Cfa Quant

Front 1

What is a parameter? What is statics?

Back 1

Population is parameter ; sample is statists

Front 2

The height of a histogram bar represents:

Back 2

Absolute frequency

Front 3

What is MEAN ABSOLUTE DEVIATION?

Back 3

Sum of |Xi-avg X|/N

Front 4

How to calculate quintile and quartile in a set of samples?

Back 4

Back (Definition)

Front 5

What is Chebysgevs inequality?

Back 5

Front 6

Difference between coefficient of variation and standard deviation?

Back 6

Coefficient of variation is relative and scale free but standard deviation is absolute

Front 7

What is coefficient variation ?how to calculate it?

Back 7

Coefficient variation is every units of average value’s standard deviation;

CV= Sd of x / avg of x

Front 8

What is 8% around the mean of Chebyshevs ?

Back 8

Back (Definition)

Front 9

For a positive skewed distribution is the mean bigger than the medium or smaller?

For negative skewed Distribution is the mode smaller or bigger than mean?

Back 9

Back (Definition)

Front 10

A return distribution with frequent small gains and a few extreme losses is mostly likely to be called:

Back 10

Negatively skewed

Front 11

What is the sequence best represents the relative sizes of the mean median and mode for a positively screwed unimodel distribution

Back 11

Mean > median >mode

Front 12

What is the opposite of leptokurtic? What is normal distribution‘s kurtosis description?

Back 12

Negative kurtosis: plattkurtic

Normal kurtosis: mesokurtic

Front 13

Went to use harmonic mean?

Back 13

Harmonic mean is appropriate for determining the average price per unit not evaluating a funds return history; Harmonic mean is applicable when ratios are repeatedly applied to a fix quantity to yield a variable numbers of units such as cost averaging

Front 14

What’s the order of arithmetic mean geometric mean and harmonic mean?

Back 14

A>= G>=H

Front 15

If the probability that Zola’s company sales exceed last years sales is 0.2, the odds for exceeding sales are closest to:

Back 15

1 to 4

Front 16

What is exhaustive event?

Back 16

Events that include all potential outcomes

Front 17

What are permutation formula and combination formula?

Back 17

Permutation: chosen in specific order

Combination: chosen and sequence doesn’t matter

Front 18

What is multinomial formula?

Back 18

Bionomial is part of the multi nominal. The experiment consists of k times repeated trial

Front 19

Pick r number of event from N number of events. If the sequence matter, what’s the formula for the number of groups? What if the sequence don’t matter?

Back 19

Sequence matter: n!/(n-r)!

Sequence doesn’t matter:

n!/(n-r)!*r!

Front 20

Over the last 10 years, a company’s annual earnings increases 7 times and decreased 3 times year over year, what is the probability that earnings will increase in exactly 5 of the next 10 years?

Back 20

Front 21

What is the formula of binomial distribution formula?

Back 21

Back (Definition)

Front 22

True or false? For a probability distribution for the number of days the air pollution is above a specific level PX =0 when x cannot occur, or PX >0 when it can

Back 22

True. Because it’s a discrete distribution

Front 23

For a probability distribution for the specific level of air pollution on a given day PX=0 even the X can occur

Back 23

True. Continuous distribution

Front 24

What’s the difference between Bernoulli random variables and binomial random variables?

Back 24

Bernoulli: only did once

Binomial: did n times

Both has two types of outcomes

Front 25

How many standard deviations of the mean will be within 95% percent of all outcome of a normal distribution?

Back 25

Z=1.96 so about 2 standard deviations

Front 26

Approximately 99percent of all outcomes of a normal random variables will be within how many standard deviations?

Back 26

3 standard deviations. Z=2.575

Front 27

What is a multivariate distribution?

Back 27

The multivariate normal distribution is useful in analyzing the relationship between multiple normally distributed variables, and thus has heavy application to biology and economics where the relationship between approximately-normal variables is of great interest. Such as a portfolio of stocks rather than one stock

Front 28

How many parameters does multi variate normal distribution have?

Back 28

N means, n variances and n(n-1)/2 correlations.

Front 29

What’s covariance return formula on Ra and zen?

Back 29

Back (Definition)

Front 30

What are the probabilities for odds for and odds against?

Back 30

Odds for: p( happen)/p( not happening)

Odds against: p( not happening)/p(happen)

Front 31

in a normal distribution, how much probability there is when k=1, k=1.65, k=1.96, k=2.58?

Back 31

k=1 P=68%,

k=1.65 P=90%,

k=1.96 P=95%,

k=2.58 P=99%

Front 32

if a distribution's X~N(2,25), then P(3<=X<=4) is?

Back 32

step 1: normalize it by Z=[(3-2)/5] and Z=[(4-2)/5]; F (1/5<=Z<=2/5)

step 2: calculation Z~N(0,1) F(2/5)-F(1/5)

Front 33

What are the features of lognormal distribution?

Back 33

Back (Definition)

Front 34

What is using lognormal distribution to measure and what is using normal distribution to measure?

Back 34

Lognormal: only positive numbers such as stock prices;

Normal distribution: numbers that can be both negative and positive, such as return

Front 35

Difference between Monte Carlo simulation vs historical simulation

Back 35

Back (Definition)

Front 36

Difference between standard deviation and standard error?

Back 36

Standard deviation: from a set of sample

Standard error: from n times of experiment each time there’s a mean; sigma X bar=sigma X/sqr of n

Front 37

What are the conditions for central limit Therom?

Back 37

N>=30

Know Mean and Sd

Front 38

What are the unbiased, efficiency and consistency about for the estimator?

Back 38

Back (Definition)

Front 39

Difference between normal distribution and t distribution?

Back 39

Normal distribution is a special example of t distribution. T distribution is more lower kurtosis and fatter tail

Front 40

What’s the formula for confidence interval for central therom estimation?

Back 40

Back (Definition)

Front 41

What are the characters of t distribution?

Back 41

1. Symmetrical

2. 决定t分布变量只有一个, degree of freedom n-1

3. Less peaked than normal distribution

4. T distribution converges to normal distribution as degree of freedom goes to infinity

5. Same significance level, t’s confidence interval is wider

Front 42

T distribution VS normal distribution?

Back 42

Back (Definition)

Front 43

What is data mining bias?

Back 43

把偶然当必然

Front 44

Is the hypothesis testing on population or sample?

Back 44

Population

Front 45

What are the characteristics for null hypothesis?

Back 45

Mu 0: Has an smaller than and equal sign

Front 46

What is Bernoulli trail example ?

Back 46

The flip of a coin; one of the twins; only two options available

Front 47

What is Bernoulli trail example ?

Back 47

The flip of a coin; one of the twins; only two options available

Front 48

How to calculate the compounded return?

Back 48

In (V1/v0)

Front 49

What’s the probability of generating the value of exactly 0.3 in a continuous uniform distribution?

Back 49

0

Front 50

Monte Carlo simulation can be used to

Back 50

Test the sensitivity of a model to changes in assumptions

Front 51

Does Monte Carlo simulation require historical record?

Back 51

No

Front 52

What’s the Rf for safety first?

Back 52

Withdrawal/ total portfolio =rf

Ri-rf/ sigma

Front 53

What’s the Rf for safety first?

Back 53

Withdrawal/ total portfolio =rf

Ri-rf/ sigma

Front 54

Why lognormal distribution is more accurate for stock prices?

Back 54

Unbounded; always positive

Front 55

If we are using a set of table of data to calculate standard deviation, should we use sample standard deviation or population standard deviation?

Back 55

Sample deviation

Front 56

What aspect of the data makes us uncomfortable about using t tables to construct confidence intervals for the population mean forecast?

Back 56

When the sample is small and the distribution appears to be bimodal we cannot compute a confidence interval for the population mean because we have to probably sample it from a distribution that is not normal

Front 57

Explain the differences between constructing a confidence interval when sampling from a normal population with a no population barriers and sampling from a normal population with an unknown variance

Back 57

I know variance:

1. Use sample standard deviation

2. Use t distribution

Front 58

What’s the difference between Ho and H alternative?

Back 58

Ho: reject, has equal sign

H alpha: accept , no equal sign

Front 59

What is P value?

Back 59

P is the the area of rejection, p>=0

Front 60

What is the formula for correlation testing?

Back 60

1. Ho:P=0,Ha: p doesn’t equal to zero

2. t=r/ [(1-r^2)/(n-2)]^0.5=r*(n-2)^0.5/(1-r^2)^0.5

Front 61

What are the distribution to test variances?

Back 61

One variance: chi

Two variances: F

Front 62

What are type I and type II errors?

Back 62

Type I error: 冤枉

Type II error:纵容

Front 63

What are type I and type II errors?

Back 63

Type I error: 冤枉

Type II error:纵容

Front 64

What is power of test?

Back 64

When the hypothesis is wrong and reject

P=1-P(II)

Front 65

What the correlation between Type I error and Type II error? How to reduce it?

Back 65

Negatively correlated; increase n population

Front 66

What are the difference between parametric tests and non parametric test?

Back 66

Parametric test is based on specific distribution of assumptions for the population； Even if the underlying distribution is unknown, parametric tests can be used on numerical data if the sample is large.

A non-parametric test is when data do not meet distribution of assumptions

when data are given in ranks or signsor groups, and they are used when numerical parameters are not known or do not meet assumptions about distributions

Front 67

When to use paired comparisons t test?

Back 67

When there null hypothesis saying Population mean one minus population mean 2 =0 versus HA population mean 1 minus population mean 2 doesn’t equal to zero; Where those samples are drawn from normally distributed populations with unknown variance the observations and the two samples are correlated

Front 68

Difference of calculating confidence interval and doing test to reject or not reject?

Back 68

Confidence interval: x= mu +/- Z* SD/sq root of n

Test: (x-mu)/[sd/ sq root of n] to reject or not reject

Front 69

Null hypothesis is considered to be true unless the sample provides evidence showing it is false

Back 69

True

Front 70

If the data is normal distributed, variance is unknown, sample size is big, can we use Z distribution?

If data is non normal distribution, sample is big, can we use Z?

Back 70

Back (Definition)

Front 71

What does statistically significant mean?

Back 71

The test got rejected.

Front 72

what is the ahlpha for a one tail test and two tail test for z distribtuion?

Back 72

alpha include all the rejectiona area no matter one tail or two tails

Front 73

Difference between exclusive and mutually exclusive

Back 73

Exclusive cover all the probability;

Mutual exclusive: independent but doesn’t cover all probability

Front 74

How to calculate mean absolute deviation?

Back 74

|X-avg X|/N

Front 75

When a P-value is less or more than or equal to the significance level, do you reject the null hypothesis?

Back 75

less

Front 76

what happens if p-value is more than a significance level?

Back 76

fail to reject the null hypotheis

Front 77

what is a F test formula?

Back 77

F= S1^2/S2^2

Front 78

when to use a pool estimator?

Back 78

pooled estimator is used when the two population variances are assumed to be equal

Front 79

when to use paired comparison?

Back 79

paired comparison test is used to test mean differences when the samples are assumed to be dependent.

Front 80

how to calculate economic profit?

Back 80

Economic profit = Accounting profit – Total implicit opportunity costs;

Accounting profit = Total revenue – Total variable costs – Total fixed costs;

Total opportunity costs = opportunity cost of capital + opportunity cost of labor