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Questions and Answers
The company's average compound annual growth rate of earnings is closest to:
The company's average compound annual growth rate of earnings is closest to:
- 7.7% (correct)
- 8.5%
- 8.0%
The sample standard deviation of the prices of condominiums is closest to:
The sample standard deviation of the prices of condominiums is closest to:
- 38.47
- 370.00
- 19.24 (correct)
Which security has the highest level of relative risk as measured by the coefficient of variation?
Which security has the highest level of relative risk as measured by the coefficient of variation?
- Y. (correct)
- Z.
- X.
The mean absolute deviation (MAD) of the dataset 25, 15, 35, 45, and 55 is closest to:
The mean absolute deviation (MAD) of the dataset 25, 15, 35, 45, and 55 is closest to:
Determine if the geometric return of the fund will be less than or greater than the arithmetic return and calculate the fund's geometric return:
Determine if the geometric return of the fund will be less than or greater than the arithmetic return and calculate the fund's geometric return:
What is the compound annual growth rate for stock A which has annual returns of 5.60%, 22.67%, and -5.23%?
What is the compound annual growth rate for stock A which has annual returns of 5.60%, 22.67%, and -5.23%?
The expected return on a portfolio invested in Stock A (expected return 6%), Stock B (expected return 10%), and a risk-free asset (return 5%) is:
The expected return on a portfolio invested in Stock A (expected return 6%), Stock B (expected return 10%), and a risk-free asset (return 5%) is:
The third quartile is calculated for the following set of stock returns: 12%, 23%, 27%, 10%, 7%, 20%, 15%. Which is it?
The third quartile is calculated for the following set of stock returns: 12%, 23%, 27%, 10%, 7%, 20%, 15%. Which is it?
Relative to a portfolio with normally distributed returns, a portfolio with a kurtosis measure of 4.2 has a:
Relative to a portfolio with normally distributed returns, a portfolio with a kurtosis measure of 4.2 has a:
The sample standard deviation from the following annual returns: Firm 1 15%, Firm 2 2%, Firm 3 5%, Firm 4 (7%), Firm 5 0% is closest to:
The sample standard deviation from the following annual returns: Firm 1 15%, Firm 2 2%, Firm 3 5%, Firm 4 (7%), Firm 5 0% is closest to:
For a unimodal distribution with negative skewness, which statement is true?
For a unimodal distribution with negative skewness, which statement is true?
What is the order (from lowest value to highest) for mode, mean, and median in a negatively skewed distribution?
What is the order (from lowest value to highest) for mode, mean, and median in a negatively skewed distribution?
What is the sample variance of the ROE over the last three years for Acme Corp with returns of 4%, 10%, and 1%?
What is the sample variance of the ROE over the last three years for Acme Corp with returns of 4%, 10%, and 1%?
The average compound annual rate over the four years for these returns: R1 = +10%, R2 = –15%, R3 = 0%, R4 = +5% is closest to:
The average compound annual rate over the four years for these returns: R1 = +10%, R2 = –15%, R3 = 0%, R4 = +5% is closest to:
A distribution with a mode of 10 and a range of 2 to 25 would most likely be:
A distribution with a mode of 10 and a range of 2 to 25 would most likely be:
The sample standard deviation of asset returns from the following: A - 1.3%, B - 1.4%, C - 2.2%, D - 3.4% is closest to:
The sample standard deviation of asset returns from the following: A - 1.3%, B - 1.4%, C - 2.2%, D - 3.4% is closest to:
The equivalent compound annual rate for XYZ Corporation with returns of 10.4%, 8.1%, 3.2%, and 15.0% is:
The equivalent compound annual rate for XYZ Corporation with returns of 10.4%, 8.1%, 3.2%, and 15.0% is:
Find the respective mean and mean absolute deviation (MAD) of a series of stock market returns (Year 1: 14%, Year 2: 20%, Year 3: 24%, Year 4: 22%):
Find the respective mean and mean absolute deviation (MAD) of a series of stock market returns (Year 1: 14%, Year 2: 20%, Year 3: 24%, Year 4: 22%):
The interquartile range for the given box-and-whisker plot is:
The interquartile range for the given box-and-whisker plot is:
Stock X's expected return is 30% and its expected standard deviation is 5%. What is Stock X's expected coefficient of variation?
Stock X's expected return is 30% and its expected standard deviation is 5%. What is Stock X's expected coefficient of variation?
Given the following data set: 17, 3, 13, 3, 5, 9, 8, the value 8 is most accurately described as the:
Given the following data set: 17, 3, 13, 3, 5, 9, 8, the value 8 is most accurately described as the:
What are the geometric and arithmetic mean returns, respectively, for the annual returns of 2002 (15%), 2003 (2%), 2004 (5%), 2005 (-7%), 2006 (0%)?
What are the geometric and arithmetic mean returns, respectively, for the annual returns of 2002 (15%), 2003 (2%), 2004 (5%), 2005 (-7%), 2006 (0%)?
A distribution of returns that has a greater percentage of small deviations from the mean compared to a normal distribution:
A distribution of returns that has a greater percentage of small deviations from the mean compared to a normal distribution:
If a distribution is positively skewed, then generally:
If a distribution is positively skewed, then generally:
The following data points are observed returns: 4.2%, 6.8%, 7.0%, 10.9%, 11.6%, 14.4%, 17.0%, 19.0%, 22.5%. What return lies at the 70th percentile?
The following data points are observed returns: 4.2%, 6.8%, 7.0%, 10.9%, 11.6%, 14.4%, 17.0%, 19.0%, 22.5%. What return lies at the 70th percentile?
Which of the following statements about kurtosis is least accurate?
Which of the following statements about kurtosis is least accurate?
Consider the following statements about the geometric and arithmetic means as measures of central tendency. Which statement is least accurate?
Consider the following statements about the geometric and arithmetic means as measures of central tendency. Which statement is least accurate?
What is the seventh decile of the following data points?
What is the seventh decile of the following data points?
The mean monthly return on a sample of small stocks is 4.56% with a standard deviation of 3.56%. If the risk-free rate is 1%, what is the coefficient of variation?
The mean monthly return on a sample of small stocks is 4.56% with a standard deviation of 3.56%. If the risk-free rate is 1%, what is the coefficient of variation?
What is the coefficient of variation for a distribution with a mean of 10 and a variance of 4?
What is the coefficient of variation for a distribution with a mean of 10 and a variance of 4?
A distribution that has positive excess kurtosis is:
A distribution that has positive excess kurtosis is:
An investor has a portfolio with 10% cash, 30% bonds, and 60% stock. If last year's returns were 2.0% (cash), 9.5% (bonds), and 25% (stock), what was the return on the portfolio?
An investor has a portfolio with 10% cash, 30% bonds, and 60% stock. If last year's returns were 2.0% (cash), 9.5% (bonds), and 25% (stock), what was the return on the portfolio?
An investor has a portfolio of $12,000 consisting of $7,000 in stock P with an expected return of 20% and $5,000 in stock Q with an expected return of 10%. What is the investor's expected return on the portfolio?
An investor has a portfolio of $12,000 consisting of $7,000 in stock P with an expected return of 20% and $5,000 in stock Q with an expected return of 10%. What is the investor's expected return on the portfolio?
Michael Philizaire decides to calculate the geometric average of the appreciation/deprecation of his home over the last five years. The year-to-year percentage changes are: 20, 15, 0, -5, -5. The geometric return is closest to:
Michael Philizaire decides to calculate the geometric average of the appreciation/deprecation of his home over the last five years. The year-to-year percentage changes are: 20, 15, 0, -5, -5. The geometric return is closest to:
The respective arithmetic mean and geometric mean returns of the following series of stock market returns: Year 1 14%, Year 2 6%, Year 3 −5%, Year 4 20%:
The respective arithmetic mean and geometric mean returns of the following series of stock market returns: Year 1 14%, Year 2 6%, Year 3 −5%, Year 4 20%:
Which of the following statements concerning kurtosis is most accurate?
Which of the following statements concerning kurtosis is most accurate?
What are the median and the third quintile of the data points: 9.2%, 10.1%, 11.5%, 11.9%, 12.2%, 12.8%, 13.1%, 13.6%, 13.9%, 14.2%, 14.8%, 14.9%, 15.4%?
What are the median and the third quintile of the data points: 9.2%, 10.1%, 11.5%, 11.9%, 12.2%, 12.8%, 13.1%, 13.6%, 13.9%, 14.2%, 14.8%, 14.9%, 15.4%?
An analyst compiles the returns on Fund Q over the last four years: Year 1 4%, Year 2 3%, Year 3 2%, Year 4 30%. Which return measure will result in the lowest mean return?
An analyst compiles the returns on Fund Q over the last four years: Year 1 4%, Year 2 3%, Year 3 2%, Year 4 30%. Which return measure will result in the lowest mean return?
The annual returns on ABC Mutual Fund for the last 10 years are 11.0%, 12.5%, 8.0%, 9.0%, 13.0%, 7.0%, 15.0%, 2.0%, -16.5%, 11.0%. Assuming a mean of 7.2%, what is the sample standard deviation?
The annual returns on ABC Mutual Fund for the last 10 years are 11.0%, 12.5%, 8.0%, 9.0%, 13.0%, 7.0%, 15.0%, 2.0%, -16.5%, 11.0%. Assuming a mean of 7.2%, what is the sample standard deviation?
Which of the following statements concerning skewness is least accurate?
Which of the following statements concerning skewness is least accurate?
A 5% trimmed mean ignores the:
A 5% trimmed mean ignores the:
Given the annual returns on 5 portfolio investments what is the return on the portfolio?
Given the annual returns on 5 portfolio investments what is the return on the portfolio?
Twenty Level I CFA candidates in a study group took a practice exam. If one candidate's score is a low outlier, including their score will most likely:
Twenty Level I CFA candidates in a study group took a practice exam. If one candidate's score is a low outlier, including their score will most likely:
The correlation between two variables is –0.74. The most appropriate way to interpret this correlation is that:
The correlation between two variables is –0.74. The most appropriate way to interpret this correlation is that:
The following annualized monthly return measures have been calculated for an investment based on its performance over the last 72 months. If for one month in the period the return was extremely high, which measure best reflects the central tendency of the investment's returns?
The following annualized monthly return measures have been calculated for an investment based on its performance over the last 72 months. If for one month in the period the return was extremely high, which measure best reflects the central tendency of the investment's returns?
In a positively skewed distribution, what is the order (from lowest value to highest) for the distribution's mode, mean, and median values?
In a positively skewed distribution, what is the order (from lowest value to highest) for the distribution's mode, mean, and median values?
The owner of a company raised the salary of one employee making the highest salary by 40%. Which of the following value(s) is (are) expected to be affected by this raise?
The owner of a company raised the salary of one employee making the highest salary by 40%. Which of the following value(s) is (are) expected to be affected by this raise?
Which of the following statements concerning a distribution with positive skewness and positive excess kurtosis is least accurate?
Which of the following statements concerning a distribution with positive skewness and positive excess kurtosis is least accurate?
The mean monthly return on a security is 0.42% with a standard deviation of 0.25%. What is the coefficient of variation?
The mean monthly return on a security is 0.42% with a standard deviation of 0.25%. What is the coefficient of variation?
What does it mean to say that an observation is at the sixty-fifth percentile?
What does it mean to say that an observation is at the sixty-fifth percentile?
If the historical mean return on an investment is 2.0%, the standard deviation is 8.8%, and the risk-free rate is 0.5%, what is the coefficient of variation (CV)?
If the historical mean return on an investment is 2.0%, the standard deviation is 8.8%, and the risk-free rate is 0.5%, what is the coefficient of variation (CV)?
Given the following annual returns, what is the mean absolute deviation?
Given the following annual returns, what is the mean absolute deviation?
A distribution that is more peaked than a normal distribution is termed:
A distribution that is more peaked than a normal distribution is termed:
Returns for a portfolio over the last four years show returns: Year 1 17.0%, Year 2 12.2%, Year 3 3.9%, Year 4 -8.4%. What is their coefficient of variation (CV)?
Returns for a portfolio over the last four years show returns: Year 1 17.0%, Year 2 12.2%, Year 3 3.9%, Year 4 -8.4%. What is their coefficient of variation (CV)?
An analyst calculates a winsorized mean return of 3.2% for an investment fund. This measure most likely:
An analyst calculates a winsorized mean return of 3.2% for an investment fund. This measure most likely:
Over the last five years, an investment fund's monthly returns were stable apart from last year, where two extremely high returns were recorded. If the arithmetic mean for the fund's monthly returns over the period is 6.7%, a trimmed or winsorized mean return is most likely to be:
Over the last five years, an investment fund's monthly returns were stable apart from last year, where two extremely high returns were recorded. If the arithmetic mean for the fund's monthly returns over the period is 6.7%, a trimmed or winsorized mean return is most likely to be:
The correlation coefficient between the return on an investment and the rate of economic growth is -0.065. An analyst should most likely interpret this correlation coefficient as indicating that returns on this investment are:
The correlation coefficient between the return on an investment and the rate of economic growth is -0.065. An analyst should most likely interpret this correlation coefficient as indicating that returns on this investment are:
If an analyst concludes that the distribution of a large sample of returns is positively skewed, which of the following relationships involving the mean, median, and mode is most likely?
If an analyst concludes that the distribution of a large sample of returns is positively skewed, which of the following relationships involving the mean, median, and mode is most likely?
An investor has the following assets: $5,000 in bonds (expected return of 8%), $10,000 in equities (expected return of 12%), $5,000 in real estate (expected return of 10%). What is the portfolio's expected return?
An investor has the following assets: $5,000 in bonds (expected return of 8%), $10,000 in equities (expected return of 12%), $5,000 in real estate (expected return of 10%). What is the portfolio's expected return?
For a positively skewed distribution, the median is greater than:
For a positively skewed distribution, the median is greater than:
For the investments shown in the table below: Investment A 12%, Investment B 14%, Investment C 9%, Investment D 13%, Investment E 7%, Investment F 8%, Investment G 12%. Which statement is most accurate?
For the investments shown in the table below: Investment A 12%, Investment B 14%, Investment C 9%, Investment D 13%, Investment E 7%, Investment F 8%, Investment G 12%. Which statement is most accurate?
Flashcards
Geometric Mean
Geometric Mean
Average growth rate over multiple periods, compounding effects included.
Sample Standard Deviation
Sample Standard Deviation
Measures the dispersion around the average in sample data.
Coefficient of Variation (CV)
Coefficient of Variation (CV)
Standard deviation divided by the arithmetic mean, measuring relative risk.
Mean Absolute Deviation (MAD)
Mean Absolute Deviation (MAD)
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Geometric Return
Geometric Return
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Compound Annual Growth Rate
Compound Annual Growth Rate
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Leptokurtic
Leptokurtic
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Standard Deviation
Standard Deviation
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Negatively Skewed Distribution
Negatively Skewed Distribution
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Geometric Mean Return
Geometric Mean Return
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70th Percentile
70th Percentile
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A 5% Trimmed Mean
A 5% Trimmed Mean
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Coefficient of Variation
Coefficient of Variation
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Positive Excess Kurtosis
Positive Excess Kurtosis
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Positively Skewed Data
Positively Skewed Data
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Winsorized Mean
Winsorized Mean
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Study Notes
Compound Annual Growth Rate
- Calculated using the geometric mean
- The geometric mean calculation:
[(1.10)(1.14)(1.12)(1.10)(0.90)(1.12)]1/6 − 1 = 0.0766, resulting in7.66%
Sample Standard Deviation
- This measures the dispersion of sample data around the sample mean
- Calculations Involve:
- Calculating the sample mean
(125 + 175 + 150 + 155 + 135) / 5 = 148- Calculating the Sample Variance
[(125 – 148)2 + (175 – 148)2 + (150 – 148)2 + (155 – 148)2 + (135 – 148)2] / (5 – 1) = 1,480 / 4 = 370- Standard Deviation:
3701/2 = 19.24%
Coefficient of Variation
- Defined as standard deviation / arithmetic mean
- Measures relative dispersion/risk
- Security Y has the highest relative risk at 3.92, since a higher CV denotes higher relative risk
- CVX = 0.7 / 0.9 = 0.78
- CVY = 4.7 / 1.2 = 3.92
- CVZ = 5.2 / 1.5 = 3.47
Mean Absolute Deviation (MAD)
- Calculated by summing the deviations around the mean (ignoring the sign) and dividing by the number of observations
- Example calculation:
- Mean is
(25+15+35+45+55)/5 = 35 - MAD is
(10+20+0+10+20) / 5 = 12
- Mean is
Geometric Return
- Geometric return <= arithmetic return
- The geometric return calculation:
[(1 + 0.25)(1 + 0.15)(1 + 0.12)(1 - 0.08)(1 – 0.14)]1/5 – 1 = 0.4960, is4.96%.
Compound Annual Growth Rate
- Defined as the geometric mean.
- Example calculation:
(1.056 × 1.2267 × 0.9477)1/3 – 1 = 7.08%
Expected Return on a Portfolio
- Calculate with the equation:
(0.333)(0.06) + (0.333)(0.10) + 0.333(0.05) = 0.07- Therefore, the expected return is7.0%
Third Quartile
- The third quartile is calculated as:
- Ly =
(n + 1) (75/100)
- Ly =
- The third quartile in the returns series
7%, 10%, 12%, 15%, 20%, 23%, 27%is23%Ly = (7 + 1) (75/100) = 6.
Kurtosis
- Leptokurtic distributions are more peaked in the middle, data is more clustered around the mean, with greater probability of outliers
Sample Standard Deviation
- The sample variance is calculated by summing the squared deviations from the mean and dividing by
(n - 1) - Example calculation:
[(15 – 3)2 + (2 – 3)2 + (5 – 3)2 + (-7 – 3)2 + (0 – 3)2] / (5 – 1) = 64.5
- Sample standard deviation is the square root of the sample variance
- Example,
√64.5 = 8.03
- Example,
Unimodal Distribution with Negative Skewness
- The mean < median < mode.
Negatively Skewed Distribution
- The lowest to highest order for distribution values is: mean, median, mode
Sample Variance of Returns on Equity (ROE)
- Calculated by
[(4 – 5)² + (10 – 5)² + (1 – 5)²] / (3 – 1) = 21(%²)
Average Compound Annual Rate
- Defined as
G = [(1.10)(0.85)(1.00)(1.05)]^(0.25) – 1 = (0.98175)^(0.25) – 1 = 0.9954 – 1 = -0.00459 ≈ −0.5%
Distribution Skewness
- A distribution with a mode of
10and a range of2to25is positively skewed, the distance is skewed to the right
Sample Standard Deviation
- Square root of the sum of squares of the position returns less the mean return, divided by the number of observations in the sample minus one
Equivalent Compound Annual Rate
(1.104 × 1.081 × 1.032 × 1.15)^0.25 – 1 = 9.1%
Mean Absolute Deviation (MAD)
MAD = [|14-20| + |20 – 20| + |24 – 20| + |22 – 20|] / 4 = 3%
Interquartile Range
- The interquartile range (IQR) spans from the first quartile (25th percentile) to the third quartile (75th percentile)
- Represented by the box in a box-and-whisker plot.
- The horizontal line inside represents the median (50th percentile).
Coefficient of Variation
- The coefficient of variation (CV) is the standard deviation divided by the mean,
5 / 30 = 0.167.
Median
- Median is middle distribution value
- Example calculation:
- Mean =
(3 + 3+5+8+9+13 + 17) / 7 = 8.28 - Mode =
3
- Mean =
Geometric And Arithmetic Mean Returns
- Geometric Mean is
(1.15 × 1.02 × 1.05 × 0.93 × 1.0)^(1/5) – 1 = 1.1454^(1/5) – 1 = 2.75% - Arithmetic Mean is
(15% + 2% + 5% - 7% + 0%) / 5 = 3.00%
Distribution of Returns
- A distribution with more small deviations/mean & more large deviations/mean compared to normal has positive excess kurtosis
Positively Skewed Distributions
- A distribution is positively skewed id mean > median > mode
Percentile Returns
- The 70th percentile is equivalent to the
(9 + 1)(70 / 100) = 7th observation, ascending.
Kurtosis
- Skewness measures the degree to which a distribution is not symmetric.
- Excess kurtosis, relative to a normal distribution, indicates peakedness and reflects the probability of extreme outcomes.
Geometric And Arithmetic Means
- Arithmetic mean estimates the average return over a one-period time horizon.
Quantiles
- Determined as:
Ly = (n + 1)(y) / (100)
Coefficient of Variation
- expresses how much dispersion exists relative to the mean of a distribution
- calculate as
CV = s / mean
A Distribution
- Described as having positive excess kurtosis that's above normal
A Portfolio
- Calculated as adding returns on cash, bonds, and stock.
The Sample Standard
- Calculated using sample variance
Distributions
- Skew should not asymmetrical, outliers should on the left and right tail
Trimmed Mean
- Should discard the lowest and highest values.
Geometric Mean
[(1.12 × 1.14 × 1.09 × 1.13 × 1.07)^(1/5)] – 1 = 10.97%
Returns
- When they grade the score, their distribution should be positively affected.
Correlation
- The high correlation suggests a negative linear association
Central Tendency
- Winsorized mean should be measured to see the distribution
Distribution
- in positively skewed distribution mode is less than median
Expected Value
- Calculate bonds, equities and real estate by dividing the assets
Distribution
- It will reverse positively to negatively skewed
The Mid-Point
- Arrange 7, 8, 9, 12, 12, 13, 14.
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