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1. CFA Ethics & Quantitative Methods > Quantitative Methods > Flashcards

Quantitative Methods Flashcards

1
Q

What are the three ways to “define” an interest rate?

A
  1. Rate of return required in equilibrium for a particular investment,
  2. The discount rate for calculating the present value of future cash flows,
  3. The opportunity cost of consuming now, rather than saving and investing.
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2
Q

The effective annual rate = ?

A
  1. Where m = compounding periods
  2. Measures the amount each dollar will grow in one year
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3
Q

How do you edit the “effective annual rate” equation for non-annual TVM problems?

A

For non-annual time value of money problems, divide the stated annual interest rate by the number of compounding periods per year, m, and multiply the number of years by the number of compounding periods per year.

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4
Q

What is the equation for the present value of a perpetual annuity?

A
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5
Q

What is an annuity?

A
  1. An annuity is a series of equal cash flows that occurs at evenly spaced intervals over time.
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6
Q

What is the “NPV rule”?

A

To accept a project if NPV > 0

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7
Q

What is the “IRR rule”?

A

To accept a project if IRR > required rate of return

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8
Q

What is NPV?

A
  1. Net Present Value
  2. The present value of a project’s future cash flows, discounted at the firm’s cost of capital, less the project’s cost
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9
Q

What is the “holding period yield”?

A

The total return for holding an investment over a certain period of time and can be calculated as:

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10
Q

Holding period yield = ?

A
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11
Q

Money market yield = ?

A

Money market yield = holding period yield × (360/n)

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12
Q

Effective annual yield = ?

A

Effective annual yield = (1 + holding period yield)^365/n − 1

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13
Q

Holding period yield = ?

A

Holding period yield = (1 + effective annual yield)^n/365 − 1

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14
Q

What does the term discounting describe?

A

The process of finding the PV of a cash flow.

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15
Q

The interest rate used in the discounting process is commonly referred to as?

A
  1. Discount rate(most common)
  2. Opportunity cost
  3. Required rate of return
  4. Cost of capital
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16
Q

What are the two types of annuities?

A
  1. Ordinary annuities
  2. Annuities due
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17
Q

What is an ordinary annuity?

A
  1. Most common type of annuity
  2. Typical cash flow pattern for many business/finance applications
  3. Cash flows occur at the END of each period
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18
Q

What is an annuity due?

A

Annuity where payments or receipts occur at the beginning of each period(t=0)

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19
Q

What are the two definitions of amortization?

A
  1. The paying off of debt in regular installments over a period of time.
  2. The deduction of capital expenses over a specific period of time (usually over the asset’s life). More specifically, this method measures the consumption of the value of intangible assets, such as a patent or a copyright.
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20
Q

What are descriptive statistics? Inferential statistics?

A

Descriptive statistics summarize the characteristics of a data set; inferential statistics are used to make probabilistic statements about a population based on a sample.

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21
Q

What are the four major categories of measurement scales?

A
  1. Nominal scale
  2. Ordinal scale
  3. Interval scale
  4. Ratio scale
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22
Q

What is a nominal scale?

A
  1. A scale where data is put into categories that have no particular order.
  2. Ex: Assigning a value of 1 to a Muni Bond Fund, 2 to a Corp Bond Fund, Etc.
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23
Q

What are ordinal scales?

A
  1. Scale where data is put into categories that can be ordered with respect to some characteristic.
  2. Ex: Assigning 1 to the top 100 performing stocks, 2 to the next 100 top performing stocks, etc.
  3. With this type of scale you can infer that a ranking of 1 is better than 2, but you can not quantify the degree that a 1 is better than a 2.
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24
Q

What are Interval scales?

A
  1. Differences in data values are meaningful, but ratios, such as twice as much or twice as large, are not meaningful.
  2. Ex: Tempurature uses an interval scale; a rise or fall of 10 degrees will always be the same no matter how hot or cold it is.
  3. The one downside of this scale is that a measurement of 0 does not necessarily mean an absence of what is being measured. (30C is no going to be three times hotter than 10C)
25
Q

What is a ratio scale?

A
  1. Ratios of values, such as twice as much or half as large, are meaningful, and zero represents the complete absence of the characteristic being measured.
  2. Ex: Money. $0 equals no purchasing power and when you have $10 you have double what you would have if you had $5, etc.
26
Q

What is a parameter?

A

Any measurable characteristic of a population.

27
Q

What does a frequency distribution

A
  1. A representation, either in a graphical or tabular format, which displays the number of observations within a given interval. The intervals must be mutually exclusive and exhaustive.
  2. Groups observations into classes, or intervals.
28
Q

What is an interval?

A
  1. A range of values
  2. Ex: The set of all numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0 and 1, as well as all numbers between them.
29
Q

What is relative frequency?

A
  1. The percentage of total observations falling within an interval.
30
Q

What is cumulative relative frequency for an interval?

A

The sum of the relative frequncies for all values less than or equal to that interval’s maximum value.

31
Q

What is a histogram?

A
  1. A bar chart of data that has been grouped into a frequency distribution
32
Q

What is a frequency polygon?

A
  1. A frequency polygon plots the midpoint of each interval on the horizontal axis and the absolute frequency for that interval on the vertical axis, and connects the midpoints with straight lines.
33
Q

What is the arithmetic mean?

A
  1. The average.
  2. A collection of numbers taken as the sum of the numbers divided by the size of the collection
  3. Ex: population mean and sample mean.
  4. Greatly influenced(or skewed) by outliers.
34
Q

What is the formula for arithmetic mean?

A
35
Q

What is the geometric mean?

A
  1. Used to find a compound growth rate
  2. Similar to the arithmetic mean, except that the numbers are multiplied and then the nth root (where n is the count of numbers in the set) of the resulting product is taken.
36
Q

What is the formula for the geometric mean?

A
37
Q

What is the weighted mean?

A
  1. The weighted mean weights each value according to its influence.
  2. Similar to arithmetic mean, but instead of each of the data points contributing equally to the final average, some data points contribute more than others.
38
Q

What is the weighted mean formula?

A
39
Q

What is the harmonic mean?

A
  1. Can be used to find an average purchase price, such as dollars per share for equal periodic investments.
  2. The preferable method for averaging multiples(P/E Ratio) in which price is in the numerator. If these ratios are averaged using an arithmetic mean (a common error), high data points are given greater weights than low data points. The harmonic mean, on the other hand, gives equal weight to each data point.
40
Q

What is the harmonic mean formula?

A
41
Q

What is the median?

A
  1. The median is the midpoint of a data set when the data is arranged from largest to smallest.
  2. Think of the median in a road!
42
Q

What is the mode of a data set?

A

The value that occurs most frequently.

43
Q

What is a quartile?

A

Quartiles—the distribution is divided into quarters.

44
Q

What is a quintile?

A

Quintile—the distribution is divided into fifths.

45
Q

What is a decile?

A

Decile—the distribution is divided into tenths.

46
Q

What is a percentile?

A

Percentile—the distribution is divided into hundredths (percents).

47
Q

What is the range?

A

The difference between the largest and smallest values in a data set.

48
Q

What is the mean absolute deviation(MAD)?

A
  1. The average of the absolute values of the deviations from the arithmetic mean
    2.
49
Q

What is the Mean Absolute Deviation?

A
  1. The average values of the deviations for the arithmetic mean.
  2. The closer the MAD is to zero, the more consistent the data.
50
Q

What is variance?

A

The mean of the squared deviations from the arithmetic mean, or from the expected value of a distribution.

51
Q

What is standard deviation?

A
  1. The positive square root of the variance
  2. Frequently used as a quantitative measure of risk
52
Q

What does Chebyshev’s inequality state?

A

The proportion of the observations within “k” standard deviations of the mean is at least 1-1/k2 for all K>1

36% of observation lie within +/- 1.25

56% of observation lie within +/- 1.50

75% of observation lie within +/- 2.00

89% of observation lie within +/- 3.00

94% of observation lie within +/- 4.00

53
Q

What is the coefficient of variation for sample data?

A

The coefficient of variation (CV) is defined as the ratio of the standard deviation to the mean

54
Q

What is the sharpe ratio?

A
  1. Measures excess return per unit of risk.
  2. The Sharpe ratio tells us whether a portfolio’s returns are due to smart investment decisions or a result of excess risk.
  3. Very useful because although one portfolio or fund can reap higher returns than its peers, it is only a good investment if those higher returns do not come with too much additional risk.
  4. The greater a portfolio’s Sharpe ratio, the better its risk-adjusted performance has been. A negative Sharpe ratio indicates that a risk-less asset would perform better than the security being analyzed.
55
Q

What is skewness?

A
  1. The degree to which a distribution is not symmetric about it’s mean.
  2. A right skewed distribution has positive skewness.
  3. A left skewed distribution has negative skewness.
56
Q

What is Kurtosis?

A

A measure of the peakedness of a distribution and the probability of extreme outcomes(thickness of tails).

57
Q

What is the kurtosis value of a “normal” distribution?

A

3

58
Q

Positive values of excess kurtosis indicate what?

A
  1. That a distribution is Leptokurtic
  2. The probability of extreme outcomes is greater than for a normal distribution
  3. Fat tails, more peaked
59
Q

Negative values of excess kurtosis indicate what?

A
  1. Platykurtic distribution
  2. Thin tails, less peaked

1. CFA Ethics & Quantitative Methods (8 decks)

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