P1.T2. Quantitative Analysis

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

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  1. Nicole Seaman

    P1.T2.507. White noise (Diebold)

    Learning outcomes: Define white noise, describe independent white noise and normal (Gaussian) white noise. Explain the characteristics of the dynamic structure of white noise. Explain how a lag operator works. Questions: 507.1. In regard to white noise, each of the following statements is true EXCEPT which is false? a. If a process is zero-mean white noise, then is must be Gaussian white...
    Learning outcomes: Define white noise, describe independent white noise and normal (Gaussian) white noise. Explain the characteristics of the dynamic structure of white noise. Explain how a lag operator works. Questions: 507.1. In regard to white noise, each of the following statements is true EXCEPT which is false? a. If a process is zero-mean white noise, then is must be Gaussian white...
    Learning outcomes: Define white noise, describe independent white noise and normal (Gaussian) white noise. Explain the characteristics of the dynamic structure of white noise. Explain how a lag operator works. Questions: 507.1. In regard to white noise, each of the following statements is true...
    Learning outcomes: Define white noise, describe independent white noise and normal (Gaussian) white noise. Explain the characteristics of the dynamic structure of white noise. Explain how a lag...
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    0
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    138
  2. Suzanne Evans

    P1.T2.206. Variance of sample average (Stock & Watson)

    I am asking kind of dumb question, but where is this formula in the Miller Chapter (please tell me reference in David's Pdf)
    I am asking kind of dumb question, but where is this formula in the Miller Chapter (please tell me reference in David's Pdf)
    I am asking kind of dumb question, but where is this formula in the Miller Chapter (please tell me reference in David's Pdf)
    I am asking kind of dumb question, but where is this formula in the Miller Chapter (please tell me reference in David's Pdf)
    Replies:
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    642
  3. David Harper CFA FRM

    L1.T2.77 Confidence interval (Gujarati)

    Hi @Jayanthi Sankaran yes, you are correct. Fixed above. Thanks!
    Hi @Jayanthi Sankaran yes, you are correct. Fixed above. Thanks!
    Hi @Jayanthi Sankaran yes, you are correct. Fixed above. Thanks!
    Hi @Jayanthi Sankaran yes, you are correct. Fixed above. Thanks!
    Replies:
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    138
  4. David Harper CFA FRM

    L1.T2.105 Generalized auto regressive conditional heteroscedasticity, GARCH(p,q) (Hull)

    Thanks you David for taking out time to answer. That clears my doubt. Have a nice evening.
    Thanks you David for taking out time to answer. That clears my doubt. Have a nice evening.
    Thanks you David for taking out time to answer. That clears my doubt. Have a nice evening.
    Thanks you David for taking out time to answer. That clears my doubt. Have a nice evening.
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    192
  5. Suzanne Evans

    P1.T2.208. Sample mean estimators (Stock & Watson)

    Hi David, I was just referring to the previous discussion to give better understanding to my question:) Thanks a lot for your time and patience. Praveen
    Hi David, I was just referring to the previous discussion to give better understanding to my question:) Thanks a lot for your time and patience. Praveen
    Hi David, I was just referring to the previous discussion to give better understanding to my question:) Thanks a lot for your time and patience. Praveen
    Hi David, I was just referring to the previous discussion to give better understanding to my question:) Thanks a lot for your time and patience. Praveen
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  6. Nicole Seaman

    Quiz-T2 P1.T2.409 Volatility, GARCH(1,1) and EWMA

    Per @Robert Paterson 's correction, the first bullet under 409.2.A corrected to read: In regard to (a), this is FALSE: because the weights sum to one (i.e., alpha + beta + gamma = 1.0) and omega = long-run variance*gamma, the long-run volatility = SQRT[omega/gamma] = sqrt[omega/(1 - alpha - gamma)] = sqrt[0.0000960/(1 - 0.060 - 0.880)] = sqrt[0.0000960/0.060] = 4.0% (+1 star for @Robert...
    Per @Robert Paterson 's correction, the first bullet under 409.2.A corrected to read: In regard to (a), this is FALSE: because the weights sum to one (i.e., alpha + beta + gamma = 1.0) and omega = long-run variance*gamma, the long-run volatility = SQRT[omega/gamma] = sqrt[omega/(1 - alpha - gamma)] = sqrt[0.0000960/(1 - 0.060 - 0.880)] = sqrt[0.0000960/0.060] = 4.0% (+1 star for @Robert...
    Per @Robert Paterson 's correction, the first bullet under 409.2.A corrected to read: In regard to (a), this is FALSE: because the weights sum to one (i.e., alpha + beta + gamma = 1.0) and omega = long-run variance*gamma, the long-run volatility = SQRT[omega/gamma] = sqrt[omega/(1 - alpha -...
    Per @Robert Paterson 's correction, the first bullet under 409.2.A corrected to read: In regard to (a), this is FALSE: because the weights sum to one (i.e., alpha + beta + gamma = 1.0) and omega...
    Replies:
    2
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    168
  7. David Harper CFA FRM

    L1.T2.128 Simulation with inverse transform method (Jorion)

    Hi @Tipo GBM doesn't contain the deviate, GBM models the asset price: price change = drift*Δt + sigma* epsilon* sqrt(Δt). Dowd's market risk VaR = -drift + sigma*deviate precisely because the +drift is positive in GBM. Say drift is 10% and sigma is 30%. We can input those into GBM to model the asset price. But how is risk measures (VaR)? It's a loss which is mitigated by the drift. So...
    Hi @Tipo GBM doesn't contain the deviate, GBM models the asset price: price change = drift*Δt + sigma* epsilon* sqrt(Δt). Dowd's market risk VaR = -drift + sigma*deviate precisely because the +drift is positive in GBM. Say drift is 10% and sigma is 30%. We can input those into GBM to model the asset price. But how is risk measures (VaR)? It's a loss which is mitigated by the drift. So...
    Hi @Tipo GBM doesn't contain the deviate, GBM models the asset price: price change = drift*Δt + sigma* epsilon* sqrt(Δt). Dowd's market risk VaR = -drift + sigma*deviate precisely because the +drift is positive in GBM. Say drift is 10% and sigma is 30%. We can input those into GBM to model...
    Hi @Tipo GBM doesn't contain the deviate, GBM models the asset price: price change = drift*Δt + sigma* epsilon* sqrt(Δt). Dowd's market risk VaR = -drift + sigma*deviate precisely because the...
    Replies:
    6
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    87
  8. David Harper CFA FRM

    L1.T2.57 Methodology of Econometrics (Gujarati)

    Hi @tosuhn this are aged questions (from Gujarati's econometrics which is no longer assigned) so most of this won't appear on the exam. Thanks,
    Hi @tosuhn this are aged questions (from Gujarati's econometrics which is no longer assigned) so most of this won't appear on the exam. Thanks,
    Hi @tosuhn this are aged questions (from Gujarati's econometrics which is no longer assigned) so most of this won't appear on the exam. Thanks,
    Hi @tosuhn this are aged questions (from Gujarati's econometrics which is no longer assigned) so most of this won't appear on the exam. Thanks,
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  9. David Harper CFA FRM

    L1.T2.101 Monte Carlo simulation accuracy (Jorion)

    Hi @Tipo I am not seeing the exact Miller reference but that does sound correct for the CI of a sample mean; i.e., CI[sample mean] = sample mean +/- (critical t)*(standard error; i.e., standard deviation of the sampling distribution). But this question concerns the confidence interval around the VaR quantile (not a sample mean): "the confidence interval for the VaR quantile is [1.245,2.045]."...
    Hi @Tipo I am not seeing the exact Miller reference but that does sound correct for the CI of a sample mean; i.e., CI[sample mean] = sample mean +/- (critical t)*(standard error; i.e., standard deviation of the sampling distribution). But this question concerns the confidence interval around the VaR quantile (not a sample mean): "the confidence interval for the VaR quantile is [1.245,2.045]."...
    Hi @Tipo I am not seeing the exact Miller reference but that does sound correct for the CI of a sample mean; i.e., CI[sample mean] = sample mean +/- (critical t)*(standard error; i.e., standard deviation of the sampling distribution). But this question concerns the confidence interval around the...
    Hi @Tipo I am not seeing the exact Miller reference but that does sound correct for the CI of a sample mean; i.e., CI[sample mean] = sample mean +/- (critical t)*(standard error; i.e., standard...
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    199
  10. David Harper CFA FRM

    L1.T2.96 Multivariate regression estimates (Gujarati)

    Hi @Aenny In regressions, the above is the most typical application (it firstly depends on how the null is defined, but when it's typical, as above, no explication is needed): the null hypothesis is that the partial slope coefficient is equal to zero; i.e., the null says there is no relationship. (A one-sided test adds the less than or greater than, < or >, but a key fact about the null is...
    Hi @Aenny In regressions, the above is the most typical application (it firstly depends on how the null is defined, but when it's typical, as above, no explication is needed): the null hypothesis is that the partial slope coefficient is equal to zero; i.e., the null says there is no relationship. (A one-sided test adds the less than or greater than, < or >, but a key fact about the null is...
    Hi @Aenny In regressions, the above is the most typical application (it firstly depends on how the null is defined, but when it's typical, as above, no explication is needed): the null hypothesis is that the partial slope coefficient is equal to zero; i.e., the null says there is no...
    Hi @Aenny In regressions, the above is the most typical application (it firstly depends on how the null is defined, but when it's typical, as above, no explication is needed): the null...
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    138
  11. David Harper CFA FRM

    L1.T2.125. Generalized Pareto distribution (GPD) (Rachov)

    Hi Aenny, I think you should recalculate the part "(1+ 0.213333)^(-8.333)". Here I get ~0.1996 which can be approximated to 0.20 and so 1-0.2 = 0.8.
    Hi Aenny, I think you should recalculate the part "(1+ 0.213333)^(-8.333)". Here I get ~0.1996 which can be approximated to 0.20 and so 1-0.2 = 0.8.
    Hi Aenny, I think you should recalculate the part "(1+ 0.213333)^(-8.333)". Here I get ~0.1996 which can be approximated to 0.20 and so 1-0.2 = 0.8.
    Hi Aenny, I think you should recalculate the part "(1+ 0.213333)^(-8.333)". Here I get ~0.1996 which can be approximated to 0.20 and so 1-0.2 = 0.8.
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  12. David Harper CFA FRM

    L1.T2.60 Bayes Theorem (Gujarati)

    Thank you David. That made it clear.
    Thank you David. That made it clear.
    Thank you David. That made it clear.
    Thank you David. That made it clear.
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  13. David Harper CFA FRM

    L1.T2.63 Chebyshev’s Inequality (Gujarati)

    Hi Aenny, when you calculate tests for VaR you should take the one-tailed test because VaR per its definition looks at the left-tail of a distribution (i.e. the maximum losses).
    Hi Aenny, when you calculate tests for VaR you should take the one-tailed test because VaR per its definition looks at the left-tail of a distribution (i.e. the maximum losses).
    Hi Aenny, when you calculate tests for VaR you should take the one-tailed test because VaR per its definition looks at the left-tail of a distribution (i.e. the maximum losses).
    Hi Aenny, when you calculate tests for VaR you should take the one-tailed test because VaR per its definition looks at the left-tail of a distribution (i.e. the maximum losses).
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    71
  14. David Harper CFA FRM

    L1.T2.117 Chi-square distribution (Rachev)

    Thanks, David, that helped! :) Especially this part: "For me personally, this is the hardest part to see: squaring the "two-sided" normal variable which is symmetrical around the zero (so includes negatives) informs a "one-sided" chi-square variable; in short, if (Z<-1.645 or Z>1.645), then abs|z|>1.645 and z^2>1.645^2" This was the part which went beyond my understanding at that...
    Thanks, David, that helped! :) Especially this part: "For me personally, this is the hardest part to see: squaring the "two-sided" normal variable which is symmetrical around the zero (so includes negatives) informs a "one-sided" chi-square variable; in short, if (Z<-1.645 or Z>1.645), then abs|z|>1.645 and z^2>1.645^2" This was the part which went beyond my understanding at that...
    Thanks, David, that helped! :) Especially this part: "For me personally, this is the hardest part to see: squaring the "two-sided" normal variable which is symmetrical around the zero (so includes negatives) informs a "one-sided" chi-square variable; in short, if (Z<-1.645 or Z>1.645), then...
    Thanks, David, that helped! :) Especially this part: "For me personally, this is the hardest part to see: squaring the "two-sided" normal variable which is symmetrical around the zero (so includes...
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  15. David Harper CFA FRM

    L1.T2.95 Multivariate regression (Gujarati)

    Hi 95.3.B might better say "and [many | several | most] partial slope coefficients" are insignificant. A classic near-perfect multicollinearity is one (or two) high t-stat for one coefficient (i.e., significance of one partial) and low t-stats for all of the others (insignificant) with ~ perfect MC ensuring a high F ratio. The key thing is that the F ratio is a test of a joint null hypothesis...
    Hi 95.3.B might better say "and [many | several | most] partial slope coefficients" are insignificant. A classic near-perfect multicollinearity is one (or two) high t-stat for one coefficient (i.e., significance of one partial) and low t-stats for all of the others (insignificant) with ~ perfect MC ensuring a high F ratio. The key thing is that the F ratio is a test of a joint null hypothesis...
    Hi 95.3.B might better say "and [many | several | most] partial slope coefficients" are insignificant. A classic near-perfect multicollinearity is one (or two) high t-stat for one coefficient (i.e., significance of one partial) and low t-stats for all of the others (insignificant) with ~...
    Hi 95.3.B might better say "and [many | several | most] partial slope coefficients" are insignificant. A classic near-perfect multicollinearity is one (or two) high t-stat for one coefficient...
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  16. David Harper CFA FRM

    L1.T2.84 Stochastic error term (Gujarati)

    Thanks David!
    Thanks David!
    Thanks David!
    Thanks David!
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  17. Nicole Seaman

    P1.T2.402. Random number generators (Fabozzi)

    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...
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    0
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  18. Suzanne Evans
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  19. David Harper CFA FRM

    L1.T2.119 Lognormal distribution (Rachev)

    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!).
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  20. David Harper CFA FRM

    L1.T2.88 Linear regression assumptions (Gujarati)

    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)...
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    81
  21. David Harper CFA FRM

    L1.T2.133 Cholesky factorization (Jorion)

    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)...
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  22. David Harper CFA FRM

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

    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...
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  23. David Harper CFA FRM

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

    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
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  24. David Harper CFA FRM

    L1.T2.100 Option simulations (MCS) (Jorion)

    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...
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  25. David Harper CFA FRM

    L1.T2.112 Rachev's properties of normal distribution (Rachov)

    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...
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    94
  26. David Harper CFA FRM

    L1.T2.65 Variance and conditional expectations (Gujarati)

    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
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    67
  27. 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!).
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  28. David Harper CFA FRM

    L1.T2.131 Standard error in Monte Carlo simulation (Jorion)

    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
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    71
  29. Suzanne Evans

    Question 16: Confidence limits

    Thanks David
    Thanks David
    Thanks David
    Thanks David
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  30. Suzanne Evans

    Question 131: 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...
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