P1.T2. Quantitative Analysis

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

Sort By:
Title
Replies Views
Last Message ↓
  1. Nicole Seaman

    P1.T2.402. Random number generators

    AIMs: Describe the inverse transform method and its implementation in discrete and continuous distributions. Describe standards for an effective pseudorandom number generator and explain midsquare technique and congruential pseudorandom number generators. Describe quasi-random (low-discrepancy) sequences and explain how they work in simulations. Explain the mechanics and characteristics of the...
    AIMs: Describe the inverse transform method and its implementation in discrete and continuous distributions. Describe standards for an effective pseudorandom number generator and explain midsquare technique and congruential pseudorandom number generators. Describe quasi-random (low-discrepancy) sequences and explain how they work in simulations. Explain the mechanics and characteristics of the...
    AIMs: Describe the inverse transform method and its implementation in discrete and continuous distributions. Describe standards for an effective pseudorandom number generator and explain midsquare technique and congruential pseudorandom number generators. Describe quasi-random (low-discrepancy)...
    AIMs: Describe the inverse transform method and its implementation in discrete and continuous distributions. Describe standards for an effective pseudorandom number generator and explain midsquare...
    Replies:
    0
    Views:
    95
  2. LMFRM

    P1. T2. Miller, Chapter 4, Pratice question 310.2

    Thks David
    Thks David
    Thks David
    Thks David
    Replies:
    2
    Views:
    25
  3. Suzanne Evans
    Replies:
    1
    Views:
    137
  4. Suzanne Evans

    P1.T2.210. Hypothesis testing (Stock & Watson)

    Hi David, I think there is a minor typo in the multiple choice answer D for question 210.1 (in the PDF). "If he reduces the significance level to 1.0%, he reduces the probability of erroneously rejecting a false null" vs If he reduces the significance level to 1.0%, he reduces the probability of erroneously accepting a false null"
    Hi David, I think there is a minor typo in the multiple choice answer D for question 210.1 (in the PDF). "If he reduces the significance level to 1.0%, he reduces the probability of erroneously rejecting a false null" vs If he reduces the significance level to 1.0%, he reduces the probability of erroneously accepting a false null"
    Hi David, I think there is a minor typo in the multiple choice answer D for question 210.1 (in the PDF). "If he reduces the significance level to 1.0%, he reduces the probability of erroneously rejecting a false null" vs If he reduces the significance level to 1.0%, he reduces the probability...
    Hi David, I think there is a minor typo in the multiple choice answer D for question 210.1 (in the PDF). "If he reduces the significance level to 1.0%, he reduces the probability of erroneously...
    Replies:
    8
    Views:
    213
  5. David Harper CFA FRM

    P1.T2.201. Random variables

    Thanks for clearing that up.
    Thanks for clearing that up.
    Thanks for clearing that up.
    Thanks for clearing that up.
    Replies:
    10
    Views:
    297
  6. Pflik

    hull 21.11

    Hi Pflik, Right, in the overall, Hull is typical among authors (e.g., Jorion) in ultimately allowing for either continuous, u = LN[S(i)/S(i-1)], or discrete, u = S(i)/S(i-1) - 1, as the return input into volatility (I realize he settles on discrete in Chapter 22, due to consistency with Chapter 21, but notice that it's actually due to an approximation of the continuous where his technical...
    Hi Pflik, Right, in the overall, Hull is typical among authors (e.g., Jorion) in ultimately allowing for either continuous, u = LN[S(i)/S(i-1)], or discrete, u = S(i)/S(i-1) - 1, as the return input into volatility (I realize he settles on discrete in Chapter 22, due to consistency with Chapter 21, but notice that it's actually due to an approximation of the continuous where his technical...
    Hi Pflik, Right, in the overall, Hull is typical among authors (e.g., Jorion) in ultimately allowing for either continuous, u = LN[S(i)/S(i-1)], or discrete, u = S(i)/S(i-1) - 1, as the return input into volatility (I realize he settles on discrete in Chapter 22, due to consistency with...
    Hi Pflik, Right, in the overall, Hull is typical among authors (e.g., Jorion) in ultimately allowing for either continuous, u = LN[S(i)/S(i-1)], or discrete, u = S(i)/S(i-1) - 1, as the return...
    Replies:
    1
    Views:
    13
  7. David Harper CFA FRM

    L1.T2.119 Lognormal distribution

    Many thanks for the thorough response David (and apologies as on second review my question seems a little basic!).
    Many thanks for the thorough response David (and apologies as on second review my question seems a little basic!).
    Many thanks for the thorough response David (and apologies as on second review my question seems a little basic!).
    Many thanks for the thorough response David (and apologies as on second review my question seems a little basic!).
    Replies:
    6
    Views:
    140
  8. Pflik

    hull 21.09 covariance estimation

    it helps very much. Still have enough to do so this will be at the end of my list for now.
    it helps very much. Still have enough to do so this will be at the end of my list for now.
    it helps very much. Still have enough to do so this will be at the end of my list for now.
    it helps very much. Still have enough to do so this will be at the end of my list for now.
    Replies:
    2
    Views:
    15
  9. Fran

    P1.T2.302. Bayes' Theorem (Miller)

    Thanks David
    Thanks David
    Thanks David
    Thanks David
    Replies:
    8
    Views:
    279
  10. David Harper CFA FRM

    L1.T2.88 Linear regression assumptions

    Hi wanderer, I don't have an easy intuition to it myself. It appears to be a feature of an OLS regression that the sum of the product of the residuals and the explanatory (i.e., independent) variables is necessarily zero. The mean of the errors must be zero, so I fear I am missing some intuition related to the cross-product necessarily being zero, but I just can't get the intuition myself. ...
    Hi wanderer, I don't have an easy intuition to it myself. It appears to be a feature of an OLS regression that the sum of the product of the residuals and the explanatory (i.e., independent) variables is necessarily zero. The mean of the errors must be zero, so I fear I am missing some intuition related to the cross-product necessarily being zero, but I just can't get the intuition myself. ...
    Hi wanderer, I don't have an easy intuition to it myself. It appears to be a feature of an OLS regression that the sum of the product of the residuals and the explanatory (i.e., independent) variables is necessarily zero. The mean of the errors must be zero, so I fear I am missing some...
    Hi wanderer, I don't have an easy intuition to it myself. It appears to be a feature of an OLS regression that the sum of the product of the residuals and the explanatory (i.e., independent)...
    Replies:
    5
    Views:
    76
  11. David Harper CFA FRM

    L1.T2.133 Cholesky factorization

    Hi bball8530 - I so wish i could say (I have for years asked GARP to settle on a formula sheet). This one is "on the fence" in my opinion: it is fundamental and it has, I think, fully three (3) occurrences in 2013 P1 (including new Miller). On the other hand, I don't recall any feedback instance that has required its memorization and further, notice this AIM is: Explain how to simulate...
    Hi bball8530 - I so wish i could say (I have for years asked GARP to settle on a formula sheet). This one is "on the fence" in my opinion: it is fundamental and it has, I think, fully three (3) occurrences in 2013 P1 (including new Miller). On the other hand, I don't recall any feedback instance that has required its memorization and further, notice this AIM is: Explain how to simulate...
    Hi bball8530 - I so wish i could say (I have for years asked GARP to settle on a formula sheet). This one is "on the fence" in my opinion: it is fundamental and it has, I think, fully three (3) occurrences in 2013 P1 (including new Miller). On the other hand, I don't recall any feedback instance...
    Hi bball8530 - I so wish i could say (I have for years asked GARP to settle on a formula sheet). This one is "on the fence" in my opinion: it is fundamental and it has, I think, fully three (3)...
    Replies:
    9
    Views:
    111
  12. David Harper CFA FRM

    L1.T2.97 Geometric Brownian motion (GBM) Monte Carlo simulation

    Hi Showstopper, With respect to MCS, the user can decide on any process, but in the case of the typical GBM, which includes a drift, I suppose a possible reason to ignore the drift is simply when the assumption is wanted that the drift = 0; i.e., it exists but is simply assumed zero. Specifically, if the time window is short (e.g., 10 days) such that the expected 10-day return is near enough...
    Hi Showstopper, With respect to MCS, the user can decide on any process, but in the case of the typical GBM, which includes a drift, I suppose a possible reason to ignore the drift is simply when the assumption is wanted that the drift = 0; i.e., it exists but is simply assumed zero. Specifically, if the time window is short (e.g., 10 days) such that the expected 10-day return is near enough...
    Hi Showstopper, With respect to MCS, the user can decide on any process, but in the case of the typical GBM, which includes a drift, I suppose a possible reason to ignore the drift is simply when the assumption is wanted that the drift = 0; i.e., it exists but is simply assumed zero....
    Hi Showstopper, With respect to MCS, the user can decide on any process, but in the case of the typical GBM, which includes a drift, I suppose a possible reason to ignore the drift is simply...
    Replies:
    13
    Views:
    197
  13. David Harper CFA FRM

    L1.T2.67 Sample variance, covariance, skew, kurtosis

    Thanks David. Really appreciate your fast reply. Now, I think I truly understand this.
    Thanks David. Really appreciate your fast reply. Now, I think I truly understand this.
    Thanks David. Really appreciate your fast reply. Now, I think I truly understand this.
    Thanks David. Really appreciate your fast reply. Now, I think I truly understand this.
    Replies:
    5
    Views:
    87
  14. orit

    Miller chapter 5

    p 74
    p 74
    p 74
    p 74
    Replies:
    1
    Views:
    13
  15. David Harper CFA FRM

    L1.T2.106 GARCH(1,1) mean reversion

    Hi Joe, only because the question asks "What is implied long-run volatility?" not long run (unconditional) variance. I agree with you that the implied LR variance = 0.0002/ (1-0.90-0.5). Hope that clarifies, thanks!
    Hi Joe, only because the question asks "What is implied long-run volatility?" not long run (unconditional) variance. I agree with you that the implied LR variance = 0.0002/ (1-0.90-0.5). Hope that clarifies, thanks!
    Hi Joe, only because the question asks "What is implied long-run volatility?" not long run (unconditional) variance. I agree with you that the implied LR variance = 0.0002/ (1-0.90-0.5). Hope that clarifies, thanks!
    Hi Joe, only because the question asks "What is implied long-run volatility?" not long run (unconditional) variance. I agree with you that the implied LR variance = 0.0002/ (1-0.90-0.5). Hope that...
    Replies:
    4
    Views:
    95
  16. David Harper CFA FRM

    L1.T2.100 Option simulations (MCS)

    Hi arnanpices, The GBM, which is common for equities, models the change in stock price as: upward drift + random shock (mean = 0). Note this implies that we expect the stock (asset price) to increase over time. (although we may expect the stock volatility/variance to revert!) But we do not expect interest rates to increase forever over time. So, the CIR model would be more appropriate when...
    Hi arnanpices, The GBM, which is common for equities, models the change in stock price as: upward drift + random shock (mean = 0). Note this implies that we expect the stock (asset price) to increase over time. (although we may expect the stock volatility/variance to revert!) But we do not expect interest rates to increase forever over time. So, the CIR model would be more appropriate when...
    Hi arnanpices, The GBM, which is common for equities, models the change in stock price as: upward drift + random shock (mean = 0). Note this implies that we expect the stock (asset price) to increase over time. (although we may expect the stock volatility/variance to revert!) But we do not...
    Hi arnanpices, The GBM, which is common for equities, models the change in stock price as: upward drift + random shock (mean = 0). Note this implies that we expect the stock (asset price) to...
    Replies:
    4
    Views:
    86
  17. amanpisces7@gmail.com

    l1-t2-112-normal

    Hi arnanpisces, The daily return is a random variable, say (X). Location-scale invariance only tell us that a*X + b is also random, where (a) and (b) are constants; e.g., location-scale invariance tells us that if we multiply the daily return by 5 and add 2%, the resulting variance (shifted and scaled) is also normal. However, to scale the daily return over a longer period, we need...
    Hi arnanpisces, The daily return is a random variable, say (X). Location-scale invariance only tell us that a*X + b is also random, where (a) and (b) are constants; e.g., location-scale invariance tells us that if we multiply the daily return by 5 and add 2%, the resulting variance (shifted and scaled) is also normal. However, to scale the daily return over a longer period, we need...
    Hi arnanpisces, The daily return is a random variable, say (X). Location-scale invariance only tell us that a*X + b is also random, where (a) and (b) are constants; e.g., location-scale invariance tells us that if we multiply the daily return by 5 and add 2%, the resulting variance (shifted...
    Hi arnanpisces, The daily return is a random variable, say (X). Location-scale invariance only tell us that a*X + b is also random, where (a) and (b) are constants; e.g., location-scale...
    Replies:
    1
    Views:
    13
  18. edegroote

    Calculation of variance

    Hi Evelyne, I agree with Byron. The (2) variance, in a sense, is superior because it is a population variance. I like to also think of it as an ex ante population variance; it implies you have a full understanding (can characterize) the distribution. For example, a six-sided die. We know it has a simple uniform distribution, 1/6th for each outcome fully characterizes the distribution. We can...
    Hi Evelyne, I agree with Byron. The (2) variance, in a sense, is superior because it is a population variance. I like to also think of it as an ex ante population variance; it implies you have a full understanding (can characterize) the distribution. For example, a six-sided die. We know it has a simple uniform distribution, 1/6th for each outcome fully characterizes the distribution. We can...
    Hi Evelyne, I agree with Byron. The (2) variance, in a sense, is superior because it is a population variance. I like to also think of it as an ex ante population variance; it implies you have a full understanding (can characterize) the distribution. For example, a six-sided die. We know it...
    Hi Evelyne, I agree with Byron. The (2) variance, in a sense, is superior because it is a population variance. I like to also think of it as an ex ante population variance; it implies you have a...
    Replies:
    2
    Views:
    23
  19. David Harper CFA FRM

    L1.T2.65 Variance and conditional expectations

    Hi bhar, thanks, I really do appreciate that. Writing questions is my core "work in the salt mines," so i love hearing that a question is liked. I wish i could claim i invented the first question, but really i just made a question out of the explain in Carol Alexander's MRA , thanks,
    Hi bhar, thanks, I really do appreciate that. Writing questions is my core "work in the salt mines," so i love hearing that a question is liked. I wish i could claim i invented the first question, but really i just made a question out of the explain in Carol Alexander's MRA , thanks,
    Hi bhar, thanks, I really do appreciate that. Writing questions is my core "work in the salt mines," so i love hearing that a question is liked. I wish i could claim i invented the first question, but really i just made a question out of the explain in Carol Alexander's MRA , thanks,
    Hi bhar, thanks, I really do appreciate that. Writing questions is my core "work in the salt mines," so i love hearing that a question is liked. I wish i could claim i invented the first...
    Replies:
    2
    Views:
    62
  20. David Harper CFA FRM

    L1.T2.112 Rachev's properties of normal distribution

    Thanks David, I was indeed over thinking on this one..
    Thanks David, I was indeed over thinking on this one..
    Thanks David, I was indeed over thinking on this one..
    Thanks David, I was indeed over thinking on this one..
    Replies:
    3
    Views:
    84
  21. David Harper CFA FRM

    L1.T2.115 Gamma distribution (Rachev)

    Hi Vikas, Yes, it should read that A, C and D are each true (as the given answer of B is correct). Thank you for catching the typo (star awarded!).
    Hi Vikas, Yes, it should read that A, C and D are each true (as the given answer of B is correct). Thank you for catching the typo (star awarded!).
    Hi Vikas, Yes, it should read that A, C and D are each true (as the given answer of B is correct). Thank you for catching the typo (star awarded!).
    Hi Vikas, Yes, it should read that A, C and D are each true (as the given answer of B is correct). Thank you for catching the typo (star awarded!).
    Replies:
    4
    Views:
    73
  22. Rosher

    Bayes Theorem

    That's Gujarati source which is still planned for an revision; i.e., it is not currently in the SP, but will be fixed in upcoming PDF Rosher refers to Q60 @ link refers to but David Harper, CFA, FRM, CIPM wants to also include Bayes:
    That's Gujarati source which is still planned for an revision; i.e., it is not currently in the SP, but will be fixed in upcoming PDF Rosher refers to Q60 @ link refers to but David Harper, CFA, FRM, CIPM wants to also include Bayes:
    That's Gujarati source which is still planned for an revision; i.e., it is not currently in the SP, but will be fixed in upcoming PDF Rosher refers to Q60 @ link refers to but David Harper, CFA, FRM, CIPM wants to also include Bayes:
    That's Gujarati source which is still planned for an revision; i.e., it is not currently in the SP, but will be fixed in upcoming PDF Rosher refers to Q60 @ link refers to but David...
    Replies:
    2
    Views:
    30
  23. Suzanne Evans

    Question 1: Continously compounded returns

    Hi Holmes, You are correct, the above is part of our 2008 batch. We are currently sweeping all of the PQs in the forum. Here is the deal: All of our recent (the most relevant) questions will soon be entirely in the Study Planner PDFs (further, we are streamlining now; e.g., so some of the chapters don't have two sources) Then there are still about three "sets" of PQ that will take us more...
    Hi Holmes, You are correct, the above is part of our 2008 batch. We are currently sweeping all of the PQs in the forum. Here is the deal: All of our recent (the most relevant) questions will soon be entirely in the Study Planner PDFs (further, we are streamlining now; e.g., so some of the chapters don't have two sources) Then there are still about three "sets" of PQ that will take us more...
    Hi Holmes, You are correct, the above is part of our 2008 batch. We are currently sweeping all of the PQs in the forum. Here is the deal: All of our recent (the most relevant) questions will soon be entirely in the Study Planner PDFs (further, we are streamlining now; e.g., so some of the...
    Hi Holmes, You are correct, the above is part of our 2008 batch. We are currently sweeping all of the PQs in the forum. Here is the deal: All of our recent (the most relevant) questions will...
    Replies:
    2
    Views:
    43
  24. David Harper CFA FRM

    L1.T2.131 Standard error in Monte Carlo simulation

    Hi choonho, I appended Jorion's source text to answers 131.2 and 131.4, I hope it explains. In regard to the VaR of a CMO, the CMO (due to the path dependent prepayments, which are embedded options) requires a simulation. Details of CMO are clearly P2 not P1, but the general idea is that a complex portfolio with embedded options probably is difficult to capture with parametric VaR (with a...
    Hi choonho, I appended Jorion's source text to answers 131.2 and 131.4, I hope it explains. In regard to the VaR of a CMO, the CMO (due to the path dependent prepayments, which are embedded options) requires a simulation. Details of CMO are clearly P2 not P1, but the general idea is that a complex portfolio with embedded options probably is difficult to capture with parametric VaR (with a...
    Hi choonho, I appended Jorion's source text to answers 131.2 and 131.4, I hope it explains. In regard to the VaR of a CMO, the CMO (due to the path dependent prepayments, which are embedded options) requires a simulation. Details of CMO are clearly P2 not P1, but the general idea is that a...
    Hi choonho, I appended Jorion's source text to answers 131.2 and 131.4, I hope it explains. In regard to the VaR of a CMO, the CMO (due to the path dependent prepayments, which are embedded...
    Replies:
    2
    Views:
    69
  25. RiskNoob

    Question 70.4 in Gujarati

    Hello Aleks, Here are the questions: 70.3 Assume the population of hedge fund returns has an unknown distribution with mean of 8% and volatility of 10%. From a sample of 40 funds, what is the probability the sample mean return will exceed 10%? 70.4 Assume instead we know the population of hedge fund returns is normal with mean of 8% but unknown volatility. What is the probability that...
    Hello Aleks, Here are the questions: 70.3 Assume the population of hedge fund returns has an unknown distribution with mean of 8% and volatility of 10%. From a sample of 40 funds, what is the probability the sample mean return will exceed 10%? 70.4 Assume instead we know the population of hedge fund returns is normal with mean of 8% but unknown volatility. What is the probability that...
    Hello Aleks, Here are the questions: 70.3 Assume the population of hedge fund returns has an unknown distribution with mean of 8% and volatility of 10%. From a sample of 40 funds, what is the probability the sample mean return will exceed 10%? 70.4 Assume instead we know the population of...
    Hello Aleks, Here are the questions: 70.3 Assume the population of hedge fund returns has an unknown distribution with mean of 8% and volatility of 10%. From a sample of 40 funds, what is the...
    Replies:
    2
    Views:
    265
  26. Suzanne Evans

    Question 132: Confidence limits

    Thanks David
    Thanks David
    Thanks David
    Thanks David
    Replies:
    5
    Views:
    37
  27. Suzanne Evans

    Question 149: Sample returns

    Hi, Can you please expand upon this point in the solution: The standard deviation of the difference is means is given by SQRT[2%^2/40 + 2%^2/40] = 0.004472. Am I correct in that the variance of the a sample set is equal to population variance over size of the sample and as these two sample returns are independent thus have no covariance would we be using the formula...
    Hi, Can you please expand upon this point in the solution: The standard deviation of the difference is means is given by SQRT[2%^2/40 + 2%^2/40] = 0.004472. Am I correct in that the variance of the a sample set is equal to population variance over size of the sample and as these two sample returns are independent thus have no covariance would we be using the formula...
    Hi, Can you please expand upon this point in the solution: The standard deviation of the difference is means is given by SQRT[2%^2/40 + 2%^2/40] = 0.004472. Am I correct in that the variance of the a sample set is equal to population variance over size of the sample and as these two sample...
    Hi, Can you please expand upon this point in the solution: The standard deviation of the difference is means is given by SQRT[2%^2/40 + 2%^2/40] = 0.004472. Am I correct in that the variance...
    Replies:
    3
    Views:
    23
  28. Suzanne Evans

    Question 15: Probability

    Great, thanks with you now. I was going wrong by only looking at one side of the formula...
    Great, thanks with you now. I was going wrong by only looking at one side of the formula...
    Great, thanks with you now. I was going wrong by only looking at one side of the formula...
    Great, thanks with you now. I was going wrong by only looking at one side of the formula...
    Replies:
    5
    Views:
    39
  29. Suzanne Evans

    Question 58: Probability

    Unlikely but conceivable, see (Bayes and Chebyshev's have been dropped). Re is theory applied the same: um, not sure how to answer, only in loose sense. CI want standard error and distributional assumption, we don't have distributional assumption and standard error here. A loose association, I guess, but it's no shortcut for understanding confidence intervals. Thanks,
    Unlikely but conceivable, see (Bayes and Chebyshev's have been dropped). Re is theory applied the same: um, not sure how to answer, only in loose sense. CI want standard error and distributional assumption, we don't have distributional assumption and standard error here. A loose association, I guess, but it's no shortcut for understanding confidence intervals. Thanks,
    Unlikely but conceivable, see (Bayes and Chebyshev's have been dropped). Re is theory applied the same: um, not sure how to answer, only in loose sense. CI want standard error and distributional assumption, we don't have distributional assumption and standard error here. A loose association, I...
    Unlikely but conceivable, see (Bayes and Chebyshev's have been dropped). Re is theory applied the same: um, not sure how to answer, only in loose sense. CI want standard error and distributional...
    Replies:
    18
    Views:
    27
  30. Suzanne Evans

    Question 126: Odds

    Apologies - I now realise how to complete this question thanks to a similar question and associated replies found in this thread: Thanks.
    Apologies - I now realise how to complete this question thanks to a similar question and associated replies found in this thread: Thanks.
    Apologies - I now realise how to complete this question thanks to a similar question and associated replies found in this thread: Thanks.
    Apologies - I now realise how to complete this question thanks to a similar question and associated replies found in this thread: Thanks.
    Replies:
    2
    Views:
    25

Thread Display Options

Loading...