Summary Financial Data Decision Analysis

Financial Data Decision Analysis

1. Introduction & Refresher

Empirical research

1. Motivation by previous studies
2. Formulation of a testable model
3. Collection of data
4. Model estimation
5. Interpret model
6. Use for further analysis, policy implications

Financial Data Characteristics I

Market data
- Frequent: daily, tick-by-tick
- High quality: no measurement error
- But: sometimes too much data, unstable relationships

Country data, macro-economic data
- Less frequently monthly, quarterly, annual
- Less reliable, data revisions

Corporate finance data
- Much data though not frequent: quarterly, annual
- Proxies, measurement errors, data revisions

Financial Data Characteristics II

Types of data
- Numbers (cardinal data)
1. Returns: -10.2%, +2.3%, …
2. P/E multiples: 3.12, 5.10, -10.28, …
- Ordered data
1. Credit ratings: AAA, AA+, AA, AA-, A+, …
- Non-ordered data
1. Issuing debt, issuing equity or retaining dividends

Cross-Sectional Data

Cross-sectional data are a sample of one or more variables collected at single point in time.
Examples of cross-sectional regressions analysis: The relationship between company size and the
return on investment in 2008

Time Series Data

Follow one country/firm/stock… over time. Examples are how the value of a company’s stock price
has varied when it announced the value of its dividend payment or what macro fundamentals do
explain the changes in a sovereign CDS spread

,Panel Data

Panel data has the dimensions of both time series and cross sections. Examples are the impact of
bank debt on corporate risk over time, the relationship between company size and the return on
investment in the last 20 years or monthly prices of a 10-year sample of 100 companies traded on
the NYSE

When doing Empirical Research

Try to get to know the data first
- Descriptive statistics (mean, sd, min, max)
- Scatter and/or rime-series plots
- Correlation analysis

Next step: Think and use your theory/intuition

Random variables and expectations

Definition: A random variable is any variable whose value cannot be predicted exactly. There are
discrete and continuous random variables:
- Discrete: specific set of possible values (e.g. throw a dice)
- Continuous: a continuous range of values (e.g. temperature)

Population: set of all possible values of the random variable

Probability distribution example: X is the sum of two dice




If there is 1/6 probability of obtaining each number on the red die and the same on the green die,
each outcome in the table will occur with 1/36 probability

,The distribution in this example is symmetrical, highest for X equal to 7 and declining on either side.

Expected Value of a Random Variable

The expected value of a discrete random variable is the weighted average of all tis possible values,
taking the probability of each outcome as its weight. You calculate it by multiplying each possible
value of the random variable by its probability and summing.
𝑛

𝐸(𝑋) = 𝑋1 𝑃1 + 𝑋2 𝑃2 + ⋯ + 𝑋𝑛 𝑃𝑛 = ∑ 𝑋𝑖 𝑃𝑖
𝑖=1

, Expected Value Rules




For example:

𝑌 = 𝑏1 + 𝑏2 𝑋

𝐸(𝑌) = 𝐸(𝑏1 + 𝑏2 𝑋)
= 𝐸(𝑏1 ) + 𝐸(𝑏2 𝑋)
= 𝑏1 + 𝑏2 𝐸(𝑋)


Let g (X) be any function of X. Then the expected value of this function is given by:
𝑛

𝐸(𝑔(𝑋)) = 𝐺(𝑋1 )𝑃1 + 𝐺(𝑋2 )𝑃2 + ⋯ + 𝐺(𝑋𝑛 )𝑃𝑛 = ∑ 𝐺(𝑋𝑖 )𝑃𝑖
𝑖=1

Population Variance of a Discrete Random Variable

The population variance is defined as the expected value of the square of the difference between X
and its mean
𝑛
2 2}
𝑉𝑎𝑟(𝑋) = 𝜎 𝑥 = 𝐸{(𝑋 − 𝜇𝑥 ) = (𝑋1 − 𝜇𝑥 ) 𝑃1 + ⋯ + (𝑋𝑛 − 𝜇𝑥 ) 𝑃𝑛 = ∑(𝑋𝑖 − 𝜇𝑥 )2 𝑃𝑖
2 2

𝑖=1

Note that: 𝜎𝑥 = √𝜎 2 𝑥