CFA® 2024
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QUANTITATIVE METHODS
PROGRESS TEST 1
LEVEL I
QUESTIONS
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Quantitative Methods
CFA Level I Progress Test Questions
1.
2.
The effective annual rate will be the same as the stated annual interest rate when:
A
The compounding period is equal to one compounding period per year.
B
The compounding period is equal to two compounding periods per year.
C
The compounding period is equal to four compounding periods per year.
What is the interest rate if the present value of a regular sum of $2,500 per annum to be
paid for an infinite period given $38,462?
3.
A
6.0%
B
6.5%
C
7.0%
You are creating a charitable trust to provide six annual payments of $20,000 each,
beginning next year. How much must you set aside now at 10% interest compounded
annually to meet the required disbursements?
4.
A
$87,105.21.
B
$95,815.74.
C
$169,743.42.
Which one of the following statements is most accurate?
A
Histogram is a graphical representation of a frequency distribution with bar
heights representing absolute frequencies
B
Frequency polygon is a graphical representation of a frequency distribution
with bar heights representing absolute frequencies
C
A relative frequency polygon is a graphical representation of a frequency
distribution with bar heights representing absolute frequencies
1
5.
Consider the following set of stock returns: 12%; 23%; 27%; 10%; 7%; 20%; 15%. The
third quartile is:
6.
A
10.0%
B
20.0%
C
23.0%
A sample of returns for four randomly selected positions in a portfolio are shown below:
Position
Return (%)
A
1.3
B
1.4
C
2.2
D
3.4
What is the standard deviation of the sample?
A
0.88%.
B
0.97%.
C
1.13%.
2
7.
The details of two investments are provided below:
A
Arithmetic mean
return
3.2%
B
4.8%
5%
1.5%
C
6%
5%
1.5%
Investment
Standard deviation
Risk free rate
5%
1.5%
Which of the following statements is most accurate?
8.
A
Investment A has the highest coefficient of variation.
B
Investment B has the highest coefficient of variation.
C
Investment C has the highest coefficient of variation.
In a negatively skewed distribution, what is the order (from lowest value to highest) for
the distribution mode, mean, and median values?
9.
A
Mode, mean, median.
B
Median, mode, mean.
C
Mean, median, mode.
Which of the following statements about probability is least accurate?
A
If the probability of winning a race is 1/8, then the odds of winning are 1 to 7.
B
The sum of all probabilities of any set of mutually exclusive and exhaustive
events would sum to 1.
C
Based on research studies, it was found that for every 10 companies that
announced a dividend change, 9 would announce a dividend increase. Thus
the subjective probability of an increase in dividend is 0.9.
10.
The probability of a new McDonald being built in town is 64%. If McDonald comes to
town, the probability of a new Burger King restaurant being built is 90%. What is the
probability of a new McDonald and a new Burger King restaurant being built?
A
0.240.
B
0.576.
C
0.675.
3
11.
Bonds rated B have a 25 percent chance of default in five years. Bonds rated CCC
have a 40 percent chance of default in five years. A portfolio consists of 30 percent B
and 70 percent CCC-rated bonds. What is the total probability of default for the
portfolio?
12.
A
0.295.
B
0.355.
C
0.650.
A client has a portfolio with 60% of her money in fund A and 40% in fund B. The
expected return on fund A is 18% and the expected return on fund B is 10%. What is
the expected return on the portfolio?
13.
A
14%
B
14.8%
C
28%
A client has a portfolio with 60% of her money in fund A and 40% in fund B. The
expected return on fund A is 18% and the expected return on fund B is 10%. The
following is a covariance matrix between two funds:
Fund
A
B
A
676
145
B
145
225
What is the portfolio’s standard deviation of returns?
A
18.68
B
348.96
C
314.16
4
14.
Bonds rated B have a 25 percent chance of default in five years. Bonds rated CCC
have a 40 percent chance of default in five years. A portfolio consists of 30 percent B
and 70 percent CCC-rated bonds. If a randomly selected bond defaults in a five-year
period, what is the probability that it was a B-rated bond?
15.
A
0.250.
B
0.211.
C
0.429.
Your firm intends to select 3 from a group of 7 vice-presidents to sit on the investment
committee. How many different groups of 3 are possible if the order of selection does
not matter?
16.
A
35
B
210
C
5,040
Which of the following statements is least likely to be correct?
A
Rate of return is an example of a discrete random variable.
B
The cumulative distribution function of all possible outcomes of a discrete
uniform distribution equal 1.
C
For a discrete uniform distribution with possible outcomes are whole numbers
from 1 to 10, the probability that the outcome is integer 7 is 0.1.
17.
Which of the following statements about the binomial distribution is least likely to be
correct?
A
A binomial random variable is defined as the number of successes in n trials
where each trial has only two outcomes.
B
Using a binomial tree to model stock price movement where the stock value at
t=0 is S, there will be three possible stock values on t=2.
C
If the number of trials in an experiment is 10 and the probability of success is
0.7, using the binomial random variable, the probability of X = 5 i.e. [P(X = 5)] is
0.3.
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18.
Which of the following statements about the normal distribution is least likely to be
correct?
A
The normal distribution has a skewness of 0.
B
The normal distribution has a mean that is greater than the median and mode.
C
The normal distribution is bell-shaped, with tails extending without limit to the
left and to the right.
19.
The Foundation portfolio has a normal distribution with a mean return of 2% per month
and a standard deviation of 14.5%. What is the probability that the rate of return will
below zero in a given month?
20.
A
5.5%
B
44.4%
C
50.0%
A study of hedge fund investors found that their annual household incomes are
normally distributed with a mean of $175,000 and a standard deviation of $25,000.
Given a 68% confidence interval, what is the range of hedge fund investors’ incomes?
21.
A
$59,500 to $119,000
B
$125,000 to $225,000
C
$150,000 to $200,000.
Given a threshold level of return of 4%, use Roy’s safety-first criterion to choose the
optimal portfolio.
Portfolio
A
B
C
E(Rp)
5%
11%
18%
sp
8%
21%
40%
A
Portfolio A
B
Portfolio B
C
Portfolio C
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22.
Which of the following statements is least likely to be correct?
A
If the holding period return on an asset is 6%, then the equivalent continuously
compounded return is ln(1 + 0.06).
B
If an asset’s continuously compounded return is normally distributed, then the
asset prices follow a lognormal distribution.
C
In using historical simulation, the research chooses the probability
distributions.
23.
Which of the following statements is least likely to be correct?
A
In simple random sampling, each item in the population has an equal chance of
being selected.
B
In stratified random sampling, the population is divided into subgroups before
random samples are being drawn.
C
Sampling error is the difference between the sample statistic derived from
simple random sampling and the statistic derived from stratified random
sampling.
24.
Under the central limit theorem, the sampling distribution from a population will be
approximately normal when the sample size is large. It assumes that:
25.
A
The population is described by the normally distribution.
B
The population is described by the lognormal distribution.
C
The population can be described by any probability distribution.
Analysts performing bootstrap:
A
seek to create statistical inferences of population parameters from a single
sample.
B
repeatedly draw samples of the same size, with replacement, from the original
population.
C
must specify probability distributions for key risk factors that drive the
underlying random variables.
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26.
The population’s mean is 30 and the mean of a sample size 100 is 28.5. The variance
of the sample is 25. What is the standard error of the sample mean?
27.
28.
A
2.5
B
0.5
C
0.25
All else equal, a larger sample size:
A
increases the width of the confidence interval.
B
decreases the width of the confidence interval.
C
has no impact on the width of the confidence interval.
A fund has advertised that it achieved a mean monthly return of 12% for the past five
years. Based on the research work done by an analyst, the sample monthly mean
return is 10%. The analyst wants to test the hypothesis that the mean monthly return of
this fund should be 12%. The correct null and alternative hypotheses that meet the
analyst’s objective is:
29.
30.
A
H0: μ = 0.12 versus Ha: μ ≠ 0.12
B
H0: μ ≠ 0.12 versus Ha: μ = 0.12
C
H0: μ ≤ 0.12 versus Ha: μ ≥ 0.12
A Type I error:
A
rejects a true null hypothesis.
B
rejects a false null hypothesis.
C
fails to reject a false null hypothesis.
A pitching machine is calibrated to deliver a fastball at a speed of 98 miles per hour.
Every day, a technician samples the speed of twenty-five fastballs in order to determine
if the machine needs adjustment. Today, the sample showed a mean speed of 99 miles
per hour with a standard deviation of 1.75 miles per hour. Assuming that the z-test is
the appropriate hypothesis test. At 95 percent confidence level, what is the z-value in
relation to the critical value? The:
A
z-value exceeds the critical value by 0.9 standard deviations.
B
critical value exceeds the z-value by 1.3 standard deviations.
C
z-value exceeds the critical value by 1.5 standard deviations.
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31.
Which of the following is required for a t-test based on a normal distribution and
assumed equal variances?
32.
A
Paired comparison
B
Modified degrees of freedom
C
Pooled estimator of the common variance
Jill Batten is analyzing how the returns on the stock of Stellar Energy Corp. are related
with the previous month’s percentage change in the US Consumer Price Index for
Energy (CPIENG). Based on 248 observations, she has computed the sample
correlation between the Stellar and CPIENG variables to be −0.1452. She also wants to
determine whether the sample correlation is significantly different from zero. The
critical value for the test statistic at the 0.05 level of significance is approximately 1.96.
Batten should conclude that the statistical relationship between Stellar and CPIENG is:
A
significant, because the calculated test statistic is outside the bounds of the
critical values for the test statistic
B
significant, because the calculated test statistic has a lower absolute value
than the critical value for the test statistic
C
insignificant, because the calculated test statistic is outside the bounds of the
critical values for the test statistic
33.
Which of the following statements is correct regarding the chi-square test of
independence?
A
The test has a one-sided rejection region
B
The null hypothesis is that the two groups are dependent
C
If there are two categories, each with three levels or groups, there are six
degrees of freedom
Use the following information to answer the following two questions.
A study was conducted by the British Department of Transportation to estimate urban travel
time between locations in London, England. Data was collected for motorcycles and passenger
cars. Simple linear regression was conducted using data sets for both types of vehicles, where
Y = urban travel time in minutes and X = distance between locations in kilometers. The following
results were obtained:
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34.
The estimated increase in travel time for a motorcycle commuter planning to move 8
km farther from his workplace in London is closest to:
35.
36.
A
31 minutes.
B
15 minutes.
C
0.154 hours.
Based on the regression results, which model is more reliable?
A
The passenger car model because 3.86 > 1.93
B
The motorcycle model because 1.93 < 3.86
C
The passenger car model because 0.758 > 0.676
Which of the following is least likely a necessary assumption of simple linear regression
analysis?
37.
A
The residuals are normally distributed
B
There is a constant variance of the error term
C
The dependent variable is uncorrelated with the residuals
Text analytics is appropriate for application to:
A
large, structured datasets
B
public but not private information
C
identifying possible short-term indicators of coming trends
~~End of Test ~~
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