P1.T2. Quantitative Analysis

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

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  1. Suzanne Evans

    P1.T2.303 Mean and variance of continuous probability density functions (pdf)

    Hi @bpdulog Because several candidates were asking, last month we asked Bill May, SVP at GARP, the following question. My question and his response: Response from Bill May (March 8, 2016):
    Hi @bpdulog Because several candidates were asking, last month we asked Bill May, SVP at GARP, the following question. My question and his response: Response from Bill May (March 8, 2016):
    Hi @bpdulog Because several candidates were asking, last month we asked Bill May, SVP at GARP, the following question. My question and his response: Response from Bill May (March 8, 2016):
    Hi @bpdulog Because several candidates were asking, last month we asked Bill May, SVP at GARP, the following question. My question and his response: Response from Bill May (March 8, 2016):
    Replies:
    24
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    527
  2. Suzanne Evans

    P1.T2.203. Skew and kurtosis (Stock & Watson)

    Hi @bpdulog of course, many distributions can have a mean of zero (e.g., student's t). The normal is but one of many.
    Hi @bpdulog of course, many distributions can have a mean of zero (e.g., student's t). The normal is but one of many.
    Hi @bpdulog of course, many distributions can have a mean of zero (e.g., student's t). The normal is but one of many.
    Hi @bpdulog of course, many distributions can have a mean of zero (e.g., student's t). The normal is but one of many.
    Replies:
    2
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    193
  3. Pam Gordon

    P1.T2.309. Probability Distributions I, Miller Chapter 4

    Thanks!, David!
    Thanks!, David!
    Thanks!, David!
    Thanks!, David!
    Replies:
    35
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    782
  4. David Harper CFA FRM

    L1.T2.110 Rachev's distributions

    Your question raised a good point. Wasn't a bad question at all
    Your question raised a good point. Wasn't a bad question at all
    Your question raised a good point. Wasn't a bad question at all
    Your question raised a good point. Wasn't a bad question at all
    Replies:
    6
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    83
  5. David Harper CFA FRM

    L1.T2.72 Student's t distribution

    David,Thanks for clarifying! Thanks Regards, Trilo
    David,Thanks for clarifying! Thanks Regards, Trilo
    David,Thanks for clarifying! Thanks Regards, Trilo
    David,Thanks for clarifying! Thanks Regards, Trilo
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    32
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    302
  6. David Harper CFA FRM

    L1.T2.73 Chi-square distribution

    Thank you @ami44 ! Terrific answers, I agree wholeheartedly with your replies to both 73.2 and 73.4!
    Thank you @ami44 ! Terrific answers, I agree wholeheartedly with your replies to both 73.2 and 73.4!
    Thank you @ami44 ! Terrific answers, I agree wholeheartedly with your replies to both 73.2 and 73.4!
    Thank you @ami44 ! Terrific answers, I agree wholeheartedly with your replies to both 73.2 and 73.4!
    Replies:
    11
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    109
  7. David Harper CFA FRM

    L1.T2.80 Confidence intervals

    Thank you @Deepak Chitnis ! It's true, [USER=38486]@ : for the test of the any individual slope coefficient in a regression, we want a student's t where (n - variables) = df, including the dependent variable. This is because it's actually the estimated coefficients that determine the df: the intercept plus the (partial) slope coefficients. In the case of y = α+β*x, as per Q80.3 above, df = n-2...
    Thank you @Deepak Chitnis ! It's true, [USER=38486]@ : for the test of the any individual slope coefficient in a regression, we want a student's t where (n - variables) = df, including the dependent variable. This is because it's actually the estimated coefficients that determine the df: the intercept plus the (partial) slope coefficients. In the case of y = α+β*x, as per Q80.3 above, df = n-2...
    Thank you @Deepak Chitnis ! It's true, [USER=38486]@ : for the test of the any individual slope coefficient in a regression, we want a student's t where (n - variables) = df, including the dependent variable. This is because it's actually the estimated coefficients that determine the df: the...
    Thank you @Deepak Chitnis ! It's true, [USER=38486]@ : for the test of the any individual slope coefficient in a regression, we want a student's t where (n - variables) = df, including the...
    Replies:
    10
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    99
  8. David Harper CFA FRM

    L1.T2.76 Critical t-values

    Thank you [USER=38486]@ I suppose another way to look at this is from the perspective that the student's t distribution converges toward the normal distribution with variance = df/(df-2), see Therefore, as sample size or df increase (where df = sample - 1, in the case of a sample mean), the variance is decreasing. Indeed, the way that I think of this is, I visualize the student's t lookup...
    Thank you [USER=38486]@ I suppose another way to look at this is from the perspective that the student's t distribution converges toward the normal distribution with variance = df/(df-2), see Therefore, as sample size or df increase (where df = sample - 1, in the case of a sample mean), the variance is decreasing. Indeed, the way that I think of this is, I visualize the student's t lookup...
    Thank you [USER=38486]@ I suppose another way to look at this is from the perspective that the student's t distribution converges toward the normal distribution with variance = df/(df-2), see Therefore, as sample size or df increase (where df = sample - 1, in the case of a sample mean), the...
    Thank you [USER=38486]@ I suppose another way to look at this is from the perspective that the student's t distribution converges toward the normal distribution with variance = df/(df-2), see ...
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    121
  9. bbeckett

    P1.T2.305. Minimum variance hedge (Miller)

    Thanks David! I did just read that update...fortunately calc is slowly coming back to me with each example. Based on Bill's comments it would seem some other prep providers I have had access to may be light in this area. Thanks for the deep dive on the great, albeit challenging, questions!
    Thanks David! I did just read that update...fortunately calc is slowly coming back to me with each example. Based on Bill's comments it would seem some other prep providers I have had access to may be light in this area. Thanks for the deep dive on the great, albeit challenging, questions!
    Thanks David! I did just read that update...fortunately calc is slowly coming back to me with each example. Based on Bill's comments it would seem some other prep providers I have had access to may be light in this area. Thanks for the deep dive on the great, albeit challenging, questions!
    Thanks David! I did just read that update...fortunately calc is slowly coming back to me with each example. Based on Bill's comments it would seem some other prep providers I have had access to...
    Replies:
    4
    Views:
    29
  10. Fran

    P1.T2.308. Coskewness and cokurtosis

    Thank you [USER=38486]@ Fixed above.
    Thank you [USER=38486]@ Fixed above.
    Thank you [USER=38486]@ Fixed above.
    Thank you [USER=38486]@ Fixed above.
    Replies:
    7
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    247
  11. Fran

    P1.T2.306. Calculate the mean and variance of sums of variables.

    It is pretty surprising to me if you have a CFA and have never heard of variance and covariance....
    It is pretty surprising to me if you have a CFA and have never heard of variance and covariance....
    It is pretty surprising to me if you have a CFA and have never heard of variance and covariance....
    It is pretty surprising to me if you have a CFA and have never heard of variance and covariance....
    Replies:
    22
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    358
  12. Suzanne Evans

    P1.T2.300. Probability functions (Miller)

    @PortoMarco79 I received a response to my question .... Bill May replied:
    @PortoMarco79 I received a response to my question .... Bill May replied:
    @PortoMarco79 I received a response to my question .... Bill May replied:
    @PortoMarco79 I received a response to my question .... Bill May replied:
    Replies:
    42
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    1,345
  13. Nicole Manley

    P1.T2.602. Bootstrapping (Brooks)

    Hi @bpdulog It is true that bootstrapping is similar to (plain old) historical simulation in the sense that both use actual historical data (e.g., returns, or vectors of returns), but bootstrapping randomly samples from the historical data; such sampling requires a random number generator. I hope that clarifies. Thanks!
    Hi @bpdulog It is true that bootstrapping is similar to (plain old) historical simulation in the sense that both use actual historical data (e.g., returns, or vectors of returns), but bootstrapping randomly samples from the historical data; such sampling requires a random number generator. I hope that clarifies. Thanks!
    Hi @bpdulog It is true that bootstrapping is similar to (plain old) historical simulation in the sense that both use actual historical data (e.g., returns, or vectors of returns), but bootstrapping randomly samples from the historical data; such sampling requires a random number generator. I...
    Hi @bpdulog It is true that bootstrapping is similar to (plain old) historical simulation in the sense that both use actual historical data (e.g., returns, or vectors of returns), but...
    Replies:
    2
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    52
  14. David Harper CFA FRM

    L1.T2.82 Chi-square and F-ratio

    sure thanks Deepak and David.
    sure thanks Deepak and David.
    sure thanks Deepak and David.
    sure thanks Deepak and David.
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  15. Nicole Manley

    P1.T2.502. Covariance updates with EWMA and GARCH(1,1) models

    Hi @cabrown085 I don't think so. lambda (λ) in EWMA is more analogous to beta (β) in GARCH: both tend to be high values (0.80 or higher) that give predominant weight ("persistence") to the most recent variance, while the most recent return ("innovation") is the shock that receives the lessor weight of (1-λ) in EWMA and alpha (α) in GARCH. So, the updated variance estimate (eg) of X in 502.2 is...
    Hi @cabrown085 I don't think so. lambda (λ) in EWMA is more analogous to beta (β) in GARCH: both tend to be high values (0.80 or higher) that give predominant weight ("persistence") to the most recent variance, while the most recent return ("innovation") is the shock that receives the lessor weight of (1-λ) in EWMA and alpha (α) in GARCH. So, the updated variance estimate (eg) of X in 502.2 is...
    Hi @cabrown085 I don't think so. lambda (λ) in EWMA is more analogous to beta (β) in GARCH: both tend to be high values (0.80 or higher) that give predominant weight ("persistence") to the most recent variance, while the most recent return ("innovation") is the shock that receives the lessor...
    Hi @cabrown085 I don't think so. lambda (λ) in EWMA is more analogous to beta (β) in GARCH: both tend to be high values (0.80 or higher) that give predominant weight ("persistence") to the most...
    Replies:
    8
    Views:
    252
  16. David Harper CFA FRM

    L1.T2.109 EWMA covariance

    Hi @FM22 From Hull 23.7:
    Hi @FM22 From Hull 23.7:
    Hi @FM22 From Hull 23.7:
    Hi @FM22 From Hull 23.7:
    Replies:
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  17. Nicole Manley

    P1.T2.506. Covariance stationary time series

    Highly appreciate if you can paste the definition here related to 506.3 please.
    Highly appreciate if you can paste the definition here related to 506.3 please.
    Highly appreciate if you can paste the definition here related to 506.3 please.
    Highly appreciate if you can paste the definition here related to 506.3 please.
    Replies:
    4
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    110
  18. Suzanne Evans

    P1.T2.214. Regression lines (Stock & Watson)

    thank you it serves the purpose
    thank you it serves the purpose
    thank you it serves the purpose
    thank you it serves the purpose
    Replies:
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  19. cabrown085

    Uses of the Probability Density Function versus the Cumulative Distribution Function

    a discrete distribution has a pmf (probability mass function) instead of a prob density function (pdf) which is its continuous analog. An easy example of pmf/CDF is a fair six-sided die: the CDF is F(X) = X/6; i.e., the probability of rolling a three or less is 3/6 = 50% the pmf is the derivative: if F(X) = 1/6*x, then f(X) = F'(X) = 1/6; ie the pmf of a fair die is f(x) = 1/6 if f(x) = ax +...
    a discrete distribution has a pmf (probability mass function) instead of a prob density function (pdf) which is its continuous analog. An easy example of pmf/CDF is a fair six-sided die: the CDF is F(X) = X/6; i.e., the probability of rolling a three or less is 3/6 = 50% the pmf is the derivative: if F(X) = 1/6*x, then f(X) = F'(X) = 1/6; ie the pmf of a fair die is f(x) = 1/6 if f(x) = ax +...
    a discrete distribution has a pmf (probability mass function) instead of a prob density function (pdf) which is its continuous analog. An easy example of pmf/CDF is a fair six-sided die: the CDF is F(X) = X/6; i.e., the probability of rolling a three or less is 3/6 = 50% the pmf is the...
    a discrete distribution has a pmf (probability mass function) instead of a prob density function (pdf) which is its continuous analog. An easy example of pmf/CDF is a fair six-sided die: the CDF...
    Replies:
    4
    Views:
    27
  20. cabrown085

    Variance and Covariance Calculation Clarification

    Hi David, Thanks! I work in Excel every day so being able to look at the numbers was a big help. What I was describing in the first part can be summed up as: Pr*(X-µ)^2 The second equation can be described as: Pr*X^2-(sum(Pr*X))^2. sum(Pr*X) = µ What you were showing in the second example was with samples it may be difficult to assign a true distribution, so instead for a sample mean, you...
    Hi David, Thanks! I work in Excel every day so being able to look at the numbers was a big help. What I was describing in the first part can be summed up as: Pr*(X-µ)^2 The second equation can be described as: Pr*X^2-(sum(Pr*X))^2. sum(Pr*X) = µ What you were showing in the second example was with samples it may be difficult to assign a true distribution, so instead for a sample mean, you...
    Hi David, Thanks! I work in Excel every day so being able to look at the numbers was a big help. What I was describing in the first part can be summed up as: Pr*(X-µ)^2 The second equation can be described as: Pr*X^2-(sum(Pr*X))^2. sum(Pr*X) = µ What you were showing in the second example was...
    Hi David, Thanks! I work in Excel every day so being able to look at the numbers was a big help. What I was describing in the first part can be summed up as: Pr*(X-µ)^2 The second equation can...
    Replies:
    3
    Views:
    22

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