Statistics

Question 1

What statistical model should you use to help a client who doesn’t understand finance and needs simple and clear materials to understand?

Answer 1

Frequency Distribution.

Question 2

What is a Frequency Distribution?

Answer 2

A tabular display of data that has been broken into a number of intervals. You can group observations of data into a table.

Question 3

What are the steps to creating a Frequency Distribution?

Answer 3

1. Sort the data in ascending order.
2. Calculate the range (largest value - smallest value)
3. Determine number of intervals you want.
4. Determine the width of interval by dividing the range by the number of desired intervals.
5. Construct the minimum and maximum values for each interval.
6. Count how many observations are in each interval.

Question 4

What are the four types of measurement scales?

Answer 4

Nominal, ordinal, interval, and ratio scales.

Question 5

What is an nominal scale? Provide an example?

Answer 5

The weakest of the scales, it simply allows you to categorize the data.

For example, organizing A-Z

Question 6

What is an ordinal scale? Provide an example?

Answer 6

Second to weakest, it allows you to put data in order by assessing the relative value of data points.

For example, “Surveys of satisfied and dissatisfied.”

Question 7

What is an interval scale? Provide an example?

Answer 7

Scale allows you to rank something, but also know the difference between rankings.

For example, a scale that ranks investors in terms of knowledge of markets based on their standardized scores on a test.

Question 8

What is a ratio scale? Provide an example?

Answer 8

The strongest measurement scale, it has a meaningful zero. For example, a listing of 10 companies with annual profits in USD.

Question 9

How are dividends calculated in the holding period return formula?

Answer 9

Rt = Pt - Pt_1 + Dt / Pt_1

Pt = price of current period
Pt_1 = price of previous period
Dt = dividends from current period

Question 10

What statistical model should you use if a client simply wants to see a picture of his returns?

Answer 10

Frequency Polygon.

Question 11

How would you create a Frequency Polygon?

Answer 11

1. Acquire the absolute frequencies.

2. Graph it with Frequencies on the Y axis and Interval Midpoints on the x axis.

Question 12

How do you calculate relative frequency?

Answer 12

Divide the observations of a frequency by the total number of observations.

Question 13

How do you calculate the cumulative relative frequency?

Answer 13

Add all relative frequencies together.

Question 14

Speaking in statistical terms, what does central tendency mean?

Answer 14

The middle of a set of data.

Question 15

What is the arithmetic mean?

Answer 15

The true middle of a set of data. It is obtained by adding the data and dividing the number of observations.

Question 16

How do you calculate the harmonic mean?

Answer 16

Dividing the number of observations, by the reciprocal of the values in a data-set. Useful in determining average price paid for through cost averaging.

Question 17

What do quartiles do?

Answer 17

They divided the distribution into four pieces.

Question 18

How do you calculate the X-percentile?

Answer 18

[ (n + 1) (X / 100)]

Question 19

How do you calculate the geometric mean?

Answer 19

[(1 + R1)(1+R2)]^1/t - 1 = 0%

Question 20

If you want to know where you’re going, what mean should you use?

Answer 20

Arithmetic. mean

Question 21

If you want to know where you’ve been, what mean should you use?

Answer 21

Geometric.

Question 22

How to calculate median?

Answer 22

(n+1 / 2)

Question 23

What is the mode?

Answer 23

The mode is a measure of central tendency defined as the most commonly occurring value in a set of data.

Question 24

What is a bimodal distribution?

Answer 24

A distribution where there are two modes.

Question 25

What is linear interpolation?

Answer 25

Use weighted average to find the correct amount between two observations.

Example: 43.6th observation to find the 10th percentile.
43rd observation is .21 and the 44th is .24

.21 + .6 (.24 - .21) =

Question 26

What value does the weighted mean equal?

Answer 26

1.

Question 27

How to calculate the weight of an asset of a portfolio?

Answer 27

wi = Size of asset class / size of entire portfolio.

Example. erhaps you invested EUR 42,000 in stocks (S), EUR 25,200 in bonds (B), and EUR 16,800 in real estate (RE).

Total portfolio would be 84,000.
Weight of stocks is wS = 42,000/84,000 = .50
Weight of bonds is wB = 25,200/84,000 = .30
Weight of real estate is wRE = 16,800/84,000 = .20

Question 28

What is dispersion?

Answer 28

Variability around the central tendency. It provides a mean of quantifying risk in a financial asset.

Question 29

How do you calculate a population variance, o^2

For example, your population might be 5 interest rates of 1%, 2%, 3%, 4%, and 5%. The mean is clearly 3%, but there is dispersion around this mean.

Answer 29

                                      5

Question 30

How do you calculate sample standard devation?

Answer 30

                                      5 - 1

Question 31

What is the difference between population variance and sample standard deviation?

Answer 31

Population variance is the whole data set and sample standard deviation is a sample of the data set.

Question 32

What is Coefficient of Variation?

Answer 32

The coefficient of variation (CV) is a measure of relative dispersion. It is the result of dividing the sample standard deviation by the sample mean.

CV = s/X

Question 33

How do you calculate semivairance?

Answer 33

Same way to calculate sample standard deviation
(X-mean)^2 + (x - mean)^2
————————————-
n - 1

Question 34

How to calculate target semivariance?

Answer 34

          n - 1