Quantitative Methods 2

Question 1

Discrete random variable

Answer 1

Number of possible outcomes can be counted

Question 2

Continuous random variable

Answer 2

Cannot describe the possible outcomes, as there are an infinite number of possibilities

Question 3

Binomial distribution - Bernoulli experiment

Answer 3

Question 4

Bernoulli and binomial variances

Answer 4

Question 5

Multivariate distribution

Answer 5

Specifies probabilities for a group of related random variables. If returns are modelled as a group, need to take into account statistical interrelationships

Question 6

Standard normal random variable, Z (descriptive)

Answer 6

1. Subtract mean of population from random variable.
2. Divide the result by the standard deviation

Question 7

Standard normal variable formula

Answer 7

Question 8

Z table example

Answer 8

Question 9

Confidence interval

Answer 9

Question 10

How to use z table for confidence intervals

Answer 10

Use normal distribution and z tables in reverse

Question 11

Roy’s safety-first criterion

Answer 11

Risk portfolio value will fall bellow a minimum acceptable level

Question 12

SFRatio

Answer 12

Question 13

Lognormal distribution

Answer 13

Distribution of the natural log of a normally distributed variable. Bounded below by zero, skewed to the right. Asset prices bounded by zero

Question 14

Normal/Lognormal distribution

Answer 14

Question 15

Continuously compounded rate of return

Answer 15

Question 16

Value at risk

Answer 16

Estimates how much a set of investments might lose given normal market conditions

Question 17

Sampling issues

Answer 17

When your sample size is 30 or above, you have enough to count as statistically ‘large’

Question 18

Central limit theorem

Answer 18

Distribution of sample means (DOSM) is approximately normal if the sample size chosen has to least 30 observations

Question 19

Standard error (s.d. of sampling distribution of the statistics)

Answer 19

Question 20

Confidence interval

Answer 20

Question 21

T distribution

Answer 21

Used if population’s standard devision is not known. DOSM is t-distributed not normally disributed

Question 22

T distribution graphical representation

Answer 22

Question 23

Sample selection bias

Answer 23

Data availability leads to certain assets being excluded from the analysis

Question 24

Look-ahead bias

Answer 24

Using information not available on the test date

Question 25

Time-period bias

Answer 25

Short time periods are likely to give results that may not reflect a longer time period

Long time periods are distortive if there has been structural change

Question 26

Formal steps in hypothesis testing

Answer 26

1. State the null hypothesis and the alternative hypothesis
2. Identify the appropriate test statistic and its probability distribution
3. Soecify the significance level
4. State the decision rule
5. Collect the data and calculate the test statistic
6. Make the statistical decision
7. Make the economic or investment decision

Question 27

T statistic

Answer 27

Question 28

Summary of rejection points

Answer 28

Question 29

Type II error

Answer 29

ACCepting afalse null hyopthesis (beta)

Question 30

Type I error

Answer 30

Rejecting a true null hypothesis

Question 31

Standard error population between means

Answer 31

Question 32

Test statistic population between means

Answer 32

Question 33

Pooled variance

Answer 33

Question 34

Hypothesis tests concerning variances

Answer 34

Question 35

Testing equality of two variances

Answer 35

Using sample variances to determine whether population variances are the same.

Calculate the ratio between the two variances and look up in F-table using n-1 for denominator and numerator.

F-statistic should always be greater than 1

Question 36

Correlation and regression

Answer 36