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#has-images #quantitative-methods-basic-concepts

The convention is to double it and call the result the bond's yield to maturity. This method ignores the effect of compounding semi-annual YTM, and the YTM calculated in this way is called a

However, yields of a semi-annual-pay and an annual-pay bond cannot be compared directly without conversion. This conversion can be done in one of the two ways:

- Convert the bond-equivalent yield of a semi-annual-pay bond to an annual-pay bond.
- Convert the equivalent annual yield of an annual-pay bond to a bond-equivalent yield.

- A Eurobond pays coupon annually. It has an annual-pay YTM of 8%.
- A U.S. corporate bond pays coupon semi-annually. It has a bond equivalent YTM of 7.8%.
- Which bond is more attractive, if all other factors are equal?

- Convert the U.S. corporate bond's bond equivalent yield to an annual-pay yield:
- Annual-pay yield = [1 + 0.078/2]
^{2}- 1 = 7.95% < 8% - The Eurobond is more attractive since it offers a higher annual-pay yield.

- Convert the Eurobond's annual-pay yield to a bond equivalent yield (BEY):
- BEY = 2 x [(1 + 0.08)
^{0.5}- 1] = 7.85% > 7.8% - The Eurobond is more attractive since it offers a higher bond equivalent yield.

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#analyst-notes #quantitative-methods-basic-concepts #statistics

Measurement is the assignment of numbers to objects or events in a systematic fashion. To choose the appropriate statistical methods for summarizing and analyzing data, we need to distinguish between different **measurement scales** or levels of measurement.

**Nominal Scale**- Nominal measurement represents the weakest level of measurement.
- It consists of assigning items to groups or categories.
- No quantitative information is conveyed and no ordering (ranking) of the items is implied.
- Nominal scales are qualitative rather than quantitative.

**Ordinal Scale**- Measurements on an ordinal scale are categorized.
- The various measurements are then ranked in their categories.
- Measurements with ordinal scales are ordered with higher numbers representing higher values. The intervals between the numbers are not necessarily equal.

*Example 1**Example 2***Interval Scale****Ratio Scale**

Note that as you move down t...

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#has-images #quantitative-methods-basic-concepts #statistics

Very often, the data available is vast, leading to a situation where dealing with individual numbers becomes laborious and messy. In such circumstances, it is neater and more convenient to summarize results into what is known as a frequency table. The data in the display is called a frequency distribution.
**interval**, also called a **class**, is a set of values within which an observation falls.
**frequency distribution** is a tabular display of data categorized into a small number of non-overlapping intervals. Note that:
**1. A histogram is a bar chart that displays a frequency distribution. It is constructed as follows:**
...

An

- Each interval has a lower limit and an upper limit.
- Intervals must be all-inclusive and non-overlapping.

A

- Each observation can only lie in one interval.
- The total number of intervals will incorporate the whole population.
- The range for an interval is unique. This means a value (observation) can only fall into one interval.

It is important to consider the number of intervals to be used. If too few intervals are used, too much data may be summarized and we may lose important characteristics; if too many intervals are used, we may not summarize enough.

A frequency distribution is constructed by dividing the scores into intervals and counting the number of scores in each interval. The actual number of scores and the percentage of scores in each interval are displayed. This helps in the analysis of large amount of statistical data, and works with all types of measurement scales.

**Absolute frequency**is the actual number of observations in a given interval.**Relative frequency**is the result of dividing the absolute frequency of each return interval by the total number of observations.**Cumulative absolute frequency**and**cumulative relative frequency**are the results from cumulating the absolute and relative frequencies as we move from the first to the last interval.

The following steps are required when organizing data into a frequency distribution together with suggestions on constructing the frequency distribution.

- Identify the highest and lowest values of the observations.
- Setup classes (groups into which data is divided). The classes must be mutually exclusive and of equal size.
- Add up the number of observations and assign each observation to its class.
- Count the number of observations in each class. This is called the class frequency.

Data can be divided into two types: discrete and continuous.

**Discrete**: The values in the data set can be counted. There are distinct spaces between the values, such as the number of children in a family or the number of shares comprising an index.**Continuous**: The values in the data set can be measured. There are normally lots of decimal places involved and (theoretically, at least) there are no gaps between permissible values (i.e., all values can be included in the data set). Examples would include the height of a person and the time to complete an assignment. These values can be measured using sufficiently accurate tools to numerous decimal places.

There are two methods that graphically represent continuous data: histograms and frequency polygons.

- The class frequencies are shown on the vertical (y) axis (by the heights of bars drawn next to each other).
- The classes (intervals) are shown on the horizontal (x) axis.
- There is no space between the bars.

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A book on Mythology must draw from widely different sources.

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