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

    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.
    Replies:
    8
    Views:
    155
  2. 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
    Replies:
    21
    Views:
    397
  3. Nicole Seaman

    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
    Views:
    143
  4. David Harper CFA FRM

    L1.T2.128 Simulation with inverse transform method

    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
    Views:
    85
  5. David Harper CFA FRM

    L1.T2.103 Weighting schemes to estimate volatility

    Hi @Tipo Per Hull 22.5 the ARCH(m) is given by: \sigma _{n}^{2}=\gamma {{V}_{L}}+\sum\limits_{i=1}^{m}{{{\alpha }_{i}}u_{n-i}^{2}} It generalizes all three: GARCH: positive gamma; i.e., at least some weight assigned to unconditional variance, V(L); and exponential weights where decay is beta EWMA: zero gamma (i.e., no unconditional variance) but exponential weights MA: zero gamma and...
    Hi @Tipo Per Hull 22.5 the ARCH(m) is given by: \sigma _{n}^{2}=\gamma {{V}_{L}}+\sum\limits_{i=1}^{m}{{{\alpha }_{i}}u_{n-i}^{2}} It generalizes all three: GARCH: positive gamma; i.e., at least some weight assigned to unconditional variance, V(L); and exponential weights where decay is beta EWMA: zero gamma (i.e., no unconditional variance) but exponential weights MA: zero gamma and...
    Hi @Tipo Per Hull 22.5 the ARCH(m) is given by: \sigma _{n}^{2}=\gamma {{V}_{L}}+\sum\limits_{i=1}^{m}{{{\alpha }_{i}}u_{n-i}^{2}} It generalizes all three: GARCH: positive gamma; i.e., at least some weight assigned to unconditional variance, V(L); and exponential weights where decay is...
    Hi @Tipo Per Hull 22.5 the ARCH(m) is given by: \sigma _{n}^{2}=\gamma {{V}_{L}}+\sum\limits_{i=1}^{m}{{{\alpha }_{i}}u_{n-i}^{2}} It generalizes all three: GARCH: positive gamma; i.e., at...
    Replies:
    9
    Views:
    325
  6. David Harper CFA FRM

    L1.T2.57 Methodology of Econometrics

    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,
    Replies:
    4
    Views:
    67
  7. David Harper CFA FRM

    L1.T2.101 Monte Carlo simulation accuracy

    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...
    Replies:
    16
    Views:
    193
  8. David Harper CFA FRM

    L1.T2.96 Multivariate regression estimates

    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...
    Replies:
    7
    Views:
    129
  9. David Harper CFA FRM

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

    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.
    Replies:
    4
    Views:
    72
  10. David Harper CFA FRM

    L1.T2.60 Bayes Theorem

    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.
    Replies:
    5
    Views:
    95
  11. David Harper CFA FRM

    L1.T2.63 Chebyshev’s Inequality

    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).
    Replies:
    3
    Views:
    67
  12. David Harper CFA FRM

    L1.T2.117 Chi-square distribution

    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...
    Replies:
    8
    Views:
    167
  13. David Harper CFA FRM

    L1.T2.95 Multivariate regression

    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...
    Replies:
    2
    Views:
    58
  14. David Harper CFA FRM

    L1.T2.84 Stochastic error term

    Thanks David!
    Thanks David!
    Thanks David!
    Thanks David!
    Replies:
    3
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    54
  15. LMFRM
    Replies:
    3
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    24
  16. 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:
    99
  17. LMFRM

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

    Thks David
    Thks David
    Thks David
    Thks David
    Replies:
    2
    Views:
    26
  18. Suzanne Evans
    Replies:
    1
    Views:
    149
  19. 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
  20. 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:
    143
  21. 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
  22. 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:
    77
  23. 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
  24. 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
  25. orit

    Miller chapter 5

    p 74
    p 74
    p 74
    p 74
    Replies:
    1
    Views:
    13
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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:
    63

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