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Question 1 of 20
1. Question
In the FRM Part 1, Quantitative Analysis has a 20% weight. If Part 1 has 100 questions, assume the exam contains twenty (20) questions drawn from the Quantitative Analysis Topic. If each question has four choices (a, b, c, or d), which is nearest to the probability of randomly guessing and answering EXACTLY ten (10) of them correctly?
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Question 2 of 20
2. Question
A portfolio is invested equally into two funds, each with normally distributed returns. The first fund has an expected return of 6.0% with return volatility of 8.0%. The second fund has an expected return of 10.0% with return volatility of 15.0%. The funds are independent (uncorrelated). Which is nearest to the probability that the portfolio return will exceed 12.0%? (Please use a lookup table. Here is a typical Z lookup table)
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Question 3 of 20
3. Question
You are examining a portfolio that consists of 400 investment grade obligors and 600 speculative grade (junk) obligors. Of the investment grade obligors, two (2) have defaulted; of the junk obligors, 18 have defaulted. If you randomly select an obligor and observe that it has defaulted, what is the probability the obligor is speculative?
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Question 4 of 20
4. Question
A sample set of nine values (n = 9) has an average of 5.0 and a sample standard deviation of 2.50. Now assume we add a tenth value (n –> 10) which is equal to 5.0, such that the average is unchanged. Which is nearest to the revised sample standard deviation (for n = 10 including the additional value of 5)?
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Question 5 of 20
5. Question
If the variance(X) = 9.0, variance(Y) = 16.0 and correlation(X,Y) = 0.5, what is the covariance(3 + 4*X, 5 + 6*Y)?
CorrectIncorrect 
Question 6 of 20
6. Question
Consider the following set of six values: {0, 1, 2, 3, 4, 8}. The second central moment (aka, variance) of this set is 40/6 ~= 6.67. Which is nearest to the population skew of this set?
Note: “population skew” implies this is not a sample; we could treat the set as a discrete probability distribution where each outcome is equally likely with probability of 1/6 = 16.67%.
CorrectIncorrect 
Question 7 of 20
7. Question
An industry sector contains 300 public firms where the mean earnings are $2.50 million with a standard deviation of $400,000. If the profit at exactly 10% of the firms exceeds a certain level, which is nearest to this profit level? Please use this Z lookup table if necessary:
https://www.bionicturtle.com/images/2014/dailypq/405_1_zlookup.png.CorrectIncorrect 
Question 8 of 20
8. Question
Please note that there is a flaw in this question. Please see the forum for the full discussion before trying to solve.
A risk manager is examining a trader’s profit and loss (P&L) record for the last week. He observes the following outcomes for the five weekdays: +20, +40, 10, +30, and +15 (all USD in millions). The profit and losses are normally distributed with a mean of $19.0 million; i.e., the sample mean matches the population mean by coincidence. Which is nearest to the probability that this trader will record a profit of at least $37.0 million on the first trading day of next week?
Please use this lookup table if necessary: https://www.bionicturtle.com/images/2014/dailypq/405_2_tlookup.png. (Question is a variation on GARP’s 2014 Practice Exam Question P1.12).
CorrectIncorrect 
Question 9 of 20
9. Question
A risk manager is aware that a manufacturing process at his firm produces a defects in 1.0% of components; for example, for every 100 components, the process produces one defect. The next batch will produce 200 components. The risk manager is in a real hurry and does not have his computer with him. Consequently, he wants to use the Poisson distribution, which is quicker, to approximate the binomial distribution (which he believes to be correct, given each component outcome is a Bernoulli and the outcomes are i.i.d.). He wants to estimate the probability that exactly five (5) components, among the run of 200, will be defective. Which is the probability given by the Poisson distribution, and is it a reasonable approximation to the binomial; i.e., is it within 20 basis points?
CorrectIncorrect 
Question 10 of 20
10. Question
A fund advertises that its maximum volatility is 10.0%. However, over the last 15 trading days (n = 15), the observed volatility is 14.0%. With 95.0% confidence, can we reject the null hypothesis that the true (population) volatility is equal to 10.0% or less? Please use this chi square lookup table: https://www.bionicturtle.com/images/2014/dailypq/406_1_chi_square.png.
CorrectIncorrect 
Question 11 of 20
11. Question
Your analysis of an asset price series determines the price follows a lognormal distribution with parameters values of mu (μ) = 3.4 and sigma (σ) = 1.0. For example, the expected mean price = exp(μ + σ^2/2) = exp(3.4^2 + 1^2/2) = $49.40. We want to specify the price level that will be exceeded with 50.0% probability; i.e., at approximately which price quantile (level) will the price exceed with 50% probability, and therefore also be lower than 50% of the time?
CorrectIncorrect 
Question 12 of 20
12. Question
Please see David’s comment in the forum regarding question 406.3 before trying to solve.
Over the last ten (n = 10) trading days, the daily volatility of two series are 5.0% and 3.0%. If the null hypothesis is that the series (samples) are drawn from the normal population, can we reject the null hypothesis and conclude these volatilities are statistically different with a confidence level of 95.0%? Please use this F distribution lookup table: https://www.bionicturtle.com/images/2014/dailypq/406_3_f_lookup.png.
CorrectIncorrect 
Question 13 of 20
13. Question
Consider a univariate ordinary least squares (OLS) regression given by the population regression function Y(i) = B(0) + B(1)*X(i) + u(i) which is estimated by its corresponding sample regression function Y(i) = b(0) + b(1)*X(i) + e(i), where e(i) is the residual term which estimates the unobserved stochastic error term, u(i). In regard to this univariate OLS regression, which of the following statements is TRUE?
CorrectIncorrect 
Question 14 of 20
14. Question
You regressed your firm’s portfolio excess returns against the excess returns of a benchmark Index over the last three months, such that your univariate regression contains 30 paired observations (20 trading days per month). The regression results are displayed below.
What is the approximate correlation between the two return series; and is the slope coefficient statistically significant with 95.0% confidence (please assume the sample is, just barely, a large sample)?
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Question 15 of 20
15. Question
You just regressed your firm’s excess portfolio returns against the excess returns of the S&P 500. The univariate regression results are below. Unfortunately, on the way to showing your boss the results page, you inadvertently dropped coffee where the coefficient of determination is displayed:
Which is nearest to the hidden coefficient of determination (R^2)?
CorrectIncorrect 
Question 16 of 20
16. Question
You regressed your firm’s portfolio excess returns against the excess returns of two factors over the last 100 trading days, such that your multivariate regression contains two independent variables, Factor 1 and Factor 2. The regression results are displayed below.
Your null hypothesis is a joint hypothesis that both Factors (i.e., both partial slope coefficients to Factor 1 and Factor 2 as independent variables) are equal to zero. Can you reject this joint null with 95.0% confidence?
CorrectIncorrect 
Question 17 of 20
17. Question
You regressed your firm’s portfolio excess returns against the excess returns of two factors over the last 80 trading days, such that your multivariate regression contains two independent variables, Factor 1 and Factor 2. The regression results are displayed below.
If this regression has a flaw (i.e., a potential violation of an assumption in the classical linear regression model), which of the following is the mostly likely interpretation of these regression results?
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Question 18 of 20
18. Question
While working from home, you regressed your firm’s portfolio excess returns against the excess returns of two factors over the last 60 trading days, such that your multivariate regression contains two independent variables, Factor 1 and Factor 2. The regression results are displayed below, but there is a problem! Your nephew, who is visiting, drew a blue crayon over three cells on your report. On the printout, you can’t see the unadjusted coefficient of determination (R^2), the F ratio, or the standard error of regression (SER):
Which are nearest, respectively, to the R^2, F ratio, and SER (as a bonus, compute the adjusted R^2)?
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Question 19 of 20
19. Question
Consider the following general form of the GARCH(1,1) for the estimate of today’s (daily) variance:
You are comparing four versions with the following parameters:
#1. omega = 0.0000120, alpha = 0.060, beta = 0.820
#2. omega = 0.0000120, alpha = 0.050, beta = 0.880
#3. omega = 0.0000160, alpha = 0.070, beta = 0.900
#4. omega = 0.0000450, alpha = 0.040, beta = 0.910Each of the following statements is true EXCEPT which is false?
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Question 20 of 20
20. Question
Peter the risk analyst is trying to decide between two different volatility models, a GARCH(1,1) model and exponentially weighted moving average (EWMA) model. The parameters for each are given below:
With respect to his historical data series, the most recent (yesterday’s) daily volatility was 12.0% and yesterday’s daily return was +8.0%. Which of the following statements is TRUE?
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