) Type II errors more likely (incorrectly conclude a variable is not statistically sig.)

29
Q

How to detect Multicollinearity?

A

When no individual coefficients are significantly different from zero while F-test is statistically significant and Rsquared is high.

30
Q

How to correct for Multicollinearity?

A

Omit one or more of the independent variables

31
Q

What are the 3 broad categories of Model Misspecification?

A

1) Functional form - Important variables are omitted - Variables should be transformed - Data is improperly pooled
2) Explanatory variables are correlated with the error term in a time series model - Lagged dependent variable is used as an independent - Function of the dependent variable is used as an independent variable - Independent variables are measured with error
3) Other time-series misspecifications that result in non-stationarity.

32
Q

What effect does Model Misspecification have?

A

1) Biased and inconsistent regression coefficients
2) Unreliable hypothesis testing and inaccurate predictions

33
Q

What are Qualitative dependent variables?

A

Takes on a value of either 1 or 0 depending on whether a specific event occurs (1) or not (0).

There are two types of models specifically used for qualitative dependent variables.

1) Probit and Logit models
2) Discriminat Models

34
Q

What are Probit and Logit Models?

A

Probit and logit models estimate the probability of a discrete outcome given the values of the independent variables used to explain that outcome.

Probit Models are based on normal distributions while Logit Models are based on logistic distributions

Both models use the Maximum likelihood methodology to estimate coeffecients. They relate to the likelihood of the event occuring or not.

35
Q

What are Discriminant Models?

A

Discriminant models result in a linear function (similar to an regression equation) that generates an overal ‘score’

The score is used to rank observations and produces a value for the dependent variable that determines if the event occurs (1) or not (0)

36
Q

What is a Time Series?

A

A set of observations for a variable over successive periods of time. These observations can be used to determine if a trend exists.

37
Q

What is a Linear Trend Model?

A

A time series pattern that can be graphed with a straight line.

38
Q

What is a Log-linear Trend Model?

A

Trends that occur when there is exponential growth (i.e. growth that is continually compounding).

Positive exponential growth means the time series increases at some constant rate of growth resulting in a convex curve

Negative exponential growth means the time series decreases at a constant rate resulting in a concave curve

39
Q

What is an Autoregressive Model?

A

Is when the dependent variable is regressed against one or more lagged values of itself (must be covariance stationary in order for results to be reliabe).

40
Q

When is a time series covariance stationary?

A

When it has

1) Constant and finite expected values - Exp value of the time series is constant over time (it has a mean-reverting level)
2) Constant and finite variance - Volatility around it’s mean does not change over time
3) Constant and finite covariance between values at any given lag (leading or lagged values of itself)

41
Q

How is an Autoregressive Model used to forecast?

A

Forecasting with an AR model uses lagged values of dependents as independents to forecast the next period.

42
Q

How to test AR Models for Serial Correlation (Autocorrelation)?

A

1) Estimate AR model to be evaluated (e.g. AR(1) model)
2) Calculate the autocorrelation of the model’s residuals from the model (i.e. level of correlation between the forecast errors from one period to the next)
3) Test whether autocorrelations are significantly different from zero. If any differ significantly from 0 than the model is not correctly specified.

43
Q

What is Mean Reversion in Time Series?

A

Mean reversion is when the value of a time series has a tendency to move towards it’s mean.

If above (below) it’s mean reverting level then the next value will be lower (higher). If it is at it’s mean reverting level then the next value will equal the current value.

All covariance stationary time series have a mean reverting level.

44
Q

What are In and Out of sample forecasts?

A

In sample forecasts - are made within the range of data used to estimate the model. They are used to compare how accurate the model is in forecasting the actual data used to develop the model.

Out of sample forecasts - are made outside of the sample period. They are used to determine how accurate a model is in forecasting the variable for a time period outside the data.

Most published research employs in-sample forecasts only.

45
Q

What is the Root Mean Squared Error used for?

A

It is used to compare the accuracy of autoregressive models in forecasting out-of-sample values

The model with a lower RMSE for the data will have smaller forecast errors and better predictive power.

46
Q

What is a Random Walk?

A

A time series in which the value of the series in one period is the value in the previous series plus an unpredictable random error.

47
Q

What is a Random Walk with a drift?

A

A random walk with a drift is present when the intercept term is not equal to zero. In addition to a random error term, the time series is expected to increase or decrease by a constant amount each period.

48
Q

Are Random Walks Covariance Stationary?

A

No. Neither a random walk or random walk with a drift exhibit covariance stationarity and both will exhibit a unit root.

A time series must have a finite mean-reverting level in order to be covariance stationary.

Standard regression analysis cannot be used on a time series that is a random walk.

49
Q

How to determine if a time series exhibits non-stationarity with Unit Roots?

A

There are two tests:

1) Run an AR model and examine the autocorrelations - The AR model is est. and statistical significance of autocorrelations at varios lags is tested. If series exhibits stationarity then no process will have no stat sig residual autocorrelations.
2) Use Dickey Fuller Test - i) Transform the AR(1) model and subtract X (t-1) from both sides. ii) Test whether new coefficients (b1- 1) is different from zero using a modified t-test. If not sign different from zero than b1 must be equal to 1 and therefore series has a unit root.

50
Q

What is First Differencing?

A

Is a proceedure used to transform data that has a random walk to a new covariance stationary time series.

It involves:

1) Subtracting the value of the time series in the preceeding period from the current value of the time series to define a new dependent variable.
2) If the original time series has a unit root the change in the dependent should then just equal the error term.

51
Q

What is a Moving Average Time Series?

A

It takes the past values of a series and smoothes them by dividing the period values by the number of observations.

Some time series (like the S&P 500 Index) follow more closely a moving average model.

Moving Avg Time series can be used in forecasting values. In order to verify if the MA model fits the autocorrelations are examined and only the first MA(q) autocorrelation will be sig different from zero.

52
Q

What is Seasonality?

A

A pattern that tends to repeat itself from year to year.

When present, modelling the time series data would be misspecified unless the AR model incorporates the effects of seasonality.

Correcting for Seasonality is done by adding an additional lag of the dependent variable that corresponds to the same period in the previous year as an independent in the original model

53
Q

What is Autoregressive Conditional Heteroskedasticity (ARCH)?

A

A condition that exists if the variance of the residuals in one period is dependent on the variance of the residuals in the previous period (an example of a ARCH(1) model).

ARCH models are used to test for autoregressive conditional hetereoskedasticity - test developed by Robert Engle.

54
Q

What effect does Autoregressive Conditional Heteroskedasticity (ARCH) have on regression analysis?

A

The standard errors of the regression coefficients in AR models and the hypothesis tests of these coefficients are invalid.

55
Q

How to test for Autoregressive Conditional Heteroskedasticity (ARCH)?

A

ARCH models are used to test.

To test for ARCH the squared residuals from an estimated time-series model are regressed on the first lag of the squared residuals.

If the coefficients in the ARCH (1) regression model are statistically different from zero then the time series is ARCH (1)

56
Q

How to correct for Autoregressive Conditional Heteroskedasticity?

A

The standard errors for the regression parameters will need to be corrected using methods such as generalised least squares.

57
Q

What is Cointegration and when does it occur?

A

When two time series are economically linked (related to same macro variables) or follow the same trend, and the relationship is not expected to change.

If both series are cointegrated the error term from regressing one of the other will result in the outcome being covariance stationary and the t-test reliable.

The residuals are then tested for a unit root with the Dickey Fuller test with t-values calculated by Engle and Granger. If the test rejects the null hypothesis of a unit root, we say the error terms generated by the 2 series are covariance stationary and cointegrated and the regression be can used to model their relationship.

58
Q

What are the 9 steps in Time-series forecasting?

A
  1. Understand the investment problem and make an initial choice of model.
  2. If using a time-series model, compile the time series and plot it to see whether it looks covariance statinary.
  3. If no significant seasonaility or shift in the time series occurs, then perhaps a linear trend or exponential trend will be sufficient to model the series
  4. If significant serial correlation is found in the residuals consider using a AR model. First reexamine the time series to determine whether it is covariance stationary
  5. Once transformed into a covariance stationary time-series attempt modelling the series with a short autoregression AR(1).
  6. If significant serial correlation is found in the residuals, use an AR(2) model and test for significant serial correlation of the residuals
  7. Check for seasonaily
  8. Test whether the residuals have autoregressive conditional heteroskedasticity.
  9. Test for the models out-of-sample forecasting performance.

CFA Level 2 (2 decks)

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