Credit Risk & Quant Risk Managment

Question 1

When comparing VaR and ES, it is correct to say that:

a. VaR is a more comprehensive measure of risk than ES.

b. ES is always less than or equal to VaR.

c. VaR and ES are always identical values for any given portfolio.

d. ES is often used to complement the information provided by VaR.

Answer 1

D

Question 2

The range of the logit function (logit(π)) in the domain π=[0,1] is:

a.
(0, ∞)

b.
(0, 1)

c.
(-∞, 0)

d.
(- ∞, ∞)

Answer 2

D

logit(0) = ln(0) = −∞
logit(1) = ln (∞) = ∞

So, the endpoints of the probability range [0, 1] get mapped to the endpoints of the logit range [−∞,∞].

Question 3

Which of the following is a correct assumption of logistic regression?

a.
Multicollinearity is not a concern in logistic regression.

b.
It requires a linear relationship between the logit of the outcome and the predictors.

c.
The dependent variable should be continuous.

d.
The residuals must be normally distributed.

Answer 3

B

Question 4

What is an important feature of logistic regression in terms of prediction?

a.
It always requires large sample sizes.

b.
It predicts the probability of different categorical outcomes.

c.
It can predict precise numerical outcomes.

d.
It is used to predict the mean of the data.

Answer 4

B

Question 5

Which of the following is true of the 99% value at risk?

a.
There is 1 chance in 1000 that the loss will be greater than the value of risk

b.
There is 1 chance in 1000 that the loss will be lower than the value of risk

c.
There is 1 chance in 100 that the loss will be greater than the value of risk

d.
There is 1 chance in 100 that the loss will be lower than the value of risk

Answer 5

C

Question 6

What is the primary difference between linear and logistic regression?

a.
Linear regression is used for predicting continuous outcomes, while logistic regression is for categorical outcomes.

b.
Logistic regression is used for predicting numerical values, while linear regression is not.

c.
There is no significant difference between the two.

d.
Linear regression is used for classification, while logistic regression is used for regression.

Answer 6

A

Question 7

In logistic regression, the role of the predictor (independent variable) is to:

a.
Always be a binary variable

b.
Be discrete, continuous, or a combination thereof

c.
Undergo a logarithmic transformation before the analysis

d.
Fall within the range of 0 to 1

Answer 7

B

Question 8

The Expected Shortfall (ES) at a 95% confidence level tells an investor:

a.
The average loss that exceeds the VaR threshold 5% of the time.

b.
The maximum loss that will be incurred 95% of the time.

c.
The total capital required to cover losses 95% of the time.

d.
The minimum profit that can be expected 95% of the time.

Answer 8

A

Question 9

Given a portfolio with a 97.5% one-day VaR of $8,000, what can be inferred about the Expected Shortfall (ES) if the portfolio has heavy-tailed risk characteristics?

a.
ES will be more than $8,000.

b.
ES cannot be determined from the given information.

c.
ES will be exactly $8,000.

d.
ES will be less than $8,000.

Answer 9

A

Question 10

When assessing risk with Value at Risk (VaR), which of the following is an accurate interpretation of a higher VaR figure?

a.
Higher potential loss and therefore higher risk.

b.
Less fluctuation in the portfolio’s value.

c.
Lower potential loss and therefore lower risk.

d.
More stable returns and therefore lower risk.

Answer 10

A

Question 11

Which of the following best explains the concept of “tail risk” in the context of VaR and ES?

a.
The risk associated with the least likely outcomes in the loss distribution.

b.
The risk linked to the most liquid assets in a portfolio.

c.
The risk of exceptionally high profits.

d.
The risk of small, frequent losses.

Answer 11

A

Question 12

Which statement best describes the purpose of the logistic regression model?

a.
To establish a linear relationship between variables.

b.
To predict values of a continuous outcome variable.

c.
To classify data into more than two categories.

d.
To model the relationship between a set of predictors and a binary outcome.

Answer 12

D

Question 13

An odds ratio less than 1 in logistic regression indicates that:

a.
The event becomes more likely as the predictor increases.

b.
The predictor has no effect on the event.

c.
The likelihood of the event decreases as the predictor increases.

d.
The event is certain to happen.

Answer 13

C

Question 14

For a portfolio, if the 99% one-day VaR is calculated to be $10,000, what would be the Expected Shortfall (ES) if the average loss on the worst 1% days is $15,000?

a.
$11,000

b.
$15,000

c.
$25,000

d.
$10,000

Answer 14

B

Question 15

Which statement is not true regarding the interpretation of odds ratios in logistic regression?

a.
An odds ratio greater than 1 suggests an increased likelihood of the event occurring.

b.
The odds ratio can never be less than 0.

c.
An odds ratio less than 1 indicates an increased likelihood of the event occurring.

d.
An odds ratio of 1 means the predictor has no effect.

Answer 15

C?
Gemini Got This Wrong

Question 16

What is the primary advantage of logistic regression over linear regression for binary outcomes?

a.
Logistic regression provides probabilities for binary outcomes.

b.
Logistic regression can be used with any number of predictor variables.

c.
Logistic regression is computationally less complex.

d.
Logistic regression can handle larger datasets.

Answer 16

A

Question 17

What type of variable is best suited for logistic regression analysis?

a.
Both continuous and categorical variables

b.
Categorical variables only

c.
Continuous variables only

d.
Time-series data

Answer 17

A

Question 18

If the 95% one-day VaR for an investment is $5,000 and the average loss for the worst 5% of days is $7,000, what is the Expected Shortfall (ES) at the 95% confidence level?

a.
$12,000

b.
$5,000

c.
$7,000

d.
$6,000

Answer 18

C

Question 19

Which factor is crucial for accurately calculating Value at Risk (VaR)?

a.
The liquidity of the underlying assets.

b.
The selection of an appropriate confidence level.

c.
The historical correlation between asset returns.

d.
The use of real-time market data.

Answer 19

B

Question 20

In logistic regression, what does the term ‘log odds’ refer to?

a.
The probability of the dependent variable occurring.

b.
The natural log of the odds of the dependent variable event occurring.

c.
A transformation of the independent variable.

d.
The ratio of the number of events to non-events.

Answer 20

B

Question 21

Why is logistic regression preferred over linear regression for binary outcomes?

a.
Because it is computationally faster.

b.
Because it predicts numerical values.

c.
Because it models the probability of binary outcomes.

d.
Because it can process more data.

Answer 21

C

Question 22

What does a logistic regression model estimate?

a.
The correlation between two variables

b.
The variance of the independent variables

c.
The probability of a specific outcome

d.
The mean of a response variable

Answer 22

C

Question 23

The Expected Shortfall at a 99% confidence level indicates that:

a.
The average loss in the worst 1% of cases will be equal to the Expected Shortfall.

b.
99% of all losses will be less than or equal to the Expected Shortfall.

c.
The portfolio will not lose more than the Expected Shortfall in 99% of cases.

d.
1% of all losses will be greater than the Expected Shortfall.

Answer 23

A

Question 24

Logistic regression is typically used for:

a.
Predicting any continuous variable from categorical variables.

b.
Predicting a categorical variable from continuous or categorical variables.

c.
Predicting a continuous variable from categorical or continuous variables.

d.
Predicting a categorical variable from several other categorical variables.

Answer 24

B

Question 25

A Value at Risk (VaR) measure does not provide information about: a. The probability of exceeding the VaR amount. b. The time period over which the VaR is calculated. c. The size of potential losses beyond the VaR threshold. d. The average loss expected within the VaR threshold.

Answer 25

C

Question 26

What is the main criticism of the Value at Risk (VaR) model in risk management? a. It fails to accurately predict the probability of extreme losses. b. It overestimates the risk in volatile markets. c. It is too complex to be implemented effectively. d. It underestimates the risk in stable markets.

Answer 26

A

Question 27

For a predictor in a logistic regression model, a coefficient close to zero indicates: a. The predictor is highly significant. b. The predictor has little effect on the probability of the outcome. c. The predictor is the only significant variable in the model. d. The predictor inversely affects the outcome.

Answer 27

B

Question 28

The logit function in logistic regression is used to: a. Directly predict the outcome variable. b. Convert all variables to a log scale. c. Normalize the predictor variables. d. Model the probability of the outcome as a linear function of the predictors.

Answer 28

D

Question 29

In the logistic regression equation, what role does the intercept play? a. It is always equal to 1. b. It represents the slope of the relationship. c. It indicates the variance of the predictors. d. It is the log odds of the outcome when all predictors are zero.

Answer 29

D

Question 30

If the Value at Risk (VaR) for a portfolio is calculated to be $5 million at a 95% confidence level, this implies: a. There is a 5% chance that the portfolio will lose more than $5 million over the specified period. b. The portfolio will definitely lose $5 million in 95% of the cases. c. There is a 95% chance that the portfolio will lose exactly $5 million. d. The portfolio will not lose more than $5 million in 95% of the cases.

Answer 30

A Both A & D are technicall correct. However, A is the most direct and commonly emphasized implication.

Question 31

If a portfolio has a 95% one-month VaR of $2 million, this means: a. The portfolio will lose at least $2 million in 5% of months. b. There is a 5% chance of losing more than $2 million in any given month. c. The portfolio will lose exactly $2 million in 95% of months. d. The portfolio is guaranteed not to lose more than $2 million in a month.

Answer 31

B

Question 32

A key difference between VaR and Expected Shortfall (ES) is that: a. ES is always higher than VaR. b. VaR is a more conservative estimate of risk. c. VaR is easier to calculate under non-normal distributions. d. ES considers the average loss beyond the VaR estimate.

Answer 32

D Why not A? ES is always higher than VaR. While ES is often higher than VaR, this isn't universally true, especially under certain unusual distribution assumptions (though it generally holds for typical financial return distributions). The ***key*** difference is what they measure.

Question 33

Which of the following is true? a. Expected shortfall is sometimes greater than VaR and sometimes less than VaR b. Expected shortfall is always greater than VaR c. Expected shortfall does not depend on the shape of the tail of the distribution d. Expected shortfall is a measure of liquidity risk whereas VaR is a measure of market risk

Answer 33

B

Question 34

A logit function in logistic regression is defined as: a. A logarithmic transformation of the response variable. b. A linear function of the predictors. c. The natural logarithm of the odds of the outcome. d. The inverse of the logistic function.

Answer 34

C

Question 35

In logistic regression, a logit link function is used to: a. Convert all variables into binary form. b. Connect the linear predictors to the probability of the outcome. c. Linearly relate the predictors to the outcome variable. d. Transform the predictors to a logarithmic scale.

Answer 35

B

Question 36

In terms of risk measurement, the primary advantage of Expected Shortfall (ES) over Value at Risk (VaR) is: a. ES is not influenced by the holding period of assets. b. ES takes into account the shape of the tail of the loss distribution. c. ES focuses solely on the maximum loss potential. d. ES is a simpler calculation than VaR.

Answer 36

B

Question 37

What does a higher Value at Risk (VaR) indicate about an investment's risk? a. A lower probability of incurring significant losses. b. A higher potential for gain. c. A more stable investment. d. A higher potential for loss.

Answer 37

D

Question 38

In the context of logistic regression, multicollinearity among predictors: a. Improves the accuracy of the model. b. Has no effect on the model's performance. c. Can distort the estimated coefficients and their significance. d. Is required for accurate predictions.

Answer 38

C

Question 39

Suppose you have a portfolio. The value at risk of your portfolio is: a. the portfolio loss that you may experience with a certain probability in the worst case b. the standard deviation of your portfolio over a specified holding period c. the average portfolio loss that you may experience over a specified holding period d. the amount of capital needed to recover your portfolio loss

Answer 39

A

Question 40

A $10 million VaR with 95% confidence means: a. there is only a 5% chance that we will gain more than $10 million. b. the loss is expected to be at most $10 million in 95% of the cases. c. the minimum loss is expected to be at least $10 million in 95% of the cases. d. the VaR is $1 million with 95% confidence.

Answer 40

B

Question 41

In logistic regression, what does a significant p-value for a coefficient suggest? a. The coefficient is less than 1. b. The coefficient is equal to 0. c. The predictor should be removed from the model. d. The predictor is likely to be a meaningful addition to the model.

Answer 41

D

Question 42

A one-day 95% value at risk of $100,000 means that: a. the loss is expected to be at least $100,000 at the 95% confidence level b. the maximum loss over one-day is about $100,000 at the 95% confidence level c. the minimum loss over one-day is about $100,000 at the 5% confidence level d. the expected shortfall is $100,000 with 95% confidence

Answer 42

B

Question 43

When flipping a fair coin, the odds of getting tails are: a. 0.5 b. 0 c. -1 d. 1

Answer 43

D

Question 44

What does an odds ratio of more than 1 signify in a logistic regression model? a. The event is more likely to occur as the predictor value increases. b. The event's probability is equal to 1. c. The event becomes less likely as the predictor increases. d. The odds ratio has no significant interpretation.

Answer 44

A

Question 45

What is the role of the logit function in logistic regression? a. It linearly relates independent variables to the probability of the outcome b. It is used for error correction c. It calculates the mean of the dataset d. It predicts continuous outcomes

Answer 45

A

Question 46

If the 95% one-day VaR for a portfolio is $500,000, what does it imply? a. The portfolio has a 95% chance of losing exactly $500,000 in a single day. b. The portfolio will lose $500,000 over the course of 95 days. c. In 95% of days, the portfolio will lose more than $500,000. d. There is a 5% probability that the portfolio will lose more than $500,000 in one day.

Answer 46

D

Question 47

In logistic regression, the outcome variable is typically: a. Continuous and normally distributed. b. A ratio or interval variable. c. Categorical, often binary. d. Any type, including numeric or categorical.

Answer 47

C

Question 48

In logistic regression, the range of the dependent variable (probability of success) is: a. (-∞, 0) b. (0, 1) c. (-∞, ∞) d. (0, ∞)

Answer 48

B

Question 49

The Expected Shortfall (ES) at a 90% confidence level generally represents: a. The average loss on the best 90% of trading days. b. The average loss in the worst 10% of cases beyond the VaR level. c. The median loss level over a specified time period. d. The maximum loss expected on the worst 10% of trading days.

Answer 49

B Key word being ***beyond***

Question 50

The logistic regression model is used when the outcome variable is: a. A categorical variable with two levels (binary). b. A high-dimensional data set. c. A time-series data. d. A continuous variable.

Answer 50

A

Question 51

Which statement is true about Value at Risk (VaR)? a. It measures the average loss over a specified time frame. b. It quantifies the worst expected loss at a specific confidence level over a set period. c. It remains constant regardless of market conditions. d. It accurately predicts the exact amount of maximum loss.

Answer 51

B

Question 52

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Question 53

What does the term 'logit' represent in logistic regression? a. The natural logarithm of the odds. b. A special type of logarithmic function. c. A logarithmic transformation of the predictors. d. The sum of the logged odds.

Answer 53

A

Question 54

What is logistic regression primarily used for? a. Predicting continuous outcomes b. Classifying outcomes into categories c. Finding correlations between variables d. Time-series analysis

Answer 54

B

Question 55

How does Expected Shortfall (ES) address a limitation of the Value at Risk (VaR) model? a. By considering only the average losses that are below the VaR threshold. b. By reducing the computation complexity in volatile markets. c. By providing a more conservative estimate of risk. d. By focusing on the tail-end losses beyond the VaR threshold.

Answer 55

D

Question 56

A Value at Risk (VaR) measure at the 97.5% confidence level means: a. The portfolio is completely safe from any loss 97.5% of the time. b. The loss will exceed the VaR amount in 2.5% of cases. c. The maximum loss will not exceed the VaR amount in 97.5% of cases. d. There is a 97.5% chance of incurring a loss greater than the VaR.

Answer 56

B

Question 57

Value at Risk for a given equity portfolio is: a. the underlying volatility of the equity portfolio b. the regulatory capital needed to cover the underlying risk in the equity portfolio c. the worst case loss that can be experienced in the equity portfolio with a certain level of probability d. the maximum loss that can be experienced in the equity portfolio over a specified holding period

Answer 57

C

Question 58

Expected Shortfall (ES) is particularly useful for: a. Measuring potential losses in highly volatile markets. b. Estimating the highest possible profit in adverse market conditions. c. Assessing the risk of assets with normal distribution of returns. d. Predicting the specific days when losses will exceed a certain amount.

Answer 58

A

Question 59

What does the coefficient in a logistic regression model represent? a. The degree of correlation between variables b. The average value of the response variable c. The error margin in predictions d. The change in the outcome's log odds for a one-unit change in the predictor

Answer 59

D

Question 60

When applying logistic regression, what is the implication of an odds ratio of 0.5 for a predictor? a. The predictor has no effect on the likelihood of the event. b. The probability of the event occurring is 50%. c. The event is twice as likely to occur with a one-unit increase in the predictor. d. The event is half as likely to occur with a one-unit increase in the predictor.

Answer 60

D

Question 61

The logit in logistic regression is: a. A logarithm of a digit b. The natural logarithm of the odds c. An instruction to record the data d. The cube root of the sample size

Answer 61

B

Question 62

How does multicollinearity affect logistic regression models? a. It ensures the model's coefficients are significant. b. It increases the predictive power of the model. c. It can lead to unreliable and unstable estimates of regression coefficients. d. It is necessary for the model to make accurate predictions.

Answer 62

C

Question 63

A portfolio has a non-normal distribution of returns with a 95% one-week VaR of $15,000. If the average weekly loss in the worst 5% of cases is $20,000, calculate the one-week Expected Shortfall. a. $15,000 b. $22,500 c. $17,500 d. $20,000

Answer 63

D

Question 64

Which of the following best describes the logistic function in logistic regression? a. It calculates the logarithm of the predictors. b. It is used to ensure the residuals are normally distributed. c. It is a linear transformation of the predictors. d. It transforms the linear regression output to a probability.

Answer 64

D

Question 65

In logistic regression, the odds ratio is defined as: a. The probability of an event occurring. b. The ratio of the probability of an event not happening to the probability of the event happening. c. The ratio of the odds after a unit change in the predictor to the original odds. d. The ratio of the probability of an event happening to the probability of the event not happening.

Answer 65

C? Gemini and ChatGPT got this wrong thinking it was D.

Question 66

Which statement is not true regarding the interpretation of odds ratios in logistic regression? a. An odds ratio less than 1 indicates an increased likelihood of the event occurring. b. The odds ratio can never be less than 0. c. An odds ratio of 1 means the predictor has no effect. d. An odds ratio greater than 1 suggests an increased likelihood of the event occurring.

Answer 66

A

Question 67

Expected Shortfall (ES) is considered a better risk measure than Value at Risk (VaR) because: a. It is easier to calculate than VaR. b. It requires less data to compute accurately. c. It accounts for all possible losses beyond the VaR threshold. d. It only considers the average loss in the worst-case scenarios.

Answer 67

C

Question 68

In logistic regression, a significant negative coefficient for a predictor variable indicates that: a. The likelihood of the outcome increases with the predictor. b. The predictor and the outcome are positively correlated. c. The predictor is irrelevant to the model. d. As the predictor increases, the probability of the outcome decreases.

Answer 68

D

Question 69

One limitation of Value at Risk (VaR) as a risk measure is that it: a. Requires an excessively long historical data series. b. Overestimates the risk in a portfolio. c. Always calculates lower risk than Expected Shortfall. d. Does not provide information about losses exceeding the VaR threshold.

Answer 69

D

Question 70

Which of the following is not related to the definition of VaR? a. Non-normality of returns b. Risk measure c. Tolerance level d. Worst case loss

Answer 70

A

Question 71

The 99% value at risk means that: a. there is 1% chance that the loss will not exceed the value at risk b. there is 99% chance that the loss will exceed the value at risk c. there is 1% chance that the loss will exceed the value at risk d. there is 99% chance that the expected shortfall will exceed the value at risk

Answer 71

C

Question 72

Which of the following is not true about Expected Shortfall (ES)? a. ES is derived from the VaR at risk for a portfolio or investment. b. The use of VaR as apposed to just ES tends to lead to a more conservative approach in terms of risk exposure. c. ES is also called Conditional VaR. d. ES attempts to address the shortcomings of the VaR model.

Answer 72

B

Question 73

The main difference between Value at Risk (VaR) and Expected Shortfall (ES) is: a. VaR accounts for the average loss in the worst-case scenario, while ES does not. b. VaR is a measure of market risk, whereas ES is a measure of credit risk. c. ES is less accurate than VaR. d. ES considers the average loss beyond the VaR threshold, while VaR does not.

Answer 73

D

Question 74

In the context of risk management, why is Expected Shortfall (ES) often preferred over VaR? a. ES is based on a more realistic distribution of returns. b. ES provides a more detailed analysis of the potential maximum loss. c. ES takes into account the magnitude of extreme losses. d. ES is less affected by the volatility of the market.

Answer 74

C

Question 75

What does a logistic regression model predict? a. The probability of occurrence of a binary outcome. b. The exact value of the outcome variable. c. The correlation between predictor variables. d. The frequency of the outcome occurrence.

Answer 75

A

Question 76

Logistic regression assumes: a. A linear relationship between predictor variables. b. A linear relationship between predictor variables and the outcome variable. c. A linear relationship between observations. d. A linear relationship between predictor variables and the logit of the outcome variable.

Answer 76

D