Practice Problems 1
PRACTICE PROBLEMS
1 Which of the following groups best illustrates a sample?
A The set of all estimates for Exxon Mobil’s FY2015 EPS
B The FTSE Eurotop 100 as a representation of the European stock market
C UK shares traded on 13 August 2015 that also closed above £120/share on
the London Stock Exchange
2 Published ratings on stocks ranging from 1 (strong sell) to 5 (strong buy) are
examples of which measurement scale?
A Ordinal
B Interval
C Nominal
3 In descriptive statistics, an example of a parameter is the:
A median of a population.
B mean of a sample of observations.
C standard deviation of a sample of observations.
4 A mutual fund has the return frequency distribution shown in the following
table.
Return Interval (%) Absolute Frequency
–10.0 to –7.0 3
–7.0 to –4.0 7
–4.0 to –1.0 10
–1.0 to +2.0 12
+2.0 to +5.0 23
+5.0 to +8.0 5
Which of the following statements is correct?
A The relative frequency of the interval “–1.0 to +2.0” is 20%.
B The relative frequency of the interval “+2.0 to +5.0” is 23%.
C The cumulative relative frequency of the interval “+5.0 to +8.0” is 91.7%.
5 An analyst is using the data in the following table to prepare a statistical report.
Portfolio’s Deviations from Benchmark Return, 2003–2014
(%)
2003 2.48 2009 –9.19
2004 –2.59 2010 –5.11
2005 9.47 2011 1.33
2006 –0.55 2012 6.84
2007 –1.69 2013 3.04
2008 –0.89 2014 4.72
© 2016 CFA Institute. All rights reserved.
8 ■ Statistical Concepts and Market Returns2
The cumulative relative frequency for the interval −1.71% ≤ x < 2.03% is closest
to:
A 0.250.
B 0.333.
C 0.583.
The following information relates to Questions
6–7
The following histogram shows a distribution of the S&P 500 Index annual returns
from 1964 to 2013:
0
1
2
3
4
5
6
7
8
33%
to 3
8%
28%
to 3
3%
23%
to 2
8%
18%
to 2
3%
13%
to 1
8%
8%
to 1
3%
3%
to 8
%
–2%
to 3
%
–7%
to –
2%
–12
% t
o –7
%
–17
% t
o –1
2%
–22
% t
o –1
7%
–27
% t
o –2
2%
–32
% t
o –2
7%
–37
% t
o –3
2%
Frequency
Return Intervals
6 The interval containing the median return is:
A 3% to 8%.
B 8% to 13%.
C 13% to 18%.
7 Based on the previous histogram, the distribution is best described as having:
A one mode.
B two modes.
C three modes.
8 The following is a frequency polygon of monthly exchange rate changes
in the US dollar/Japanese yen spot exchange rate from January 2010 to
December 2013. A positive change represents yen appreciation (the yen buys
more dollars), and a negative change represents yen depreciation (the yen buys
fewer dollars).
Practice Problems 3
Monthly Changes in the US Dollar/Japanese Yen Spot Exchange Rate
0
5
10
15
20
3.0%1.0%–1.0%–3.0%–5.0%
Frequency
Return Interval Midpoint
Based on the chart, yen appreciation:
A occurred more than 50% of the time.
B was less frequent than yen depreciation.
C in the 0.0 to 2.0 interval occurred 20% of the time.
9 The annual returns for three portfolios are shown in the following table.
Portfolios P and R were created in 2009, Portfolio Q in 2010.
Annual Portfolio Returns (%)
2009 2010 2011 2012 2013
Portfolio P –3.0 4.0 5.0 3.0 7.0
Portfolio Q –3.0 6.0 4.0 8.0
Portfolio R 1.0 –1.0 4.0 4.0 3.0
The median annual return from portfolio creation to 2013 for:
A Portfolio P is 4.5%.
B Portfolio Q is 4.0%.
C Portfolio R is higher than its arithmetic mean annual return.
10 In 2015, an investor allocated his retirement savings in the asset classes shown
in the following table.
Asset Class
Asset Allocation
(%)
Asset Class Return
(%)
Large- cap US equities 20.0 8.0
Small- cap US equities 40.0 12.0
Emerging market equities 25.0 –3.0
High- yield bonds 15.0 4.0
■ Statistical Concepts and Market Returns4
The portfolio return in 2015 is closest to:
A 5.1%.
B 5.3%.
C 6.3%.
11 The following table shows the annual returns for Fund Y.
Fund Y (%)
2010 19.5
2011 –1.9
2012 19.7
2013 35.0
2014 5.7
The geometric mean for Fund Y is closest to:
A 14.9%.
B 15.6%.
C 19.5%.
12 A manager invests €5,000 annually in a security for four years at the prices
shown in the following table.
Purchase Price of
Security (€)
Year 1 62.00
Year 2 76.00
Year 3 84.00
Year 4 90.00
The average price paid for the security is closest to:
A €76.48.
B €77.26.
C €78.00.
The following information relates to Questions
13–14
The following table shows the annual MSCI World Index total returns for 2004–2013.
2004 15.25% 2009 30.79%
2005 10.02% 2010 12.34%
2006 20.65% 2011 –5.02%
2007 9.57% 2012 16.54%
2008 –40.33% 2013 27.37%
13 The fourth quintile return for the MSCI World Index is closest to:
A 20.65%.
B 26.03%.
Practice Problems 5
C 27.37%.
14 For 2009–2013, the mean absolute deviation of the MSCI World Index total
returns is closest to:
A 10.20%.
B 12.74%.
C 16.40%.
15 Annual returns and summary statistics for three funds are listed in the follow-
ing table:
Annual Returns (%)
Year Fund ABC Fund XYZ Fund PQR
2009 –20.0 –33.0 –14.0
2010 23.0 –12.0 –18.0
2011 –14.0 –12.0 6.0
2012 5.0 –8.0 –2.0
2013 –14.0 11.0 3.0
Mean –4.0 –10.8 –5.0
Standard deviation 17.8 15.6 10.5
The fund that shows the highest dispersion is:
A Fund PQR if the measure of dispersion is the range.
B Fund XYZ if the measure of dispersion is the variance.
C Fund ABC if the measure of dispersion is the mean absolute deviation.
16 Over the past 240 months, an investor’s portfolio had a mean monthly return
of 0.79%, with a standard deviation of monthly returns of 1.16%. According to
Chebyshev’s inequality, the minimum number of the 240 monthly returns that
fall into the range of −0.95% to 2.53% is closest to:
A 80.
B 107.
C 133.
17 The mean monthly return and the standard deviation for three industry sectors
are shown in the following table.
Sector
Mean Monthly Return
(%)
Standard Deviation of
Return (%)
Utilities (UTIL) 2.10 1.23
Materials (MATR) 1.25 1.35
Industrials (INDU) 3.01 1.52
Based on the coefficient of variation, the riskiest sector is:
A utilities.
B materials.
C industrials.
18 Three equity fund managers have performance records summarized in the fol-
lowing table:
■ Statistical Concepts and Market Returns6
Mean Annual Return (%)
Standard Deviation of
Return (%)
Manager 1 14.38 10.53
Manager 2 9.25 6.35
Manager 3 13.10 8.23
Given a risk- free rate of return of 2.60%, which manager performed best based
on the Sharpe ratio?
A Manager 1
B Manager 2
C Manager 3
The following information relates to Questions
19–21
The following table shows various statistics for Portfolios 1, 2, and 3.
Mean Return
(%)
Standard
Deviation of
Returns (%) Skewness
Excess
Kurtosis
Portfolio 1 7.8 15.1 0.0 0.7
Portfolio 2 10.2 20.5 0.9 –1.8
Portfolio 3 12.9 29.3 –1.5 6.2
19 An investment adviser bases his allocation on the Sharpe ratio. Assuming a
risk- free rate of 1.5%, which portfolio is he most likely to recommend?
A Portfolio 1
B Portfolio 2
C Portfolio 3
20 The skewness of Portfolio 1 indicates its mean return is most likely:
A less than its median.
B equal to its median.
C greater than its median.
21 Compared with a normal distribution, the distribution of returns for Portfolio 3
most likely:
A is less peaked.
B has a greater number of extreme returns.
C has fewer small deviations from its mean.
22 Two portfolios have unimodal return distributions. Portfolio 1 has a skewness
of 0.77, and Portfolio 2 has a skewness of –1.11.
Which of the following is correct?
A For Portfolio 1, the median is less than the mean.
B For Portfolio 1, the mode is greater than the mean.
Practice Problems 7
C For Portfolio 2, the mean is greater than the median.
23 When analyzing investment returns, which of the following statements is
correct?
A The geometric mean will exceed the arithmetic mean for a series with non-
zero variance.
B The geometric mean measures an investment’s compound rate of growth
over multiple periods.
C The arithmetic mean accurately estimates an investment’s terminal value
over multiple periods.










































































































































































































































































































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