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CFA Prep (LV1) > Quantitative Methods > Flashcards

Quantitative Methods Flashcards

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1
Q

What is “frequency?”

A

The number of times something appears

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2
Q

What is “relative frequency?”

A

The number of times something appears as a percentage of the total observations.

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3
Q

What does the Sharpe ratio represent?

A

The excess return earned per unit of risk taken

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4
Q

What does standard deviation represent?

A

Standard Deviation is the measure of dispersion away from the mean of a data set.

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5
Q

Name the steps in calculating variance.

A
  1. Take the differences of each data point from the mean.
  2. Square the differences
  3. sum the squared differences.
  4. Divide the sum of squares by the number of data points.
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6
Q

How do you convert variance to standard deviation?

A

Take the square root

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7
Q

What is the conceptual difference between variance and standard deviation

A

They are the same however, standard deviation is in the same units as the mean, whereas variance is in squared units.

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8
Q

If fund A’s coefficient of variation is lower than fund B, which fund has inherently more risk, all things being equal?

A

Fund A

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9
Q

What is the formula for a combination binomial

A

n!/r!(n-r)!

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10
Q

When would you use a combination binomial?

A

When determining the number of possible outcomes.

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11
Q

What are the four types of scales and describe them.

A

Nominal - Categorize or count data but do not rank them.

Ordinal scales- sort data into categories and then are ranked but do not tell us anything about the differences between the categories

Interval scales - rank observations and describe the diferences in between observations but does not have a true zero point. For example the difference between two temperatures.

Ratio scales - interval and have a true zero. I.E. Dividends paid.

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12
Q

Name three characteristics of the geometric mean

A
  1. The geometric mean is always less than, or equal to the arithmetic mean
  2. The geometric mean equals the arithmetic mean only when all observations are equal.
  3. The difference between the geometric and arithmetic mean increases as the dispersion in observed values increases.
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13
Q

What is the Harmonic Mean?

A

Much like the weighted mean where the weight of an observation is inversely proportional to its magnitude.

It will always bea less than the geometric mean and therefore the rithmetic mean.

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14
Q

What is the mean absolute deviation?

A

The average of the absolute differences from the mean.

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15
Q

What is Chebyshev’s Inequality? What is the equation?

A

It shows the % observation within k standard deviations from the mean. It is calculated as: 1 - 1/k^2

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16
Q

Explain the Coefficient of Variation, how its calculated and why it is usefull.

A

It represents a ratio of the standard deviation to its mean. It illustrates a meaningful ratio for datasets with varying observations. CV = s/mean

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17
Q

Explain Kurtosis and and the different classifications of Kurtosis.

A

Kurtosis measures the extent to which a distribution is more or less peaked than a normal distribution. Normal distributions will have a Kurtosis of 3.

A distribution that is more peaked and has fatter tails than a normal distribution and has a Kurtosis of greater than three is called leptokurtic.

Platykurtic is less peaked and has thinner tails than a nomral distribution, and has a kurtosis less than zero.

Mesokurtic is identical to a normal distribution and has n excess kurtosis of zero.

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18
Q

What is an outcome?

A

the observed value of a random variable

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19
Q

What is an event?

A

a single outcome or set of outcomes.

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20
Q

Explain the difference between empirical, subjective, and a priori probability.

A

Empirical estimates the probability of an event based on its frequency of occurrence in the past. A subjective probability draws on subjective reasoning and personal judgement. Priori is based on formal analysis and reasoning.

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21
Q

Give the formulas for odds for and odds against

A

F= a/(a+b) A=b/(a+b)

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22
Q

What does the Dutch Book Theorem state?

A

The Dutch Book Theorem states that if the probabilities reflected in the stock prices are not consistent, they give risk to profit opportunities. As investors take positions to take advantage of such opportunities, the inconsistency is eventually eliminated.

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23
Q

What is the formula for conditional probability?

A

P(A|B)=P(AB)/P(B)

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24
Q

What is P(A|B) where A =1 and B=2?

A

1/2

25
Q

What is P(AB) where A=1 and B=2?

A

P(AB) = P(A|B) * P(B). P(AB)= (1/2 * 2)= 1

26
Q

Give the formula for P(A OR B)

A

P(A or B) = P(A) + P(B) - P(AB)

27
Q

Give the formula for P(A and B)

A

P(A and B)= P(A) * P(B)

28
Q

What is the difference between Variance and Covariance?

A

Variance measures how a random variable varies with itself, while covariance measures how a particular random variable varies with one another. Variance can only be positive. Covariance can be negative or positive.

29
Q

What does negative covariance indicate?

A

A negative relationship among variables.

30
Q

What does a covariance of zero indicate?

A

The variables are unrelated.

31
Q

Explain the limitations of covariance

A

Covariances cannot be used across datasets because the covariance represents the same units it was calculated in. Covariance also does not tell us about the strength in relationship between variables.

32
Q

What is the correlation coefficient?

A

It measures the strength and direction of a linear relationship between to random variables. It is obtained by dividing the covariance between two random variables by the product of their standard deviations. The solution is a number between -1 and 1.

33
Q

A small sample is considered to be a sample of less than?

A

30

34
Q

When sampling from a normal distribution with a known variance, what is the appropriate confidence interval to rely upon for a small sample? For a large sample?

A

Z-statistic, Z-statistic

35
Q

When sampling from a non-normal distribution with a known variance, what is the appropriate confidence interval to rely upon for a large sample? Same but with an unknown variance

A

Z-Statistic, T or Z-Statistic

36
Q

When sampling from a normal distribution with a unknown variance, what is the appropriate confidence interval to rely upon for a small sample? For a large sample?

A

T-statistic, T or Z-statistic

37
Q

Name the four characteristics of t-distributions.

A

It is symmetrical
It is defined by a single parameter, the degrees of freedom, (df), where the degrees of freedom equal sample size minus one (n-1)
It has a lower peak than the normal curve, but fatter tails.
As the degrees of freedom increase, the shape of the t-distribution approaches the shape of the standard normal curve.

38
Q

What does the central limit theorem tell us?

A

That when the sample size is greater than 30, the sample mean will be normal distributed.
The mean of the population and sample are equal.

39
Q

Name the two types of chart patterns.

A

Reversal and Continuation.

40
Q

name the four types of Reversal Patterns.

A

Head and Shoulders
Inverse Head and Shoulders
Double Tops and bottoms
Triple Tops and Bottoms

41
Q

Name the three types of head and shoulder patterns and what they represent. Explain an inverse head and shoulder pattern and what it represents. Explain how to set a target price based on each.

A

Left Shoulder- strong rally, high volume
Right Shoulder-similar to left shoulder but low volume
Head - Second high is higher than the first high, but with lower volume.

Inverse-the price characteristics are reversed but the volume characteristics are the same as in the above.

Price target = Neckline - (Head - Neckline)
(Inverse) Price target = Neckline + (neckline - head)

42
Q

Explain the three types of continuation patterns

A

Triangle patters are formed when the range of highs and lows over a period narrows down on the price chart. The line connecting the highs over the period eventually meets the line connecting the lows, forming a triangle.

There are three types of triangles: Ascending, Descending triangle, and symmetrical. Ascending is formed when the trend line connecting the highs are horizontal while the trend line connecting the lows is upward-sloping. Share prices are expected to rise.

Descending suggests the stock price will continue to decline.

Symmetrical suggests the preceding formation is indicative of the subsequent continuation pattern.

Rectangle patters represent are similar to symmetrical triangle patterns.

Flags and Pennants - both indicate the same thing as rectangle patterns.

43
Q

What is a momentum oscillator and on what scale are they calculated. How is it computed.

A

It measures change in market sentiment. Usually it is between 0-100.

M=(last closing price (V) - price x days ago (Vx) (usually 10))*100

M=V/Vx*100

44
Q

Explain the relative strength index and how it is computed.

A

It measures a security’s gains with its losses over a given time period.

RSI=100 - 100/(1+RS)

RS= Sum of up changes for the period/sum of down changes for the period.

45
Q

Explain what a stochastic Oscillator is and how it is computed.

A

Based on the assumption that in an uptrend, the stock price tends to close near the high of its recent range, while in a downtrend it tends to close around its recent low. A value of greater than 80 indicates that the security is overbought and should be sold. Lower than 20 oversold and should be bought.

%K= 100((Last close - L14)/(H14 - L14))
L = Lowest price past 14 days, H=Highest
46
Q

What are Kondratieff Waves?

A

Nikolai Kondratieff suggested that economics went through a 54-year economic cycle.

47
Q

What does a 18-year cycle refer to?

A

Most commonly refers to real estate markets

48
Q

Decennial pattern refers to

A

The DJIA has histrorically performed poorly in years ending with a 0 while the best have years that end with a 5.

49
Q

Elliott Wave Theory states that

A

markets move in regular cycles or waves. In a bull market the market moves up in five waves: 1 up 2 down 3 up 4 down 5 up. Which is followed by three corrective waves: 1 down 2 up 3 down. The same pattern is refersed in a bear market. Elliot also discovered that market waves followed patters that were ratios of numbers in a Fibonacci sequence:

Positive price movements would take prices up by a factor equal to the ratio of a Fibonacci number to its preceding number.

Negative price movements would reverse prices by a factor of a Fibonacci number to the next number.

Elliot wave theory is used along with Dow Theory, trend analysis, pattern analysis, and oscillator analysis to forecast market movements.

Its biggest advantage is that it can be applied in short-term trading as well as long-term economic analysis.

50
Q

Opposite of accepting the null hypothesis is:

A

Fail to reject the null.

51
Q

Explain the difference between a one and two tailed test.

A

A one tail test means that the alternative hypothesis is greater than or equal OR less than or equal to the mean. A two tailed test means that the alternative hypothesis is NOT equal to the mean (could be less than or greater than).

52
Q

How is the power of a test computed?

A

Power of test = 1 - Probability of Type II error

53
Q

When do you use a t-test

A

When the variance of the population is unknown and:

The sample size is large
The same size si small, but the pop is normally dist.

54
Q

What is the test statistic?

A

The value of the alternative hypothesis

55
Q

What is the critical value

A

The value of either the t or z statistic

56
Q

What is the P-Value

A

The smallest level of significance at which the null hypothesis can be rejected.

57
Q

How is Chi-Square (one degree of freedom) computed

A

X^2=((n-1)(∑(i-1)^n (sum of)〖(x(i- x ̅ ))〗^2 )/(n-1))/(σ_0^2 ) refer to page 632

58
Q

How is F test computed and when is it used?

A

Sample variance of pop 1 divided by sample variance of pop 2. Is used when comparing two population variances.

59
Q

What is the fundamental difference between parametric and non-parametric tests

A

Parametric tests are concerned with defining the population or sample by parameters, defining features of a distributions. A non-parametric test is only concerned with quantities other than the parameters of the distribution.

CFA Prep (LV1) (10 decks)

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