CHAPTER 1 (INTRODUCTION)

Question 1

Outline steps in formulating an economic model

Answer 1

1. General Statement of the problem - Involves a theoretical model or intuition from financial theory that two or more variables should be related to one another in a certain way.
2. Collection of data - The data required may be through a financial info provider or through a survey (primary data)
3. Choice of estimation method - Single equation or multiple equation technique to be used?
4. Statistical evaluation of the model - What assumptions were required to estimate the model optimally. Does this model adequately describe the data. If not, go back, reformautle, collect more data or select a different estimation tech.
5. Evaluation of the model from a theoretical perspective - Are the parameter estimates of the sizes and signs that the theory or intuition from step 1 suggested? If not, return to stages 1-3.
6. Use of the model - When satisifed with the model it can be used for testing the theory specified in step 1 or for formualting forecasts or suggested courses of action

Question 2

Types of data structure

Answer 2

1. Cross-sectional - data on multiple entities collected at a single point in time (Stock returns: The stock returns for Microsoft, IBM, and Samsung on December 31, 2018
   - Household income and spending: A survey of annual household income and spending
   - Country GDPs: The GDPs of different countries in a single year)
2. Time series data: Data on a single entity collected time (stock return of one company over the years)
3. Pooled cross-sectional data: data on multiple entities collected at different points in
   time (Example: CPS - current population survey 60,000 random householeds selected in the US every month)
4. Panel or longitudinal data: Data on multiple entities collected over time (Same as pooled, only that the multiple entities remain fixed)

Question 3

Continuous vs discrete data

Answer 3

Continuous data: Can take on any value and is only limited by thier precision

Discrete data: Can only take on certain values - typically integers

Question 4

Outline the data measurement scales

Answer 4

Nominal scale: Observations are classified with no particular order

Ordinal scale: Observations are assigned to one of several categories

Interval scale: Provides relative ranking, like ordinal scale plus that difference between scale values are equal. Further, 0 does not necessarily indicate the absence of something.

Ratio scale:
Provides ranking and equal difference between scale values - zero point is the origin. e.g. measurement of financial return

Question 5

Please provide simple and log returns

Answer 5

Simple return: Rt = (Pt-Pt-1)/(Pt-1) x 100

Log return: rt = ln(Pt/Pt-1) x 100

Question 6

How do you convert a simple return to a log return and vice versa

Answer 6

rt = ln(1+Rt)

Rt = e^rt - 1

Question 7

Simple vs log returns of a portfolio

Answer 7

Simple return: Rpt = w1Ra1+w2Ra2

Log return:
rpt = w1ra1 + w2ra2

Question 8

Please explain and provide formula for geometric and weighted mean

Answer 8

Geometric mean: The geometric mean return (often called the compound annual growth rate, or CAGR, in finance) measures the average rate of return that accounts for the effects of compounding over multiple periods. Unlike the arithmetic mean, which is a simple average, the geometric mean considers how each period’s return builds on the previous periods’ returns. This makes it useful for measuring long-term investment growth or performance over time.

(Provide formula)

The weighted mean return (or weighted average return) calculates an average return where each period or asset’s return is given a specific weight. This weight represents the relative importance or size of each return in the context of the portfolio or time period - similar to portfolio return

Question 9

Measures of dispersion:

Range, Interquartile range, mean absolute deviation

Answer 9

Range: Max-min

IQ range: Q3-Q1

MAD = How much each data point on average deviates from the mean of the population (Provide formula)

Question 10

What is degrees of freedom?

Answer 10

When dealing with a sample size rather than population, we use N-1 rather than N as N is only appropriate for the entire population

Question 11

Skewness:
Please provide explain what this displays and provide the formula

Answer 11

Skewness is the extent to which the distribution is not symmetrical. Positive skew means a long tail to the right and vice versa.

Skewness lower than -1 highly skewed to the left. Skewness higher than 1, highly skewed to the right.

Question 12

Kurtosis:
Measures whether the sample is more or less peaked than usual.

Please explain, mesokurtic, leptokurtic and platykurtic as well as their respective values

Answer 12

Mesokurtic: This represents a normal distribution and will have a kurtosis value close to 3

Leptokurtic: This will have a high, sharp peak and heavy tails. Will have a kurtosis value greater than 3

Platykurtic: This will have a lower, flatter peak with lighter tails. Chance of extreme values and outliers is lower. The kurtosis value will be lower than 3.

Question 13

Covariance and correlation

Answer 13

Covariance tells us the relationship between two variables (X,Y) and how one moves in relation to the other. Positive values indicate that they tend to move in the same direction. Example: height and weight.

Negative: Opposite direction, stock and a hedge

zero: no relationship

Correlation: Tells us the strenght of the linear relationship between the two variables. It goes from -1 to 1. However, it is important to remember that correlation can be affected by outliers and may also be spurious (not any plausible explanation for correlation)