P1.T2. Quantitative Analysis

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

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  1. David Harper CFA FRM

    L1.T2.121 Extreme value distributions

    Hi @SheldonZ Jayanthi Sankaran[/USER] is correct: extreme value distributions was previously in the FRM Part 1 (Topic 2) because the assigned distribution reading included EV, but Miller doesn't address it, so EVT currently is only to be found in FRM Part 2 (Topic 6) and nowhere in Part 1; i.e., this is on older question. For Part 1, therefore, you don't need to worry about it. For Part 2,...
    Hi @SheldonZ Jayanthi Sankaran[/USER] is correct: extreme value distributions was previously in the FRM Part 1 (Topic 2) because the assigned distribution reading included EV, but Miller doesn't address it, so EVT currently is only to be found in FRM Part 2 (Topic 6) and nowhere in Part 1; i.e., this is on older question. For Part 1, therefore, you don't need to worry about it. For Part 2,...
    Hi @SheldonZ Jayanthi Sankaran[/USER] is correct: extreme value distributions was previously in the FRM Part 1 (Topic 2) because the assigned distribution reading included EV, but Miller doesn't address it, so EVT currently is only to be found in FRM Part 2 (Topic 6) and nowhere in Part 1;...
    Hi @SheldonZ Jayanthi Sankaran[/USER] is correct: extreme value distributions was previously in the FRM Part 1 (Topic 2) because the assigned distribution reading included EV, but Miller doesn't...
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  2. Fran

    P1.T2.301. Miller's probability matrix

    HI @ami44 Those are really thoughtful points, thank you. Yes, I do agree with your first point: default is a random variable characterized by a Bernoulli distribution (i.e., two discrete outcomes). The default probability (PD; aka, EDF) is really the mean (expected value) of the Bernoulli such that PD = E(X) = Prob(default) or P(X = 1) Similarly, my LGD is imprecise (at best). As you say,...
    HI @ami44 Those are really thoughtful points, thank you. Yes, I do agree with your first point: default is a random variable characterized by a Bernoulli distribution (i.e., two discrete outcomes). The default probability (PD; aka, EDF) is really the mean (expected value) of the Bernoulli such that PD = E(X) = Prob(default) or P(X = 1) Similarly, my LGD is imprecise (at best). As you say,...
    HI @ami44 Those are really thoughtful points, thank you. Yes, I do agree with your first point: default is a random variable characterized by a Bernoulli distribution (i.e., two discrete outcomes). The default probability (PD; aka, EDF) is really the mean (expected value) of the Bernoulli such...
    HI @ami44 Those are really thoughtful points, thank you. Yes, I do agree with your first point: default is a random variable characterized by a Bernoulli distribution (i.e., two discrete...
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  3. David Harper CFA FRM

    L1.T2.79 Hypothesis testing

    Thank you @Nicole Manley, your link is the correct reference :) @SheldonZ I fixed it above, but it's the same as Nicole already provided. Thanks!
    Thank you @Nicole Manley, your link is the correct reference :) @SheldonZ I fixed it above, but it's the same as Nicole already provided. Thanks!
    Thank you @Nicole Manley, your link is the correct reference :) @SheldonZ I fixed it above, but it's the same as Nicole already provided. Thanks!
    Thank you @Nicole Manley, your link is the correct reference :) @SheldonZ I fixed it above, but it's the same as Nicole already provided. Thanks!
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  4. Suzanne Evans

    P1.T2.217. Regression coefficients (Stock & Watson)

    Hi @SheldonZ I'm not sure which previous question to which you refer, but they are strictly correct. As I tried to explain above, if we really want to be strictly correct, the rules are: If we know the population variance, where X is the sample mean, then normal Z = (X - µ) / [σ/sqrt(n)] If we don't know the population variance, σ, which is almost always the use case, and we are using the...
    Hi @SheldonZ I'm not sure which previous question to which you refer, but they are strictly correct. As I tried to explain above, if we really want to be strictly correct, the rules are: If we know the population variance, where X is the sample mean, then normal Z = (X - µ) / [σ/sqrt(n)] If we don't know the population variance, σ, which is almost always the use case, and we are using the...
    Hi @SheldonZ I'm not sure which previous question to which you refer, but they are strictly correct. As I tried to explain above, if we really want to be strictly correct, the rules are: If we know the population variance, where X is the sample mean, then normal Z = (X - µ) / [σ/sqrt(n)] If...
    Hi @SheldonZ I'm not sure which previous question to which you refer, but they are strictly correct. As I tried to explain above, if we really want to be strictly correct, the rules are: If we...
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    157
  5. Nicole Manley

    P1.T2.600. Monte Carlo simulation, sampling error (Brooks)

    Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should read "In regard to true (A), (B), and (D), ..." You might notice that the explanation itemizes each of the TRUE (A), (B), and (D), specifically:
    Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should read "In regard to true (A), (B), and (D), ..." You might notice that the explanation itemizes each of the TRUE (A), (B), and (D), specifically:
    Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should read "In regard to true (A), (B), and (D), ..." You might notice that the explanation itemizes each...
    Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should...
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  6. Nicole Manley

    P1.T2.400. Fabozzi on simulations

    Hi [USER=38486]@ good question: no, the 95% confidence interval is not used because it cannot be used and is not needed. The CI is given by µ(sample) +/- (critical t)*(standard error), where (standard error) = (sample standard deviation)/sqrt(N). The 1/sqrt(N) indicates the key relationship between the length of the interval and sample size: for any given µ, critical-t, and sample standard...
    Hi [USER=38486]@ good question: no, the 95% confidence interval is not used because it cannot be used and is not needed. The CI is given by µ(sample) +/- (critical t)*(standard error), where (standard error) = (sample standard deviation)/sqrt(N). The 1/sqrt(N) indicates the key relationship between the length of the interval and sample size: for any given µ, critical-t, and sample standard...
    Hi [USER=38486]@ good question: no, the 95% confidence interval is not used because it cannot be used and is not needed. The CI is given by µ(sample) +/- (critical t)*(standard error), where (standard error) = (sample standard deviation)/sqrt(N). The 1/sqrt(N) indicates the key relationship...
    Hi [USER=38486]@ good question: no, the 95% confidence interval is not used because it cannot be used and is not needed. The CI is given by µ(sample) +/- (critical t)*(standard error), where...
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  7. David Harper CFA FRM

    L1.T2.72 Student's t distribution

    Hi SheldonZ, the df does not enter the calculation of the test statistic. Its calculated as: t = (x -mu) * sqrt(n)/ s where s is the sample standard deviation. The df comes into play at determining the critical value from the t - distribution, which you than use to compare it to the t - statistics from above, but that is not part of this exercise. I hope that helped. Addendum: Sometimes the...
    Hi SheldonZ, the df does not enter the calculation of the test statistic. Its calculated as: t = (x -mu) * sqrt(n)/ s where s is the sample standard deviation. The df comes into play at determining the critical value from the t - distribution, which you than use to compare it to the t - statistics from above, but that is not part of this exercise. I hope that helped. Addendum: Sometimes the...
    Hi SheldonZ, the df does not enter the calculation of the test statistic. Its calculated as: t = (x -mu) * sqrt(n)/ s where s is the sample standard deviation. The df comes into play at determining the critical value from the t - distribution, which you than use to compare it to the t -...
    Hi SheldonZ, the df does not enter the calculation of the test statistic. Its calculated as: t = (x -mu) * sqrt(n)/ s where s is the sample standard deviation. The df comes into play at...
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  8. Nicole Manley

    P1.T2.407. Univariate linear regression

    Got it now. Thanks everyone!
    Got it now. Thanks everyone!
    Got it now. Thanks everyone!
    Got it now. Thanks everyone!
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  9. Suzanne Evans

    P1.T2.221. Joint null hypothesis in multiple OLS regression

    @bpdulog Please note: I moved the new thread that you created to this thread, as this has already been discussed here. Thank you, Nicole
    @bpdulog Please note: I moved the new thread that you created to this thread, as this has already been discussed here. Thank you, Nicole
    @bpdulog Please note: I moved the new thread that you created to this thread, as this has already been discussed here. Thank you, Nicole
    @bpdulog Please note: I moved the new thread that you created to this thread, as this has already been discussed here. Thank you, Nicole
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  10. David Harper CFA FRM

    L1.T2.124 Exponential versus Poisson

    @bpdulog Those are correct using a binomial P [X<=2]. Your answers match the correct 124.2 :). Given the same assumptions (i.e., accurate 95% VaR model), 124.2 is looking for a binomial and 124.3 is looking for a Poisson distribution, with slightly different results.
    @bpdulog Those are correct using a binomial P [X<=2]. Your answers match the correct 124.2 :). Given the same assumptions (i.e., accurate 95% VaR model), 124.2 is looking for a binomial and 124.3 is looking for a Poisson distribution, with slightly different results.
    @bpdulog Those are correct using a binomial P [X<=2]. Your answers match the correct 124.2 :). Given the same assumptions (i.e., accurate 95% VaR model), 124.2 is looking for a binomial and 124.3 is looking for a Poisson distribution, with slightly different results.
    @bpdulog Those are correct using a binomial P [X=2]. Your answers match the correct 124.2 :). Given the same assumptions (i.e., accurate 95% VaR model), 124.2 is looking for a binomial and 124.3 is...
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    12
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  11. David Harper CFA FRM

    P1.T2.511. First-order autoregressive, AR(1), process

    [USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
    [USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
    [USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
    [USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
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  12. David Harper CFA FRM

    L1.T2.108 Volatility forecast with GARCH(1,1)

    Hi @Tania Pereira Right, either is acceptable and, in the case of question 108.3 above, it makes a difference: the given answer is 2.363% but if we instead computed a discrete daily return (i.e., 11.052/10 - 1 = 3.83%) then the 10-day volatility forecast is 2.429%, a difference of 0.066%. That's why this older question of mine is clearly imprecise (sorry): the question needs to specify that...
    Hi @Tania Pereira Right, either is acceptable and, in the case of question 108.3 above, it makes a difference: the given answer is 2.363% but if we instead computed a discrete daily return (i.e., 11.052/10 - 1 = 3.83%) then the 10-day volatility forecast is 2.429%, a difference of 0.066%. That's why this older question of mine is clearly imprecise (sorry): the question needs to specify that...
    Hi @Tania Pereira Right, either is acceptable and, in the case of question 108.3 above, it makes a difference: the given answer is 2.363% but if we instead computed a discrete daily return (i.e., 11.052/10 - 1 = 3.83%) then the 10-day volatility forecast is 2.429%, a difference of 0.066%. That's...
    Hi @Tania Pereira Right, either is acceptable and, in the case of question 108.3 above, it makes a difference: the given answer is 2.363% but if we instead computed a discrete daily return (i.e.,...
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    380
  13. David Harper CFA FRM

    L1.T2.70 Standard error

    Oh okay, sorry @bpdulog thank you for the heads-up! (you already copied Nicole so I won't again ....)
    Oh okay, sorry @bpdulog thank you for the heads-up! (you already copied Nicole so I won't again ....)
    Oh okay, sorry @bpdulog thank you for the heads-up! (you already copied Nicole so I won't again ....)
    Oh okay, sorry @bpdulog thank you for the heads-up! (you already copied Nicole so I won't again ....)
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  14. David Harper CFA FRM

    L1.T2.69 Sampling distribution

    Hi @bpdulog the variance is (technically) the second moment about the mean (or "around the mean"); aka, the second central moment. See As the standard deviation is the square root of variance, we can say the standard deviation is a function of the second (central) moment. The question just means to query this idea: the standard deviation of a sampling distribution is called a standard error....
    Hi @bpdulog the variance is (technically) the second moment about the mean (or "around the mean"); aka, the second central moment. See As the standard deviation is the square root of variance, we can say the standard deviation is a function of the second (central) moment. The question just means to query this idea: the standard deviation of a sampling distribution is called a standard error....
    Hi @bpdulog the variance is (technically) the second moment about the mean (or "around the mean"); aka, the second central moment. See As the standard deviation is the square root of variance, we can say the standard deviation is a function of the second (central) moment. The question just...
    Hi @bpdulog the variance is (technically) the second moment about the mean (or "around the mean"); aka, the second central moment. See As the standard deviation is the square root of variance, we...
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  15. David Harper CFA FRM

    L1.T2.71 Central limit theorem (CLT)

    Hi @bpdulog, I see this as, we are asked to calculate the probability of more than 120 loans will default but we are not given the mean value. But we have pd and n as you know we can calculate the mean=n*p=5000*2%=100 that is mean or we can say probability of default is 100. Thank you :)
    Hi @bpdulog, I see this as, we are asked to calculate the probability of more than 120 loans will default but we are not given the mean value. But we have pd and n as you know we can calculate the mean=n*p=5000*2%=100 that is mean or we can say probability of default is 100. Thank you :)
    Hi @bpdulog, I see this as, we are asked to calculate the probability of more than 120 loans will default but we are not given the mean value. But we have pd and n as you know we can calculate the mean=n*p=5000*2%=100 that is mean or we can say probability of default is 100. Thank you :)
    Hi @bpdulog, I see this as, we are asked to calculate the probability of more than 120 loans will default but we are not given the mean value. But we have pd and n as you know we can calculate...
    Replies:
    14
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    170
  16. Nicole Manley

    P1.T2.404. Basic Statistics

    Hi @theproman23 Yes, for observations i = {1 ....n), the sample variance is [Σ (Xi - µ)^2] /(N-1), where the numerator is the sum of squared differences (from the sample mean, µ, which i am here using to denote sample mean although it should be x-bar). Sample standard deviation is the square root of the sample variance. This question is testing logic against an understanding of these...
    Hi @theproman23 Yes, for observations i = {1 ....n), the sample variance is [Σ (Xi - µ)^2] /(N-1), where the numerator is the sum of squared differences (from the sample mean, µ, which i am here using to denote sample mean although it should be x-bar). Sample standard deviation is the square root of the sample variance. This question is testing logic against an understanding of these...
    Hi @theproman23 Yes, for observations i = {1 ....n), the sample variance is [Σ (Xi - µ)^2] /(N-1), where the numerator is the sum of squared differences (from the sample mean, µ, which i am here using to denote sample mean although it should be x-bar). Sample standard deviation is the square...
    Hi @theproman23 Yes, for observations i = {1 ....n), the sample variance is [Σ (Xi - µ)^2] /(N-1), where the numerator is the sum of squared differences (from the sample mean, µ, which i am here...
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    2
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  17. Nicole Manley

    P1.T2.405. Distributions I

    HI @theproman23 There is no sample so there is no standard error; question 405.1 is just asking about the properties of the given distribution. To contrast, let me ask a question that does invoke the standard error (which, in this case, is the standard deviation of a sample mean not a population). Here is the alternate question just for contrast: Assume a population with mean earnings of $2.5...
    HI @theproman23 There is no sample so there is no standard error; question 405.1 is just asking about the properties of the given distribution. To contrast, let me ask a question that does invoke the standard error (which, in this case, is the standard deviation of a sample mean not a population). Here is the alternate question just for contrast: Assume a population with mean earnings of $2.5...
    HI @theproman23 There is no sample so there is no standard error; question 405.1 is just asking about the properties of the given distribution. To contrast, let me ask a question that does invoke the standard error (which, in this case, is the standard deviation of a sample mean not a...
    HI @theproman23 There is no sample so there is no standard error; question 405.1 is just asking about the properties of the given distribution. To contrast, let me ask a question that does invoke...
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  18. Nicole Manley

    P1.T2.406. Distributions II

    Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e., we just take the ratio of the two sample variances, and this F-ratio (aka, variance ratio) is used to test the null hypothesis that the (underlying population) variances are equal. If the population...
    Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e., we just take the ratio of the two sample variances, and this F-ratio (aka, variance ratio) is used to test the null hypothesis that the (underlying population) variances are equal. If the population...
    Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e., we just take the ratio of the two sample variances, and this F-ratio (aka, variance ratio) is used to...
    Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e.,...
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  19. David Harper CFA FRM

    L1.T2.62 Expectation & variance of variable

    Hi @bpdulog (b) is a constant, given the domain it must be 0.10, such that the function is: f(x) = 0.1*x over [0, 1, 2, 3, 4]. So f(1) = 0.1, f(2) = 0.2, f(3) = 0.3 and f(4) = 0.4; these sum to 1.0 per the definition of a probability (the requirement is how we solved for constant b). Separately, we can ask, what is the mean of this function? The answer to that question is the sum of X*f(x),...
    Hi @bpdulog (b) is a constant, given the domain it must be 0.10, such that the function is: f(x) = 0.1*x over [0, 1, 2, 3, 4]. So f(1) = 0.1, f(2) = 0.2, f(3) = 0.3 and f(4) = 0.4; these sum to 1.0 per the definition of a probability (the requirement is how we solved for constant b). Separately, we can ask, what is the mean of this function? The answer to that question is the sum of X*f(x),...
    Hi @bpdulog (b) is a constant, given the domain it must be 0.10, such that the function is: f(x) = 0.1*x over [0, 1, 2, 3, 4]. So f(1) = 0.1, f(2) = 0.2, f(3) = 0.3 and f(4) = 0.4; these sum to 1.0 per the definition of a probability (the requirement is how we solved for constant b). Separately,...
    Hi @bpdulog (b) is a constant, given the domain it must be 0.10, such that the function is: f(x) = 0.1*x over [0, 1, 2, 3, 4]. So f(1) = 0.1, f(2) = 0.2, f(3) = 0.3 and f(4) = 0.4; these sum to...
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  20. Nicole Manley

    P1.T2.503. One-factor model (Hull)

    Hi @bpdulog I apologize for the confusion, I inadvertently posted from the wrong Hull text such that I posted the Factor model (which applies to questions 503.2 and 503.3, while 503.1 refers to correlated normal random variables). They are essentially similar but there is a difference. Superficially, the factor model generates a vector (i.e., a single column) of random standard normals U(1),...
    Hi @bpdulog I apologize for the confusion, I inadvertently posted from the wrong Hull text such that I posted the Factor model (which applies to questions 503.2 and 503.3, while 503.1 refers to correlated normal random variables). They are essentially similar but there is a difference. Superficially, the factor model generates a vector (i.e., a single column) of random standard normals U(1),...
    Hi @bpdulog I apologize for the confusion, I inadvertently posted from the wrong Hull text such that I posted the Factor model (which applies to questions 503.2 and 503.3, while 503.1 refers to correlated normal random variables). They are essentially similar but there is a difference....
    Hi @bpdulog I apologize for the confusion, I inadvertently posted from the wrong Hull text such that I posted the Factor model (which applies to questions 503.2 and 503.3, while 503.1 refers to...
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    15
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