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Quantitative Methods > READING 3 STATISTICAL MEASURES OF ASSET RETURNS > Flashcards

READING 3 STATISTICAL MEASURES OF ASSET RETURNS Flashcards

1
Q

Identify the center, or average, of a dataset. This central point can then be used to represent the typical or expected value in the dataset.

A

Measures of a central tendency

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2
Q

What is the most widely used measure of central tendency?

A

Arithmetic mean

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3
Q

the sum of all the values in a sample of a population, ΣX, divided by the number of observations in the sample, n. It is used to make inferences about the population mean.

A

Sample mean which is an example of arithmetic mean

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4
Q

Midpoint of a data set, where the data are arranged in ascending or descending order.

A

Median

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5
Q

When is the median better measure of central tendency than the mean?

A

When the mean is affected by outliers

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6
Q

What is the median return for five portfolio managers with a 10-year annualized total returns record of 30%, 15%, 25%, 21%, and 23%?

A

23%

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7
Q

What is the median return for five portfolio managers with a 10-year annualized total returns record of 30%, 15%, 25%, 21%, and 23%

Suppose we add a sixth manager to the previous example with a return of 28%. What is the median return?

A

24%

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8
Q

The value that occurs most frequently in a dataset

A

Mode

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9
Q

When a distribution has one value that appears most frequently, it is said to be

A

Unimodal

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10
Q

When a dataset has two or three values that occur most frequently, it is said to be

A

Bimodal and Trimodal

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11
Q

What is the mode of the following dataset?
Dataset: 30%, 28%, 25%, 23%, 28%, 15%, 5%

A

28%

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12
Q

True or false

For continuous data, such as investment returns, we typically do not identify a single outcome as the mode. Instead, we divide the relevant range of outcomes into intervals, and we identify the modal interval as the one into which the largest number of observations fall

A

True

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13
Q

In some cases, a researcher may decide that outliers should be excluded from a measure of central tendency, what techniques should he use?

A

Trimmed and Winsorized mean

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14
Q

A technique that excludes a stated percentage of the most extreme observations. A 1% mean, for example, would discard the lowest 0.5% and the highest 0.5% of the observations

A

Trimmed mean

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15
Q

A technique that instead of removing the extreme values, this method replaces them with the nearest values that are not considered outliers. For example, in a 90% mean, the lowest 5% of values are replaced with the 5th percentile value, and the highest 5% of values are replaced with the 95th percentile value. Then, the mean is calculated using these adjusted values

A

Winsorized mean

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16
Q

Is the general term for a value at or below which a stated proportion of the data in a distribution lies. Or values that divide a dataset into equal parts. They help in understanding the distribution of data

A

Quantile

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17
Q

The distribution is divided into quarters

A

Quartile

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18
Q

The distribution is divided into fifths

A

Quintile

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19
Q

The distribution is divided into tenths

A

Decile

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20
Q

The distribution is divided into hundredths (percentages)

A

Percentile

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21
Q

Note that any quantile may be expressed as a percentile. For example, the third quartile partitions the distribution at a value such that three-fourths, or 75%, of the observations fall below that value. Thus, the third quartile is the 75th percentile

What is the difference between the third quartile and the first quartile (25th percentile) known as?

A

Interquartile range

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22
Q

What is defined as the variability around the central tendency?

A

Dispersion

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23
Q

True or false

The common theme in finance and investments is the tradeoff between reward and variability, where the central tendency is the measure of risk and dispersion is the measure of reward

A

False

Correction: The central tendency is the measure of reward and dispersion is the measure of risk

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24
Q

Relatively simple measure of variability, but when used with other measures, it provides useful information. The distance between the largest and the smallest value in the dataset

A

Range

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25
Q

What is the range for the 5-year annualized total returns for five investment managers if the managers’ individual returns were 30%, 12%, 25%, 20%, and 23%?

A

Range = 30 − 12 = 18%

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26
Q

The average of the absolute values of the deviations of individual observations from the arithmetic mean

A

The mean absolute deviation (MAD)

27
Q

True or false

The computation of the MAD uses the absolute values of each deviation from the mean because the sum of the actual deviations from the arithmetic mean is zero

A

True

28
Q

Managers’ individual returns were 30%, 12%, 25%, 20%, and 23%

What is the MAD of the investment returns?

A

4.8%

29
Q

What is the measure of dispersion that applies when we are evaluating a sample of n observations from a population

A

Sample variance

30
Q

Explain why the denominator for s2 or simple variance is n − 1, one less than the sample size n?

A

Based on the mathematical theory behind statistical procedures, the use of the entire number of sample observations, n, instead of n − 1 as the divisor in the computation of s2, will systematically underestimate the population variance—particularly for small sample sizes. This systematic underestimation causes the sample variance to be a biased estimator of the population variance.

31
Q

Assume that the 5-year annualized total returns for the Five investment managers used in the preceding examples represent only a sample of the managers at a large investment firm. What is the sample variance of these returns?

30%, 12%, 25%, 20%, 23%

A

Thus, the sample variance of 44.5(%2) can be interpreted to be an unbiased estimator of the population variance.

Note that 44.5 “percent squared” is 0.00445, and you will get this value if you put the percentage returns in decimal form [e.g., (0.30 − 0.22)2]

32
Q

What is the major problem with using variance?

A

The computed variance, unlike the mean, is in terms of squared units of measurement. How does one interpret squared percentages, squared dollars, or squared riyals? This problem is mitigated through the use of the standard deviation.

33
Q

Is the square root of the sample variance

A

Standard deviation

An example equation of standard deviation would just be square root of the existing sample variance

34
Q

A direct comparison between two or more measures of dispersion may be difficult.

To make a meaningful comparison, a relative measure of dispersion must be used. It is the amount of variability in a distribution around a reference point or benchmark

A

Relative dispersion

35
Q

Relative dispersion is commonly measured with the?

A

Coefficient of variation

36
Q

Measure the amount of dispersion in a distribution relative to the distribution’s mean. This is useful because it enables us to compare dispersion across different sets of data. In an investment setting, It is used to measure the risk (variability) per unit of expected return (mean). The lower it is the better

A

Coefficient of variation

37
Q

You have just been presented with a report that indicates that the mean monthly return on T-bills is 0.25% with a standard deviation of 0.36%, and the mean monthly return for the S&P 500 is 1.09% with a standard deviation of 7.30%. Your manager has asked you to compute the CV for these two investments and to interpret your results.

A

CV T-Bills = 1.44
CV S&P 500 = 6.70

These results indicate that there is less dispersion (risk) per unit of monthly return for T-bills than for the S&P 500 (1.44 vs. 6.70).

38
Q

In some situations, it may be more appropriate to consider only outcomes less than the mean (or some other specific value) in calculating a risk measure. In this case, we are measuring

A

Downside risks

39
Q

One measure of downside risk is

A

Target downside deviation, which is also known as target semi deviation.

40
Q

What is target downside deviation?

A

Target downside deviation is a risk measure that focuses on the negative deviations of returns from a specified target return.

Unlike standard deviation, which considers both positive and negative deviations, target downside deviation only considers outcomes that fall below the target.

This makes it particularly useful for investors who are more concerned about downside risk (i.e., the risk of losing money) than upside potential.

41
Q

Calculate the target downside deviation based on the data in the preceding examples, for a target return equal to the mean (22%), and for a target return of 24%.

30%, 12%, 25%, 20%, 23%

A

Deviation from mean = 5.10%
Deviation from target = 6.34%

42
Q

Implies that intervals of losses and gains will exhibit the same frequency

A

Distributional symmetry

For example, a symmetrical distribution with a mean return of zero will have losses in the −6% to −4% interval as frequently as it will have gains in the +4% to +6% interval.

43
Q

refers to the extent to which a distribution is not symmetrical

A

Skewness

44
Q

True or false

Symmetrical distributions may be either positively or negatively skewed and result from the occurrence of outliers in the dataset

A

False

Correction: Nonsymmetrical

45
Q

Observations extraordinarily far from the mean

A

Outliers

46
Q

A distribution that is characterized by outliers greater than the mean (in the upper region, or right tail). The distribution is said to be skewed to the right because of its relatively long upper (right) tail

A

A positively skewed distribution

47
Q

A distribution that has a disproportionately large number of outliers less than the mean that fall within its lower (left) tail. It is said to be skewed left because of its long lower tail.

A

A negatively skewed distribution

48
Q

For a …. distribution, the mean, median, and mode are equal

A

Symmetrical

49
Q

Effects of the location of the mean, median, and mode in a positive skewed distribution

A

Mean > Median > Mode

The mean is pulled to the right (higher values)

50
Q

Effects of the location of the mean, median, and mode in a negative skewed distribution

A

Mean < Median < Mode

The mean is pulled to the left (lower values)

51
Q

The key to remembering how measures of central tendency are affected by skewed data is to recognize that skew affects the …. more than the …. and …. and the …. is pulled in the direction of the skew. Note that the …. is between the other two measures for positively or negatively skewed distributions.

A
  1. Mean
  2. Median
  3. Mode
  4. Mean
  5. Median
52
Q

is equal to the sum of the cubed deviations from the mean divided by the cubed standard deviation and by the number of observations.

A

Sample skewness

Note that the denominator is always positive, but that the numerator can be positive or negative depending on whether observations above the mean or observations below the mean tend to be farther from the mean, on average. When a distribution is right skewed, sample skewness is positive because the deviations above the mean are larger, on average. A left-skewed distribution has a negative sample skewness

The LOS requires us to “interpret and evaluate” measures of skewness and kurtosis, but not to calculate them

53
Q

Is a measure of the degree to which a distribution is more or less peaked than a normal distribution

A

Kurtosis

54
Q

Describes a distribution that is more peaked than a normal distribution

A

Leptokurtic

55
Q

Refers to a distribution that is less peaked, or flatter than a normal one

A

Platykurtic

56
Q

A distribution is …. if it has the same kurtosis as a normal distribution

A

Mesokurtic

57
Q

True or false

The computed kurtosis for all normal distributions is three. Statisticians, however, sometimes report excess kurtosis, which is defined as kurtosis minus three. Thus, a normal distribution has excess kurtosis equal to zero, a leptokurtic distribution has excess kurtosis less than zero, and platykurtic distributions will have excess kurtosis greater than zero.

A

False

Correction: A leptokurtic distribution has excess kurtosis greater than zero, and platykurtic distributions will have excess kurtosis less than zero

58
Q

Large samples approximated using deviations raised to the fourth power

A

Sample kurtosis

59
Q

Method for displaying the relationship between two variables

A

Scatter plot

60
Q

Measure of how two variables move together

A

Covariance

61
Q

A standardized measure of the linear relationship between two variables

A

Correlation coefficient or Correlation

62
Q

Correlation that is either the result of chance or present due to changes in both variables over time that is caused by their association with a third variable

A

Spurious correlation

63
Q
A

Quantitative Methods (11 decks)

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