Quant Flashcards

Question

What are the 4 levels of measurement scales?

Answer 1

NOIR 1. Nominal 2. Ordinal 3. Interval 4. Ratio

Answer 2

Sample statistic: A measure used to describe a characteristic of a sample Parameter: A measure used to describe a characteristic of a population

Answer 3

Define the intervals Tally the observations / assign to relevant interval Count the observations

Answer 4

Relative frequency: A histogram with entries in the bar chart out of described out of 100%

Answer 5

Histogram: Bar chart of absolute frequencies of a distribution (same as a frequency distribution)

Answer 6

Frequency polygon: Absolute frequency line chart with midpoints of the intervals plotted

Answer 7

\( Sum\ of\ mean\ deviations: \Sigma(X_i - \mu) = 0 \)

Answer 8

\( Median = \frac{(n+1)}{2}th\ entry \)

Answer 9

\( Geometric\ mean = (X_1X_2....X_n)^{1/n} \)

Answer 10

\( Geometric\ mean = ((1+X_1)...(1+X_n))^{1/n} -1 \)

Answer 11

When looking at multi year returns

Answer 12

Average cost of shares purchased over time when you buy same dollar amount in shares

Answer 13

\( Harmonic\ mean = \frac{n}{\Sigma 1/X_i} \)

Answer 14

You use the arithmetic mean when you purchase the same number of shares, use harmonic mean when you purchase same dollar amount of shares

Answer 15

\( Measure\ of\ location\ in\ a\ dataset: L_y = (n+1)\frac{y}{100} \)

Answer 16

Decile: A distribution divided into tenths

Answer 17

Quintile: A distribution divided into fifths

Answer 18

Dispersion: Variability around the central tendency

Answer 19

\( MAD = \frac{\Sigma |X_i - \mu |}{n} \)

Answer 20

The average that an individual return will deviate from the mean return

Answer 21

\( Variance = \frac{\Sigma (X_i - \mu)^2}{n} \)

Answer 22

\( Variance = \frac{\Sigma (X_i - \mu)^2}{n-1} \)

Answer 23

An estimator where the estimator's expected value and the true value of the parameter are unequal

Answer 24

Chebyshevs inequality: 1- 1/k^2 The % of observations that lie within k standard observations of the mean is at least 1-1/k^2 for all k > 1

Answer 25

k = range we are looking around the mean divided by the standard deviation

Answer 26

\( c_v = \frac{\sigma}{\mu} \)

Answer 27

\( Sharpe\ Ratio = \frac{R_p - R_f}{\sigma} \)

Answer 28

Kurtosis is a measure of how more or less peaked a distribution is and also how fat the tails are compared to a normal distribution

Answer 29

1. Leptokurtic 2. Mesokurtic 3. Platykurtic

Answer 30

Excess kurtosis = Kurtosis – 3. Measures whether the distribution has more or less kurtosis than a normal distribution

Answer 31

1. 0 =< p =< 1 | 2. If a set of events is mutually exclusive and exhaustive the sum of all these outcomes = 1

Answer 32

Empirical probability: A probability established by analysing past data

Answer 33

Priori probability: A probability determined using a formal reasoning and inspection process

Answer 34

A probability based on a personal feeling or hunch

Answer 35

Empirical and priori probabilities

Answer 36

\( Odds = \frac{p}{1-p} \)

Answer 37

\( p = \frac{1}{1+odds} \)

Answer 38

\( Multiplication\ rule\ of\ probability = P(ANB) = P(A/B) * P(B) \)

Answer 39

\( Conditional\ probability: P(A/B) = \frac{P(ANB)}{P(B)} \)

Answer 40

\( Addition\ rule\ of\ probability: P(ANB) = P(A) + P(B) - P(ANB) \)

Answer 41

\(Total\ probability\ rule: P(A) = P(A/B_1) * P(B_1) +...+ P(A/B_n) * P(B_n)\)

Answer 42

P(ANB) = 0

Answer 43

P(ANB) = P(A)P(B)

Answer 44

\( E[X] = \Sigma E[X|A_i] * P(A_i) \)

Answer 45

Covariance measures how one random variable moves in relation to another

Answer 46

\( Cov(X,Y) = E[XY] - E[X]E[Y] \)

Answer 47

Covariance ranges from minus infinity to plus infinity

Answer 48

\( Correlation\ coefficient: p_{ij} = \frac{Cov_{ij}}{\sigma_i \sigma_j} \)

Answer 49

It ranges from -1 to +1

Answer 50

Spurious correlation: 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

Answer 51

\( E[R_p] = w_AE[R_A] + w_BE[R_B] \)

Answer 52

\( \sigma_p^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 +2w_Aw_B\sigma_A \sigma_B p_{AB} \)

Answer 53

To update a probability based on new information available

Answer 54

\( P(A/B) = \frac{P(B/A)P(A)}{P(B)} \)

Answer 55

When ordering matters in the question, use the permutation formula. If ordering does not matter in the question, use the combination formula

Answer 56

A probability distribution where the set of all possible outcomes can be counted

Answer 57

A probability distribution where the set of all possible outcomes cannot be counted

Answer 58

It represents the cumulative probability up until a random variable

Answer 59

Discrete Uniform Distribution: All outcomes are equally likely to occur. 2 parameters "a" and "b"

Answer 60

Bernoulli Random variable: the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q=1-p, that is, the probability distribution of any single experiment that asks a yes–no question. It is binary

Answer 61

Binomial distribution: binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n Bernoulli trials

Answer 62

``` Mean = np Variance = np(1-p) ```

Answer 63

Confidence Interval: The range around the expected value that the outcome us expected to be found in

Answer 64

\( Confidence\ interval = Point\ estimate \pm reliability\ factor * standard\ error \)

Answer 65

\( Z = \frac{(x-\mu)}{\sigma} \)

Answer 66

Shortfall Risk: The risk that the return Rp falls below a threshold level Rl over a given time period

Answer 67

Bounded below at 0 | Positively skewed

Answer 68

Fairly complex Provides answers that are no better than the assumptions / inputs around the distribution Cannot provide the insight that an analytic solution can

Answer 69

Uses historical information so no estimates required Past changes in risk factors are not necessarily a good indicator of future changes Cannot address “what if” questions like monte carlo simulation can (sensitivity analysis)

Answer 70

Simple random sampling: A sampling method where every member of a population has equal chance of being chosen for the sample Systematic sampling: Selecting the nth member from a population for a sample Stratified random sampling: Uses a classification system to separate the population into smaller groups based on one or more distinguishing characteristics into stratum

Answer 71

Guarantees we have a certain number of samples from each stratum in our pool

Answer 72

Sampling error: The difference between the population metric and the equivalent sample metric

Answer 73

Time series data: Observations taken over a period of time at specific and equally spaced intervals e.g. McDonalds P/E ratio from 2004 to 2019 Longitudinal data: Observations over time of multiple characteristics of the same entity e.g. McDonalds P/E ratio, share price and dividend yield from 2004 to 2019 Panel data: Observations over time of multiple characteristics of multiple entities. e.g. McDonalds and Apples, P/E ratio, share price and dividend yield from 2004 to 2019 Cross sectional data: Observations taken at a single point in time e.g. EPS of all S&P 500 companies at 31/12/04

Answer 74

Central limit theorem: In a population of size n with mean µ and variance σ^2, the sampling distribution of the sample mean x approaches a normal distribution N-( µ, σ^2/n) as the sample size becomes large (n> 30)

Answer 75

1. Unbiased 2. Efficient 3. Consistent

Answer 76

As n gets larger the distribution closer approaches the normal distribution - therefore a normal distribution is more appropriate

Answer 77

Symmetric Appropriate to use when constructing confidence intervals on small samples (n<30) on a distribution with an unknown variance Defined by a single parameter: Degrees of freedom = n-1 Fatter tails than normal distributions

Answer 78

1. Point estimate 2. Reliability factor 3. Confidence intervals

Answer 79

t or Z statistic

Answer 80

Survivorship bias: Only include funds in a sample that over the years have survived. They do not include funds that have ceased to trade / failed. Very common bias in mutual funds

Answer 81

Sample selection bias occurs when the sample selected does not represent the overall population (does not have the same characteristics as the population).

Answer 82

Look ahead bias occurs when test is conducted using data that was not available at the time of the test (ex predicting earnings for the year whereas fourth quarter earnings are not yet available.)

Answer 83

Time period bias: Using sample series which is too short or not seasonally adjusted or even too long sample time series can cause biased estimators

Answer 84

1. State the hypothesis test 2. Select the test statistic 3. Specify the significance level (alpha) 4. Set a decision rule 5. Collect data and calculate sample statistics 6. Make decision on the hypothesis test 7. Make decision as to the validity of the overall test

Answer 85

Null hypothesis: The hypothesis the researcher wants to reject

Answer 86

Alternative hypothesis: The conclusion made if there is significant evidence to reject the null hypothesis

Answer 87

Null hypothesis always contains an equals sign

Answer 88

\( Z = \frac{\bar{x}-\mu_0}{\sigma/\sqrt{n}} \)

Answer 89

Type 1 error: Probability of rejecting null hypothesis when it is actually true

Answer 90

Type 2 error: Probability of not rejecting null hypothesis when it is actually false

Answer 91

1- P(Type II error)

Answer 92

If a P(type 1 error) goes up the P(type II error) goes down, they have an inverse relationship

Answer 93

p-value: the lowest level of significance at which we can reject the null hypothesis

Answer 94

Sample size Distribution (normal or non-normal) Variance (known or non- known)

Answer 95

t-test paired comparisons test

Answer 96

Chi-square test is used for hypothesis tests concerning the value of the variance of a normally distributed population.

Answer 97

It is asymmetric

Answer 98

\( X_{n-1}^2 = \frac{(n-1)s^2}{\sigma_0^2} \)

Answer 99

When we test whether the variance of one population is equal to the variance of another population

Answer 100

\( F = \frac{S_1^2}{S_2^2} \)

Answer 101

Parametric Tests: E.g. t test, F test, chi squared test - rely on the test statistic to test statistical significance Non-Parametric Tests: distribution-free tests by some researchers – are tests that do not make any assumption regarding the distribution of the parameter under study