In a previous article, we introduced the CFA Institute
Investment Foundation Program (Read
more here). It is a free program
designed for anyone who wants to enter or advance within the investment
management industry, including IT, operations, accounting, administration, and
marketing. Candidates who successfully
pass the online exam earn the CFA Institute Investment Foundations Certificate.
There are total of 20 Chapters in 7 modules, covering all
the essential topics in finance, economics, ethics and regulations. This series of articles will highlight the
core knowledge of each chapter.
Chapter 8 provides an overview of quantitative concepts. The
learning outcome of chapter 8 is as follows:
·
Define the concept of interest;
·
Compare simple and compound interest;
·
Define present value, future value, and discount
rate;
·
Describe how time and discount rate affect
present and future values;
·
Explain the relevance of net present value in
valuing financial investments;
·
Describe applications of time value of money;
·
Explain uses of mean, median, and mode, which
are measures of frequency or central tendency;
·
Explain uses of range, percentile, standard
deviation, and variance, which are measures of dispersion;
·
Describe and interpret the characteristics of a
normal distribution;
·
Describe and interpret correlation.
Part II of this series will be focusing on descriptive
statistics. Below are the summaries of
descriptive statistics.
·
The role of descriptive statistics is to
summarise the information given in large quantities of data for the purpose of
making comparisons, predicting future values, and better understanding the
data.
·
The purpose of measures of frequency or central
tendency is to describe a group of individual data scores with a single
measurement. This measure is intended to be representative of the individual
scores. Measures of central tendency include arithmetic mean, geometric mean,
median, and mode. Different measures are appropriate for different types of
data.
·
The arithmetic mean is the most commonly used
measure. It represents the sum of all the observations divided by the number of
observations. It is an easy measure to understand but may not be a good
representative measure when there are outliers.
·
The geometric mean return is the average compounded
return for each period—that is, the average return for each period assuming
that returns are compounding. It is frequently the preferred measure of central
tendency for returns in the investment industry.
·
When observations are ranked in order of size,
the median is the middle value. It is not sensitive to outliers and may be a
more representative measure than the mean when data are skewed.
·
The mode is the most frequently occurring value
in a data set. A data set may have no identifiable unique mode. It may not be a
meaningful representative measure of central tendency.
·
Measures of dispersion are important for
describing the spread of the data, or its variation around a central value. Two
common measures of dispersion are range and standard deviation.
·
Range is the difference between the highest and
lowest values in a data set. It is easy to measure, but it is sensitive to
outliers.
·
Standard deviation measures the variability of a
data set around the mean of the data set. It is in the same unit of measurement
as the mean.
·
A distribution is simply the values that a
variable can take, showing its observed or theoretical frequency of occurrence.
·
For a perfectly symmetrical distribution, the
mean, median, and mode will be identical.
·
A common symmetrical distribution is the normal
distribution, a bell-shaped curve that is represented by its mean and standard
deviation. In a normal distribution, 68% of all the observations lie within one
standard deviation of the mean and about 95% of the observations are within two
standard deviations.
·
The strength of a relationship between two
variables can be measured by using correlation.
·
Correlation is measured by the correlation
coefficient on a scale from –1 to +1. When two variables move exactly in tandem
with each other, the variables are said to be perfectly positively correlated
and the correlation coefficient is +1. When two variables move exactly in
opposite directions, they are perfectly negatively correlated and the
correlation coefficient is –1. Variables with no relationship to each other
will have a correlation coefficient close to 0.
·
It is important to realise that correlation does
not imply causation.
Sample Question
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