# P1.T2. Quantitative Analysis

Practice questions for Quantitative Analysis: Econometrics, MCS, Volatility, Probability Distributions and VaR (Intro)

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1. ### Test-Questions as collection?

T. Flockert, Thanks for appreciating these quant questions... 1. They are from the 2008 season: I wrote them all. See http://www.bionicturtle.com/premium/quizzes/category/frm_product/ for inventory of practice questions. Near the bottom @ http://www.bionicturtle.com/premium/quiz/2008_quantitative/ (in the flash quiz that has printout ability) 2. Yes, that is the goal but, beyond the...
T. Flockert, Thanks for appreciating these quant questions... 1. They are from the 2008 season: I wrote them all. See http://www.bionicturtle.com/premium/quizzes/category/frm_product/ for inventory of practice questions. Near the bottom @ http://www.bionicturtle.com/premium/quiz/2008_quantitative/ (in the flash quiz that has printout ability) 2. Yes, that is the goal but, beyond the...
T. Flockert, Thanks for appreciating these quant questions... 1. They are from the 2008 season: I wrote them all. See http://www.bionicturtle.com/premium/quizzes/category/frm_product/ for inventory of practice questions. Near the bottom @...
T. Flockert, Thanks for appreciating these quant questions... 1. They are from the 2008 season: I wrote them all. See http://www.bionicturtle.com/premium/quizzes/category/frm_product/ for...
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2. ### Question 9: Key operational process

Question: We observe that 5 errors per day are made with respect to a key operational process. What are the odds that tomorrow (a full day) we will observe at least two (2) errors? A. 86.72% B. 4.25% C. 91.26% D. 95.96% Answer: D Explanation: This calls for a Poisson(5) distribution. The odds are 1 - [P(X=0) + P(X=1)] because it's the odds that we don't observe zero or one errors....
Question: We observe that 5 errors per day are made with respect to a key operational process. What are the odds that tomorrow (a full day) we will observe at least two (2) errors? A. 86.72% B. 4.25% C. 91.26% D. 95.96% Answer: D Explanation: This calls for a Poisson(5) distribution. The odds are 1 - [P(X=0) + P(X=1)] because it's the odds that we don't observe zero or one errors....
Question: We observe that 5 errors per day are made with respect to a key operational process. What are the odds that tomorrow (a full day) we will observe at least two (2) errors? A. 86.72% B. 4.25% C. 91.26% D. 95.96% Answer: D Explanation: This calls for a Poisson(5) distribution....
Question: We observe that 5 errors per day are made with respect to a key operational process. What are the odds that tomorrow (a full day) we will observe at least two (2) errors? A. 86.72% ...
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3. ### Question 99: Actual asset returns

Question: According to Linda Allen, actual asset returns tend to differ from the a normal distribution in each of the following ways EXCEPT FOR: A. Fat-tailed B. Skewed C. Unstable D. Lognormal Answer: D Explanation: Actual returns tend to be fat-tailed (leptokurtosis), skewed (asymmetrical), and unstable (parameters vary over time). Period returns do not tend to be lognormal;...
Question: According to Linda Allen, actual asset returns tend to differ from the a normal distribution in each of the following ways EXCEPT FOR: A. Fat-tailed B. Skewed C. Unstable D. Lognormal Answer: D Explanation: Actual returns tend to be fat-tailed (leptokurtosis), skewed (asymmetrical), and unstable (parameters vary over time). Period returns do not tend to be lognormal;...
Question: According to Linda Allen, actual asset returns tend to differ from the a normal distribution in each of the following ways EXCEPT FOR: A. Fat-tailed B. Skewed C. Unstable D. Lognormal Answer: D Explanation: Actual returns tend to be fat-tailed (leptokurtosis), skewed...
Question: According to Linda Allen, actual asset returns tend to differ from the a normal distribution in each of the following ways EXCEPT FOR: A. Fat-tailed B. Skewed C. Unstable D....
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4. ### Question 98: Implied standard deviation

Question: Say we want to follow Jorion's advice: "whenever possible, VAR should use implied parameters."If we want to estimate the implied standard deviation (ISD) of an option, which of the following makes our task MOST DIFFICULT? A. Lack of market price B. Volatility smile or smirk C. Volatility clustering D. Options on same asset trade differently Answer: A Explanation: We need...
Question: Say we want to follow Jorion's advice: "whenever possible, VAR should use implied parameters."If we want to estimate the implied standard deviation (ISD) of an option, which of the following makes our task MOST DIFFICULT? A. Lack of market price B. Volatility smile or smirk C. Volatility clustering D. Options on same asset trade differently Answer: A Explanation: We need...
Question: Say we want to follow Jorion's advice: "whenever possible, VAR should use implied parameters."If we want to estimate the implied standard deviation (ISD) of an option, which of the following makes our task MOST DIFFICULT? A. Lack of market price B. Volatility smile or smirk C....
Question: Say we want to follow Jorion's advice: "whenever possible, VAR should use implied parameters."If we want to estimate the implied standard deviation (ISD) of an option, which of the...
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5. ### Question 97: Estimating correlation

Question: When estimating correlation, what is the main challenge of in extending the GARCH model used for volatility to the multivariate GARCH model for correlations? A. Correlation not necessarily mean reverting B. Almost impossible to parameterize persistence C. Accuracy requires many lagged factors (long time series) D. Number of parameters increases exponentially Answer: D ...
Question: When estimating correlation, what is the main challenge of in extending the GARCH model used for volatility to the multivariate GARCH model for correlations? A. Correlation not necessarily mean reverting B. Almost impossible to parameterize persistence C. Accuracy requires many lagged factors (long time series) D. Number of parameters increases exponentially Answer: D ...
Question: When estimating correlation, what is the main challenge of in extending the GARCH model used for volatility to the multivariate GARCH model for correlations? A. Correlation not necessarily mean reverting B. Almost impossible to parameterize persistence C. Accuracy requires many...
Question: When estimating correlation, what is the main challenge of in extending the GARCH model used for volatility to the multivariate GARCH model for correlations? A. Correlation not...
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6. ### Question 96: Squared return

Question: If the average lambda under the RiskMetrics approach is 0.94 under daily intervals, what weight is effectively assigned to the squared return on day n-2 (not yesterday, but the day before yesterday)? A. 0.06 B. 0.0036 C. 0.0564 D. 0.94 Answer: C Explanation: The most recent weight is (1-lambda) = 6%. Throughout the series, each weight is a constant proportion of its...
Question: If the average lambda under the RiskMetrics approach is 0.94 under daily intervals, what weight is effectively assigned to the squared return on day n-2 (not yesterday, but the day before yesterday)? A. 0.06 B. 0.0036 C. 0.0564 D. 0.94 Answer: C Explanation: The most recent weight is (1-lambda) = 6%. Throughout the series, each weight is a constant proportion of its...
Question: If the average lambda under the RiskMetrics approach is 0.94 under daily intervals, what weight is effectively assigned to the squared return on day n-2 (not yesterday, but the day before yesterday)? A. 0.06 B. 0.0036 C. 0.0564 D. 0.94 Answer: C Explanation: The most recent...
Question: If the average lambda under the RiskMetrics approach is 0.94 under daily intervals, what weight is effectively assigned to the squared return on day n-2 (not yesterday, but the day...
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7. ### Question 95: Mean-reverting

Question: Here is the GARCH(1,1) specification: variance = omega + (alpha)(lagged, squared return)+(beta)(lagged variance). In the first series, alpha = 0.1 and beta = 0.7. In the second series, alpha = 0.2 and beta = 0.9. Which series is mean-reverting? A. First B. Second C. Both D. Neither Answer: A Explanation: Alpha and beta are here the weights assigned, respectively, to the...
Question: Here is the GARCH(1,1) specification: variance = omega + (alpha)(lagged, squared return)+(beta)(lagged variance). In the first series, alpha = 0.1 and beta = 0.7. In the second series, alpha = 0.2 and beta = 0.9. Which series is mean-reverting? A. First B. Second C. Both D. Neither Answer: A Explanation: Alpha and beta are here the weights assigned, respectively, to the...
Question: Here is the GARCH(1,1) specification: variance = omega + (alpha)(lagged, squared return)+(beta)(lagged variance). In the first series, alpha = 0.1 and beta = 0.7. In the second series, alpha = 0.2 and beta = 0.9. Which series is mean-reverting? A. First B. Second C. Both D....
Question: Here is the GARCH(1,1) specification: variance = omega + (alpha)(lagged, squared return)+(beta)(lagged variance). In the first series, alpha = 0.1 and beta = 0.7. In the second series,...
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8. ### Question 94: GARCH (1,1) and EWMA

Question: Which are advantages of the GARCH(1,1) approach over the EWMA approach? I. More weight on recent information, II. Mean reversion, III. Persistence A. I only B. II only C. II and III D. I, II, and III Answer: B Explanation: GARCH(1,1) incorporates reversion to the mean but EWMA does not. Both models, unlike the moving average, assign greater weight to more recent...
Question: Which are advantages of the GARCH(1,1) approach over the EWMA approach? I. More weight on recent information, II. Mean reversion, III. Persistence A. I only B. II only C. II and III D. I, II, and III Answer: B Explanation: GARCH(1,1) incorporates reversion to the mean but EWMA does not. Both models, unlike the moving average, assign greater weight to more recent...
Question: Which are advantages of the GARCH(1,1) approach over the EWMA approach? I. More weight on recent information, II. Mean reversion, III. Persistence A. I only B. II only C. II and III D. I, II, and III Answer: B Explanation: GARCH(1,1) incorporates reversion to the mean but...
Question: Which are advantages of the GARCH(1,1) approach over the EWMA approach? I. More weight on recent information, II. Mean reversion, III. Persistence A. I only B. II only C. II and...
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9. ### Question 93: Moving average

Question: The three prior daily returns for a stock are +1% , +2%, and +3% (day n-1 to day n-3, respectively). Apply Jorion's moving average (MA) over the three day window [i.e., MA(3)] to estimate current volatility. A. 0.02 B. 0.004 C. 0.0216 D. 0.024 Answer: C Explanation: Square each return (under MA the order does not matter) to produce this series: 0.0001, 0.0004, and 0.0009....
Question: The three prior daily returns for a stock are +1% , +2%, and +3% (day n-1 to day n-3, respectively). Apply Jorion's moving average (MA) over the three day window [i.e., MA(3)] to estimate current volatility. A. 0.02 B. 0.004 C. 0.0216 D. 0.024 Answer: C Explanation: Square each return (under MA the order does not matter) to produce this series: 0.0001, 0.0004, and 0.0009....
Question: The three prior daily returns for a stock are +1% , +2%, and +3% (day n-1 to day n-3, respectively). Apply Jorion's moving average (MA) over the three day window [i.e., MA(3)] to estimate current volatility. A. 0.02 B. 0.004 C. 0.0216 D. 0.024 Answer: C Explanation: Square...
Question: The three prior daily returns for a stock are +1% , +2%, and +3% (day n-1 to day n-3, respectively). Apply Jorion's moving average (MA) over the three day window [i.e., MA(3)] to...
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10. ### Question 92: Distribution

Question: An analysis of typical financial asset returns produces a distribution that has fatter tails than implied by a normal distribution. Which explanation is LEAST LIKELY? A. Non-normal distribution B. Sample too small; larger will converge to normal C. mean is time-varying D. volatility is time-varying Answer: B Explanation: Although the sample may be too small, the best...
Question: An analysis of typical financial asset returns produces a distribution that has fatter tails than implied by a normal distribution. Which explanation is LEAST LIKELY? A. Non-normal distribution B. Sample too small; larger will converge to normal C. mean is time-varying D. volatility is time-varying Answer: B Explanation: Although the sample may be too small, the best...
Question: An analysis of typical financial asset returns produces a distribution that has fatter tails than implied by a normal distribution. Which explanation is LEAST LIKELY? A. Non-normal distribution B. Sample too small; larger will converge to normal C. mean is time-varying D....
Question: An analysis of typical financial asset returns produces a distribution that has fatter tails than implied by a normal distribution. Which explanation is LEAST LIKELY? A. Non-normal...
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11. ### Question 91: P value

Hi Mike, It's tricky, strictly speaking, there is a difference (but i think an indirect relationship if you will) between the p-value and the significance level (the significance level = probably of committing a Type I error; i.e., mistakenly rejecting a true null). The trick part is that the p-value is the "exact significance level" The link above, in case you didn't drill down, is the...
Hi Mike, It's tricky, strictly speaking, there is a difference (but i think an indirect relationship if you will) between the p-value and the significance level (the significance level = probably of committing a Type I error; i.e., mistakenly rejecting a true null). The trick part is that the p-value is the "exact significance level" The link above, in case you didn't drill down, is the...
Hi Mike, It's tricky, strictly speaking, there is a difference (but i think an indirect relationship if you will) between the p-value and the significance level (the significance level = probably of committing a Type I error; i.e., mistakenly rejecting a true null). The trick part is that the...
Hi Mike, It's tricky, strictly speaking, there is a difference (but i think an indirect relationship if you will) between the p-value and the significance level (the significance level =...
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12. ### Question 90: Two-tailed test

Question: When working, our machine produces ball bearings that are 10 centimeters in diameter. But not perfectly, as the (population) standard deviation is known to be 0.4 centimeters. We recently took a sample of 64 ball bearings. The sample mean diameter was 10.1 centimeters. Is the machine broken at, respectively, 1% and 5% significance levels using a two-tailed test? A. No (at 1%) and...
Question: When working, our machine produces ball bearings that are 10 centimeters in diameter. But not perfectly, as the (population) standard deviation is known to be 0.4 centimeters. We recently took a sample of 64 ball bearings. The sample mean diameter was 10.1 centimeters. Is the machine broken at, respectively, 1% and 5% significance levels using a two-tailed test? A. No (at 1%) and...
Question: When working, our machine produces ball bearings that are 10 centimeters in diameter. But not perfectly, as the (population) standard deviation is known to be 0.4 centimeters. We recently took a sample of 64 ball bearings. The sample mean diameter was 10.1 centimeters. Is the machine...
Question: When working, our machine produces ball bearings that are 10 centimeters in diameter. But not perfectly, as the (population) standard deviation is known to be 0.4 centimeters. We...
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13. ### Question 8: Expected value and variance

Question: You have determined that tomorrow's price for a stock will be either $10,$12, $15 or$18 with probabilities of 20%, 30%, 30%, and 20%, respectively. What is the expected value and variance of the tomorrow's stock price? A. $13.7 and$7.81 B. $14.0 and$6.5 C. $12.8 and$8.0 D. $15.0 and$2.5 Answer: A Explanation: The expected value is (10 x 20%) + (12 x 30%) + (15 x...
Question: You have determined that tomorrow's price for a stock will be either $10,$12, $15 or$18 with probabilities of 20%, 30%, 30%, and 20%, respectively. What is the expected value and variance of the tomorrow's stock price? A. $13.7 and$7.81 B. $14.0 and$6.5 C. $12.8 and$8.0 D. $15.0 and$2.5 Answer: A Explanation: The expected value is (10 x 20%) + (12 x 30%) + (15 x...
Question: You have determined that tomorrow's price for a stock will be either $10,$12, $15 or$18 with probabilities of 20%, 30%, 30%, and 20%, respectively. What is the expected value and variance of the tomorrow's stock price? A. $13.7 and$7.81 B. $14.0 and$6.5 C. $12.8 and$8.0 D....
Question: You have determined that tomorrow's price for a stock will be either $10,$12, $15 or$18 with probabilities of 20%, 30%, 30%, and 20%, respectively. What is the expected value and...
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14. ### Question 89: Confidence interval

Question: A sample of 25 firms gives a mean PE ratio of 19. We happen to know the population standard deviation is 10. What is the 95% confidence interval? A. 15.1 and 22.9 B. 15.8 and 22.3 C. 16.4 and 21.5 D. 17.5 and 22.5 Answer: A Explanation: The standard error = 10/SQRT(25) = 2.0. The confidence interval = 19 +/- (1.96)(2). Note we know the population variance, so we can use...
Question: A sample of 25 firms gives a mean PE ratio of 19. We happen to know the population standard deviation is 10. What is the 95% confidence interval? A. 15.1 and 22.9 B. 15.8 and 22.3 C. 16.4 and 21.5 D. 17.5 and 22.5 Answer: A Explanation: The standard error = 10/SQRT(25) = 2.0. The confidence interval = 19 +/- (1.96)(2). Note we know the population variance, so we can use...
Question: A sample of 25 firms gives a mean PE ratio of 19. We happen to know the population standard deviation is 10. What is the 95% confidence interval? A. 15.1 and 22.9 B. 15.8 and 22.3 C. 16.4 and 21.5 D. 17.5 and 22.5 Answer: A Explanation: The standard error = 10/SQRT(25) =...
Question: A sample of 25 firms gives a mean PE ratio of 19. We happen to know the population standard deviation is 10. What is the 95% confidence interval? A. 15.1 and 22.9 B. 15.8 and 22.3 ...
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15. ### Question 88: Outcome

Question: Which of the following is the least likely outcome? A. Reject null but make Type I error B. Reject null with no error C. Fail to reject null but Type II error D. Fail to reject null but make Type I error Answer: D Explanation: A Type I error is to mistakenly reject a true null, so (D) is not only unlikely, (D) is IMPOSSIBLE. If we do not reject the error, either our...
Question: Which of the following is the least likely outcome? A. Reject null but make Type I error B. Reject null with no error C. Fail to reject null but Type II error D. Fail to reject null but make Type I error Answer: D Explanation: A Type I error is to mistakenly reject a true null, so (D) is not only unlikely, (D) is IMPOSSIBLE. If we do not reject the error, either our...
Question: Which of the following is the least likely outcome? A. Reject null but make Type I error B. Reject null with no error C. Fail to reject null but Type II error D. Fail to reject null but make Type I error Answer: D Explanation: A Type I error is to mistakenly reject a true...
Question: Which of the following is the least likely outcome? A. Reject null but make Type I error B. Reject null with no error C. Fail to reject null but Type II error D. Fail to reject...
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16. ### Question 87: Null hypothesis

Question: Which of the following cannot be a NULL hypothesis? A. True mean = 18.5 B. True mean >= 18.5 C. True mean <= 18.5 D. True mean <> 18.5 Answer: D Explanation: The null cannot be the hypothesis that the true mean is either less than or greater than some value. We cannot know where to anchor our test. A, B, and C can be null hypotheses; A is two-tailed while B and C are...
Question: Which of the following cannot be a NULL hypothesis? A. True mean = 18.5 B. True mean >= 18.5 C. True mean <= 18.5 D. True mean <> 18.5 Answer: D Explanation: The null cannot be the hypothesis that the true mean is either less than or greater than some value. We cannot know where to anchor our test. A, B, and C can be null hypotheses; A is two-tailed while B and C are...
Question: Which of the following cannot be a NULL hypothesis? A. True mean = 18.5 B. True mean >= 18.5 C. True mean <= 18.5 D. True mean <> 18.5 Answer: D Explanation: The null cannot be the hypothesis that the true mean is either less than or greater than some value. We cannot know...
Question: Which of the following cannot be a NULL hypothesis? A. True mean = 18.5 B. True mean >= 18.5 C. True mean <= 18.5 D. True mean <> 18.5 Answer: D Explanation: The null cannot...
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17. ### Question 86: Estimator

Question: If an estimator is BLUE, all of the following must be true except: A. Minimum variance B. Normality C. Linearity D. Efficiency Answer: B Explanation: Regarding (D), an efficient estimator is the smallest variance among unbiased estimators; so the BLUE property generally implies the efficiency property. However, BLUE does not require any distributional assumption.
Question: If an estimator is BLUE, all of the following must be true except: A. Minimum variance B. Normality C. Linearity D. Efficiency Answer: B Explanation: Regarding (D), an efficient estimator is the smallest variance among unbiased estimators; so the BLUE property generally implies the efficiency property. However, BLUE does not require any distributional assumption.
Question: If an estimator is BLUE, all of the following must be true except: A. Minimum variance B. Normality C. Linearity D. Efficiency Answer: B Explanation: Regarding (D), an efficient estimator is the smallest variance among unbiased estimators; so the BLUE property generally...
Question: If an estimator is BLUE, all of the following must be true except: A. Minimum variance B. Normality C. Linearity D. Efficiency Answer: B Explanation: Regarding (D), an...
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18. ### Question 85: Property

Question: If we estimate the sample mean as the sum of observations divided by (n-1), what property does our estimator exhibit? A. Unbiased B. Efficient C. BLUE D. Consistent Answer: D Explanation: Both BLUE and efficient include the unbiased criteria. But this estimator is biased (repeated applications do not on average coincide with the population mean). However, this estimator...
Question: If we estimate the sample mean as the sum of observations divided by (n-1), what property does our estimator exhibit? A. Unbiased B. Efficient C. BLUE D. Consistent Answer: D Explanation: Both BLUE and efficient include the unbiased criteria. But this estimator is biased (repeated applications do not on average coincide with the population mean). However, this estimator...
Question: If we estimate the sample mean as the sum of observations divided by (n-1), what property does our estimator exhibit? A. Unbiased B. Efficient C. BLUE D. Consistent Answer: D Explanation: Both BLUE and efficient include the unbiased criteria. But this estimator is biased...
Question: If we estimate the sample mean as the sum of observations divided by (n-1), what property does our estimator exhibit? A. Unbiased B. Efficient C. BLUE D. Consistent Answer: D ...
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19. ### Question 84: Assertions

Question: Consider these two assertions. 1. An unbiased estimator must equal the parameter; 2. An estimator can be minimum variance without being unbiased. A. True, True B. True, False C. False, True D. False, False Answer: C Explanation: 1. False: Unbiased means that E[estimator] = population parameter. But the estimator is a random variable, it will fluctuate around the...
Question: Consider these two assertions. 1. An unbiased estimator must equal the parameter; 2. An estimator can be minimum variance without being unbiased. A. True, True B. True, False C. False, True D. False, False Answer: C Explanation: 1. False: Unbiased means that E[estimator] = population parameter. But the estimator is a random variable, it will fluctuate around the...
Question: Consider these two assertions. 1. An unbiased estimator must equal the parameter; 2. An estimator can be minimum variance without being unbiased. A. True, True B. True, False C. False, True D. False, False Answer: C Explanation: 1. False: Unbiased means that E[estimator] =...
Question: Consider these two assertions. 1. An unbiased estimator must equal the parameter; 2. An estimator can be minimum variance without being unbiased. A. True, True B. True, False C....
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20. ### Question 83: Zones

Question: Under the Basel II internal models approach (IMA) to market risk, a bank must BACKTEST its VaR model. The null hypothesis in the backtest is "the bank's VaR model is 99% accurate." Because it cannot be proven that a VaR model is flawed, Basel uses traffic light zones (red, yellow, green). In which zone can a Type II error be committed? A. Green B. Yellow C. Red D. Green or Red ...
Question: Under the Basel II internal models approach (IMA) to market risk, a bank must BACKTEST its VaR model. The null hypothesis in the backtest is "the bank's VaR model is 99% accurate." Because it cannot be proven that a VaR model is flawed, Basel uses traffic light zones (red, yellow, green). In which zone can a Type II error be committed? A. Green B. Yellow C. Red D. Green or Red ...
Question: Under the Basel II internal models approach (IMA) to market risk, a bank must BACKTEST its VaR model. The null hypothesis in the backtest is "the bank's VaR model is 99% accurate." Because it cannot be proven that a VaR model is flawed, Basel uses traffic light zones (red, yellow,...
Question: Under the Basel II internal models approach (IMA) to market risk, a bank must BACKTEST its VaR model. The null hypothesis in the backtest is "the bank's VaR model is 99% accurate."...
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21. ### Question 82: Probability

Question: The sample mean P/E ratio among firms is 20. We want to test the null hypothesis that the true population mean is greater than or equal to 15 (null: population mean >= 15). If our desired confidence level is 95%, what is the probability of committing a Type I error? A. 0.95 B. 0.975 C. 0.05 D. 0.025 Answer: C Explanation: The significance of the test = 1 - confidence;...
Question: The sample mean P/E ratio among firms is 20. We want to test the null hypothesis that the true population mean is greater than or equal to 15 (null: population mean >= 15). If our desired confidence level is 95%, what is the probability of committing a Type I error? A. 0.95 B. 0.975 C. 0.05 D. 0.025 Answer: C Explanation: The significance of the test = 1 - confidence;...
Question: The sample mean P/E ratio among firms is 20. We want to test the null hypothesis that the true population mean is greater than or equal to 15 (null: population mean >= 15). If our desired confidence level is 95%, what is the probability of committing a Type I error? A. 0.95 B....
Question: The sample mean P/E ratio among firms is 20. We want to test the null hypothesis that the true population mean is greater than or equal to 15 (null: population mean >= 15). If our...
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22. ### Question 81: Probability

Question: How can we reduce the probability of both a Type I and Type II error simultaneously? A. Increase sample size B. Increase confidence and significance C. Decrease confidence and significance D. Impossible. Necessary trade-off Answer: A Explanation: To make a Type I error is to mistakenly reject a false null; to make a Type II error is to mistakenly accept a false null. If...
Question: How can we reduce the probability of both a Type I and Type II error simultaneously? A. Increase sample size B. Increase confidence and significance C. Decrease confidence and significance D. Impossible. Necessary trade-off Answer: A Explanation: To make a Type I error is to mistakenly reject a false null; to make a Type II error is to mistakenly accept a false null. If...
Question: How can we reduce the probability of both a Type I and Type II error simultaneously? A. Increase sample size B. Increase confidence and significance C. Decrease confidence and significance D. Impossible. Necessary trade-off Answer: A Explanation: To make a Type I error is...
Question: How can we reduce the probability of both a Type I and Type II error simultaneously? A. Increase sample size B. Increase confidence and significance C. Decrease confidence and...
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23. ### Question 80: Confidence interval

Question: If the confidence interval around a sample mean is a random interval, which of the following is true? A. Can't define limits B. Limits are random C. Don't know sample mean distribution D. None of above Answer: D Explanation: The confidence interval, by definition, is a random interval because we can expect a different interval (and sample mean) for each sample. Please...
Question: If the confidence interval around a sample mean is a random interval, which of the following is true? A. Can't define limits B. Limits are random C. Don't know sample mean distribution D. None of above Answer: D Explanation: The confidence interval, by definition, is a random interval because we can expect a different interval (and sample mean) for each sample. Please...
Question: If the confidence interval around a sample mean is a random interval, which of the following is true? A. Can't define limits B. Limits are random C. Don't know sample mean distribution D. None of above Answer: D Explanation: The confidence interval, by definition, is a...
Question: If the confidence interval around a sample mean is a random interval, which of the following is true? A. Can't define limits B. Limits are random C. Don't know sample mean...
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24. ### Question 7: Distribution

Ok thanks Hervé
Ok thanks Hervé
Ok thanks Hervé
Ok thanks Hervé
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25. ### Question 79: Critical t-value

Thanks. That's clear. Regards Hervé
Thanks. That's clear. Regards Hervé
Thanks. That's clear. Regards Hervé
Thanks. That's clear. Regards Hervé
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26. ### Question 78: Blue property

Question: The BLUE property combines all of the following properties EXCEPT: A. Linearity B. Unbiasedness C. Minimum variance D. Normality Answer: D Explanation: An estimator is called a best linear unbiased estimator (BLUE) if it is linear, unbiased and has a minimum variance. Note this will also tend to make it efficient.
Question: The BLUE property combines all of the following properties EXCEPT: A. Linearity B. Unbiasedness C. Minimum variance D. Normality Answer: D Explanation: An estimator is called a best linear unbiased estimator (BLUE) if it is linear, unbiased and has a minimum variance. Note this will also tend to make it efficient.
Question: The BLUE property combines all of the following properties EXCEPT: A. Linearity B. Unbiasedness C. Minimum variance D. Normality Answer: D Explanation: An estimator is called a best linear unbiased estimator (BLUE) if it is linear, unbiased and has a minimum variance. Note...
Question: The BLUE property combines all of the following properties EXCEPT: A. Linearity B. Unbiasedness C. Minimum variance D. Normality Answer: D Explanation: An estimator is called...
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27. ### Question 77: Which of the following doesn't belong

Question: Which of the following does not belong with others? A. Statistic B. Estimator C. Parameter D. SRF Answer: C Explanation: Statistic, estimator and sample regression function (SRF) all relate to samples; Parameters relate to population. Statistical interference is about collecting samples; e.g., we calculate a SAMPLE MEAN which is an ESTIMATOR or (sample) STATISTIC. We use...
Question: Which of the following does not belong with others? A. Statistic B. Estimator C. Parameter D. SRF Answer: C Explanation: Statistic, estimator and sample regression function (SRF) all relate to samples; Parameters relate to population. Statistical interference is about collecting samples; e.g., we calculate a SAMPLE MEAN which is an ESTIMATOR or (sample) STATISTIC. We use...
Question: Which of the following does not belong with others? A. Statistic B. Estimator C. Parameter D. SRF Answer: C Explanation: Statistic, estimator and sample regression function (SRF) all relate to samples; Parameters relate to population. Statistical interference is about...
Question: Which of the following does not belong with others? A. Statistic B. Estimator C. Parameter D. SRF Answer: C Explanation: Statistic, estimator and sample regression function...
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28. ### Question 76: Distribution

Question: As the degrees of freedom increase, to which distribution does the (i) student's t, (ii) chi-square and (iii) F distribution converge? A. normal, normal, normal B. normal, normal, Poisson C. normal, binomial, normal D. binomial, binomial, normal Answer: A Explanation: The student's t converges to the standard normal; i.e., it has mean of 0 and variance = df/(df-2). The...
Question: As the degrees of freedom increase, to which distribution does the (i) student's t, (ii) chi-square and (iii) F distribution converge? A. normal, normal, normal B. normal, normal, Poisson C. normal, binomial, normal D. binomial, binomial, normal Answer: A Explanation: The student's t converges to the standard normal; i.e., it has mean of 0 and variance = df/(df-2). The...
Question: As the degrees of freedom increase, to which distribution does the (i) student's t, (ii) chi-square and (iii) F distribution converge? A. normal, normal, normal B. normal, normal, Poisson C. normal, binomial, normal D. binomial, binomial, normal Answer: A Explanation: The...
Question: As the degrees of freedom increase, to which distribution does the (i) student's t, (ii) chi-square and (iii) F distribution converge? A. normal, normal, normal B. normal, normal,...
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29. ### Question 75: P value

Hi @SAhmed Apologies that even I can't find the link, this is an old question. It's looking for the F test of equality of variances (based on previously assigned Gujarati) So per F ratio = variance (larger)/variance(smaller), here the F ratio = 0.12^2/0.10^2 = 1.44 and the p-value (in Excel, but can be achieved via lookup) is given by F.DIST.RT(1.44, 29 df, 29 df) = 0.165836; i.e., the area...
Hi @SAhmed Apologies that even I can't find the link, this is an old question. It's looking for the F test of equality of variances (based on previously assigned Gujarati) So per F ratio = variance (larger)/variance(smaller), here the F ratio = 0.12^2/0.10^2 = 1.44 and the p-value (in Excel, but can be achieved via lookup) is given by F.DIST.RT(1.44, 29 df, 29 df) = 0.165836; i.e., the area...
Hi @SAhmed Apologies that even I can't find the link, this is an old question. It's looking for the F test of equality of variances (based on previously assigned Gujarati) So per F ratio = variance (larger)/variance(smaller), here the F ratio = 0.12^2/0.10^2 = 1.44 and the p-value (in Excel,...
Hi @SAhmed Apologies that even I can't find the link, this is an old question. It's looking for the F test of equality of variances (based on previously assigned Gujarati) So per F ratio =...
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30. ### Question 74: Null hypothesis

Question: We analyzed thirty daily returns (sample n = 30) and calculated a daily sample volatility of 1.2%. Can we reject the null hypothesis that 1.0% is the population volatility (i) with 95% confidence and (ii) with 99% confidence? A. no and no B. no and yes C. yes and no D. yes and yes Answer: A Explanation: This link goes to an EditGrid spreadsheet. Please see the SECOND...
Question: We analyzed thirty daily returns (sample n = 30) and calculated a daily sample volatility of 1.2%. Can we reject the null hypothesis that 1.0% is the population volatility (i) with 95% confidence and (ii) with 99% confidence? A. no and no B. no and yes C. yes and no D. yes and yes Answer: A Explanation: This link goes to an EditGrid spreadsheet. Please see the SECOND...
Question: We analyzed thirty daily returns (sample n = 30) and calculated a daily sample volatility of 1.2%. Can we reject the null hypothesis that 1.0% is the population volatility (i) with 95% confidence and (ii) with 99% confidence? A. no and no B. no and yes C. yes and no D. yes and...
Question: We analyzed thirty daily returns (sample n = 30) and calculated a daily sample volatility of 1.2%. Can we reject the null hypothesis that 1.0% is the population volatility (i) with 95%...
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