Statistical Concepts Applicable to Security Market Returns

Authors

• Narayana Rao

Published

Creative Commons Attribution 3.0 License

Version 3

Last edited: 16 Nov 2008

Exported: 26 Nov 2011

Original URL: http://knol.google.com/k/-/-/2utb2lsm2k7a/498

 

a)  Population and a sample;

A Population is defined as all members of a specified group.

A Sample is a subset of a defined population.

 

b) Parameter;

A Parameter is a descriptive measure or characteristic of a defined population. It is thus the actual true measure of the population’s characteristic(s).

 

c) Types of measurement scales;

Nominal Scale: categorizes each member of the population or sample using an integer for each category. It is the weakest level of measurement with no implied ranking or intensity.

Ordinal Scale: each member of the population or sample is placed into a category and these categories are ordered with respect to some characteristic. It is a stronger level of measurement because it allows ordering across members. Think Letter Grades.

Interval Scale: each member is assigned a number from a scale. This scale provides a ranking across members and assurance that differences between scale values are equal. Scale values can thus be added or subtracted in a meaningful way. Think temperature either Celsius or Fahrenheit.

Ratio Scale: All the characteristics of interval scales plus a true zero point. Allows computation of meaningful ratios, as well as addition and subtraction. Think rates of asset returns or height.

 

d) Frequency distribution;

Frequency Distribution: is a tabular display of data summarized into a relatively small number of intervals. The frequency distribution is the list of intervals together with the corresponding measures of frequency for the variable of interest.

 

e)  Calculation of a holding period return;

Holding Period Return: is expressed in percent terms, i.e. independent of currency units, and is calculated over a period of time.

R_t   =  [P_t  - P_t-1  + D_t ]/ P_t-1

Where

Holding Period Return = R_t

Share Price end of time t = P_t

Share Price end of time t-1 = P_t-1

Cash Distributions during period t = D_t

 

Holding Period Return, R_t, consists of capital gains over the period plus distributions during the period divided by the beginning price (distribution yield).

 

f)  Use of intervals to summarize data;

An interval is a set of values in which observations on a random variable’s outcomes may fall. The set of intervals must be mutually exclusive and exhaustive, that is each observation must fall into one and only one interval.

The frequency with which observations fall into each interval is used to construct the frequency distribution for a random variable’s outcomes.

 

g)  Relative frequencies, given a frequency distribution;

A frequency distribution shows the absolute number of observations in each interval. A relative frequency divides each corresponding absolute frequency by the total number of observations. Thus a relative frequency distribution shows the percentage of total observations in each interval.

 

h) Histogram and frequency polygon;

A histogram is the graphical equivalent of a frequency distribution; it is a bar chart where continuous data on a random variable’s observations have been grouped into a frequency distribution.

A frequency polygon is the line graph equivalent of a frequency distribution; it is a line graph that joins the frequency for each interval, plotted at the midpoint of that interval.