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Investment - Embedded Provisions Found in Some Bonds
Common embedded clauses include call, put, and conversion provisions.
Call
Call provisions are the issuer’s right to purchase back the bond before to maturity.
Put
Put provisions are the bondholder’s right to sell back the bond to the issuer before to maturity.
Conversion
Conversion clauses are the bondholder’s right to convert the bond into shares of the issuer’s stock prior to maturity.
Callable Bonds
A call provision allows the issuer the right to purchase back the bond issue prior to the maturity date. Bonds that contain a call provision are referred to as callable bonds. A callable bond allows the issuer the right to buy back (or call) the bond from bondholders before to the maturity date at a pre-specified price, referred to as the call price. The call price normally represents the par value of the bond plus an amount referred to as the call premium.
For most callable bonds, the bond issuer cannot exercise the call provision until a predetermined number of years following issuance. The pre-specified call price at which bonds can be bought back early may be set regardless of the call date, but in most circumstances, the call price changes over time. Under a typical call schedule, the call price tends to drop and move towards the par value over time.
In general, bond issuers seek to include a call provision so that if interest rates fall after a bond has been issued, they can issue new bonds at a lower interest rate and use the revenues to call the higher interest rate bonds. It is vital to remember that the call provision is a benefit to the issuer and a disadvantage to the bondholder. If called, bondholders are disadvantaged since they would likely have to reinvest the funds in new bonds at lower interest rates.
Consequently, the coupon rate on a callable bond will normally be greater than a comparable bond without an incorporated call provision to compensate the bondholder for the risk that the bond may be retired early. This danger is referred to as call risk.
Putable Bonds
A put provision offers the bondholder the right to sell the bond back to the issuer prior to the maturity date. Bonds that contain a put provision are termed putable bonds.
A putable bond allows bondholders the right to sell (or put back) their bonds to the issuer before to the maturity date at a pre-specified price, referred to as the put price. Bondholders could desire to exercise this privilege if market interest rates rise, and they can earn a greater rate by buying another bond that reflects the interest rate increase. Most putable bonds do not start providing bondholders with put protection until a few years after issuance.
In contrast to the call provision, which is a right of the issuer, a put provision is a right of the bondholder.
Consequently, the coupon rate on a putable bond will often be lower than the coupon rate on a comparable bond without an incorporated put provision. Bondholders are ready to accept a somewhat lower coupon rate on a bond with a put provision because, should interest rates rise in the economy, they have an opportunity to sell the bonds back to the company and reinvest in new bonds with higher coupon rates.
Convertible Bonds
A conversion clause allows the bondholder the right to swap the bond into a pre-specified number of the issuer’s common shares prior to the bond’s maturity date. Bonds that feature a conversion provision are referred to as convertible bonds.
Convertible bonds are debt securities prior to conversion, but the fact that they can be converted to common shares makes their value partially contingent on the price of the common shares.
The number of common shares that the bondholder will get from converting the bond is known as the conversion ratio. The conversion ratio may be stable for the security’s life, or it may change over time.
The conversion value of a convertible bond is the value of the bond if it is converted to common shares. The conversion value is equal to the conversion ratio multiplied by the share price.
If the share price of the firm dramatically increases, the conversion value of the bond will grow and may become more than the value of the convertible bond as a regular bond (i.e., the value of the bond if it were not convertible). If this happens, converting the bond becomes attractive.
Because the conversion feature is a benefit to bondholders, convertible bonds often offer a coupon rate that is lower than the coupon rate on a similar bond without a conversion feature. At conversion, the bonds are retired (stop to exist) and common shares are issued. If the bonds are not converted to common stock before to maturity, they will be paid off like any other bond and retired at the maturity date.
Asset-Backed Securities
Securitisation refers to the development and issuing of new debt instruments, termed asset-backed securities, that are backed by a pool of other debt securities.
The most prevalent sort of asset-backed instrument is backed by a pool of mortgages. In some parts of the world, these asset-backed securities may be referred to as mortgage-backed securities (MBS).
Mortgage-backed securities are based on a pool of underlying residential mortgage loans (home loans) or a pool of underlying commercial mortgage loans.
Mortgage loans are loans to homeowners or owners of other real estate who return the loans through monthly payments.
To produce mortgage-backed securities, a financial intermediary will buy and package a pool of mortgage loans from lenders using a special purpose company. The intermediary will then issue new debt instruments against the bundled pool of home loans.
Typical Asset-Backed Securitisation
Investors who acquire these new mortgage-backed securities earn a part of the pooled monthly loan payments.
Unlike traditional bonds, most asset-backed securities give monthly payments to their owners that comprise both an interest component and a principal component.
Other asset-backed securities are constructed similarly to mortgage-backed securities, only the types of underlying assets varies.
For instance, the underlying assets can include credit card receivables, vehicle loans, and corporate bonds.
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Investment - Descriptive Statistics
As the name suggests, descriptive statistics are used to characterize data. Often, you are confronted by data that you need to structure in order to understand.
Let's take everyday commute time as an example. You have the sensation that the commute home from work is growing slower, and you are thinking of altering your route. How could you judge whether the travel actually is growing slower? Suppose you calculated and compared your average daily travel time each month over a year.
The first thing you need to address is: What is meant by average?
There are a lot of alternative approaches to calculate averages, as you shall see, each of which has advantages and downsides.
Types of Descriptive Statistics
In general, descriptive statistics are figures that summarise fundamental properties of a data set. A data set pertains to a certain variable — for example, the time it takes to travel home from work. The data set includes several observations – that is, observable values for the variable. For example, if you keep track of your everyday commute time for a year, you will end up with around 250 observations. The distribution of a variable refers to the values a variable can take, and the number of observations associated with each of these values.
We shall cover two forms of descriptive statistics:
Those that describe the central trend of a data set (e.g., the average or mean)
Those that describe the dispersion or spread of the data (e.g., the standard deviation)
In addition to understanding whether the travel to work is getting slower (by comparing monthly averages), you might also want to discover a technique to determine how much variance there is between journey times from one day to another (by utilizing standard deviation).
Businesses have comparable demands to summarise data. Descriptive statistics quickly summarise information from vast quantities of data for the aim of comprehending the data and establishing comparisons across specific data sets for risk assessment. Measures of Frequency and Average
The goal of assessing the frequency of outcomes or 'central tendency' is to describe a set of individual data points with a single measurement. The value used to characterize the group will be the one value considered to be best representative of all the individual data points.
Measures of central tendency are important for drawing comparisons between groups of persons or between sets of figures. Such metrics reduce a huge number of measurements to a single figure. For instance, the mean or average temperature in Country X in July from 1961 to 2022 is calculated to be 16.1°C. Over the same period, the average temperature in Country X in September is 13.6°C. Because it is a long time series, you can legitimately assume that it is usually warmer in July than September in Country X.
The following are common metrics of central tendency:
Arithmetic mean
Geometric mean
Median Mode
The right measure for a given data collection depends on the features of the data and the aim of your calculation. These measures are examined in the following sections.
Arithmetic Mean
The arithmetic mean is the most often used measure of central tendency and is recognizable to most people. It is generally abbreviated to just ‘mean’ or ‘average’.
To calculate the mean, you put all the numbers in the data set together and divide by the number of observations (items in the data set). The arithmetic mean presupposes that each observation is equally likely to occur.
How to Calculate the Mean
The arithmetic mean return, or average yearly return during the 10-year period, is equal to 6.3% and is computed as follows:
Mean = (1.3 + 2.4 + 0.8 + 3.7 + 8.0 + 3.7 + 7.2 + 26.4 + 4.2 + 5.2)/10 = 6.3%
Geometric Mean
An alternative average to the arithmetic mean is the geometric average or geometric mean. Applied to investment returns, the geometric mean return is the average return assuming that returns are compounding.
Consider Tom Parker who recently sold his company and has USD10 million to invest. He invests in a fund that returns 8% the first year, 3% the second year, and 7% the third year. How much return did Tom Parker accumulate during these three years? The following slides illustrate how to calculate geometric mean.
Multiply 1 Plus Each Annual Return
The first step in computing the geometric mean return is to multiply 1 plus each annual return together, which gives you the amount Mike would have accumulated at the end of the three years per dollar of investment:
[(1 + 8%) × (1 + 3%) × (1 + 7%) ≈ 1.1903].
This figure of 1.1903 indicates three years of investment, however the geometric mean return should record an average rate of return for each of the three years.
Raise the Accumulation to the Power of 1 Over Periods Held
The second step entails raising the accumulation to the power of ‘one over the number of periods held’ (three in this specific case); this computation may alternatively be expressed as taking ‘the number of periods held’ root of the value ((1.1903)1/3 = 1.0598).
This number of 1.0598 comprises both the original investment and the average yearly return on the investment each year (1 plus the geometric mean return).
Subtract 1 from the Value in Step 2
The third step is to deduct 1 from this figure to get at the return that would have to be earned on average each year to attain to the total accumulation over the three years (1.0598 – 1 = 0.0598 or 5.98%).
The geometric mean return is 5.98%, which is less than the arithmetic mean return (6.0% = (8% + 3% + 7%)/3). Geometric mean is often the favored measure for the investing business.
Take Away Notes
An key element to observe is that the geometric mean is lower than the arithmetic mean, even though the yearly returns over the 10-year holding period are identical. This conclusion is because the returns are compounded when computing the geometric mean return. Compounding will result in a bigger value over time, so a lower rate of return is necessary to obtain the same amount. In fact, if the same set of numbers is used to calculate both means, the geometric mean return is never more than the arithmetic mean return and is generally lower.
When you are working with interest rates, percentage changes, or returns on investment portfolios, which can be volatile, it is better and more accurate to use geometric mean. And the extended term (10 years in this example) makes the compounding impact more essential, hence the use of a geometric mean. Conversely, for data sets in which the numbers are neither skewed or reliant on each other, the arithmetic mean is better appropriate because it is easy to use and understand.
Median
If you put data in ascending order of size from the smallest to the largest, the median is the midpoint value. If there is an even number of items in a data set, then you average the two middle observations to derive the median. Hence, in many circumstances (i.e., when the sample size is odd or when the two middle-ranked items of an even-numbered data set are the same) the median will be a number that actually occurs in the data set. The example below displays the calculation of the median for the sample 10 years of returns.
When the returns are ordered from low to high, the median value is the arithmetic mean of the fifth and sixth ordered observations.
The mode is the most often occurring value in a data set. The following explains how the mode is derived for the same set of data in the Median section above. We can see that one value occurs twice, 3.7%, as seen in the example below. This number is the mode of the data.
The mode can be used as a measure of central tendency for data that have been categorized into categories or groups. For example, if all the employees of a company were asked what method of transportation they used to come to work each day, it would be able to arrange the answers into groups, such as automobile, bus, train, bicycle, and walking. The category with the highest number would be the mode.
A difficulty with the mode is that it is often not unique, in which case there is no mode. Another difficulty with the mode is that the most frequently occurring observation may be far removed from the rest of the data and does not meaningfully reflect them.
As you have seen, the arithmetic mean is often used to locate the middle position of the distribution of a group of data points. But it is not always a reliable indicator. When there are outliers, the mode or median can better illustrate the core tendency of a set of data points than the mean.
In a positively-skewed data set, the median and mode are smaller than the arithmetic mean, as seen in the following graph.
As the name suggests, descriptive statistics are used to characterize data. Often, you are confronted by data that you need to structure in order to understand.
Let's take everyday commute time as an example. You have the sensation that the commute home from work is growing slower, and you are thinking of altering your route. How could you judge whether the travel actually is growing slower? Suppose you calculated and compared your average daily travel time each month over a year.
The first thing you need to address is: What is meant by average?
There are a lot of alternative approaches to calculate averages, as you shall see, each of which has advantages and downsides.
Types of Descriptive Statistics
In general, descriptive statistics are figures that summarise fundamental properties of a data set. A data set pertains to a certain variable — for example, the time it takes to travel home from work. The data set includes several observations – that is, observable values for the variable. For example, if you keep track of your everyday commute time for a year, you will end up with around 250 observations. The distribution of a variable refers to the values a variable can take, and the number of observations associated with each of these values.
We shall cover two forms of descriptive statistics:
Those that describe the central trend of a data set (e.g., the average or mean)
Those that describe the dispersion or spread of the data (e.g., the standard deviation)
In addition to understanding whether the travel to work is getting slower (by comparing monthly averages), you might also want to discover a technique to determine how much variance there is between journey times from one day to another (by utilizing standard deviation).
Businesses have comparable demands to summarise data. Descriptive statistics quickly summarise information from vast quantities of data for the aim of comprehending the data and establishing comparisons across specific data sets for risk assessment. Measures of Frequency and Average
The goal of assessing the frequency of outcomes or 'central tendency' is to describe a set of individual data points with a single measurement. The value used to characterize the group will be the one value considered to be best representative of all the individual data points.
Measures of central tendency are important for drawing comparisons between groups of persons or between sets of figures. Such metrics reduce a huge number of measurements to a single figure. For instance, the mean or average temperature in Country X in July from 1961 to 2022 is calculated to be 16.1°C. Over the same period, the average temperature in Country X in September is 13.6°C. Because it is a long time series, you can legitimately assume that it is usually warmer in July than September in Country X.
The following are common metrics of central tendency:
Arithmetic mean
Geometric mean
Median Mode
The right measure for a given data collection depends on the features of the data and the aim of your calculation. These measures are examined in the following sections.
Arithmetic Mean
The arithmetic mean is the most often used measure of central tendency and is recognizable to most people. It is generally abbreviated to just ‘mean’ or ‘average’.
To calculate the mean, you put all the numbers in the data set together and divide by the number of observations (items in the data set). The arithmetic mean presupposes that each observation is equally likely to occur.
How to Calculate the Mean
The arithmetic mean return, or average yearly return during the 10-year period, is equal to 6.3% and is computed as follows:
Mean = (1.3 + 2.4 + 0.8 + 3.7 + 8.0 + 3.7 + 7.2 + 26.4 + 4.2 + 5.2)/10 = 6.3%
Geometric Mean
An alternative average to the arithmetic mean is the geometric average or geometric mean. Applied to investment returns, the geometric mean return is the average return assuming that returns are compounding.
Consider Tom Parker who recently sold his company and has USD10 million to invest. He invests in a fund that returns 8% the first year, 3% the second year, and 7% the third year. How much return did Tom Parker accumulate during these three years? The following slides illustrate how to calculate geometric mean.
Multiply 1 Plus Each Annual Return
The first step in computing the geometric mean return is to multiply 1 plus each annual return together, which gives you the amount Mike would have accumulated at the end of the three years per dollar of investment:
[(1 + 8%) × (1 + 3%) × (1 + 7%) ≈ 1.1903].
This figure of 1.1903 indicates three years of investment, however the geometric mean return should record an average rate of return for each of the three years.
Raise the Accumulation to the Power of 1 Over Periods Held
The second step entails raising the accumulation to the power of ‘one over the number of periods held’ (three in this specific case); this computation may alternatively be expressed as taking ‘the number of periods held’ root of the value ((1.1903)1/3 = 1.0598).
This number of 1.0598 comprises both the original investment and the average yearly return on the investment each year (1 plus the geometric mean return).
Subtract 1 from the Value in Step 2
The third step is to deduct 1 from this figure to get at the return that would have to be earned on average each year to attain to the total accumulation over the three years (1.0598 – 1 = 0.0598 or 5.98%).
The geometric mean return is 5.98%, which is less than the arithmetic mean return (6.0% = (8% + 3% + 7%)/3). Geometric mean is often the favored measure for the investing business.
Take Away Notes
An key element to observe is that the geometric mean is lower than the arithmetic mean, even though the yearly returns over the 10-year holding period are identical. This conclusion is because the returns are compounded when computing the geometric mean return. Compounding will result in a bigger value over time, so a lower rate of return is necessary to obtain the same amount. In fact, if the same set of numbers is used to calculate both means, the geometric mean return is never more than the arithmetic mean return and is generally lower.
When you are working with interest rates, percentage changes, or returns on investment portfolios, which can be volatile, it is better and more accurate to use geometric mean. And the extended term (10 years in this example) makes the compounding impact more essential, hence the use of a geometric mean. Conversely, for data sets in which the numbers are neither skewed or reliant on each other, the arithmetic mean is better appropriate because it is easy to use and understand.
Median
If you put data in ascending order of size from the smallest to the largest, the median is the midpoint value. If there is an even number of items in a data set, then you average the two middle observations to derive the median. Hence, in many circumstances (i.e., when the sample size is odd or when the two middle-ranked items of an even-numbered data set are the same) the median will be a number that actually occurs in the data set. The example below displays the calculation of the median for the sample 10 years of returns.
When the returns are ordered from low to high, the median value is the arithmetic mean of the fifth and sixth ordered observations.
The mode is the most often occurring value in a data set. The following explains how the mode is derived for the same set of data in the Median section above. We can see that one value occurs twice, 3.7%, as seen in the example below. This number is the mode of the data.
The mode can be used as a measure of central tendency for data that have been categorized into categories or groups. For example, if all the employees of a company were asked what method of transportation they used to come to work each day, it would be able to arrange the answers into groups, such as automobile, bus, train, bicycle, and walking. The category with the highest number would be the mode.
A difficulty with the mode is that it is often not unique, in which case there is no mode. Another difficulty with the mode is that the most frequently occurring observation may be far removed from the rest of the data and does not meaningfully reflect them.
As you have seen, the arithmetic mean is often used to locate the middle position of the distribution of a group of data points. But it is not always a reliable indicator. When there are outliers, the mode or median can better illustrate the core tendency of a set of data points than the mean.
In a positively-skewed data set, the median and mode are smaller than the arithmetic mean, as seen in the following graph.
In a negatively-skewed data set, the median and mode are bigger than the arithmetic mean, as demonstrated in the following graph.
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Investment-Measures of Dispersion
Whereas measures of central tendency are used to estimate representative or center values of a data collection, measurements of dispersion are crucial for describing the spread of the data or its variation around a central value. Two data sets may have the same mean or median but radically different amounts of variability or vice versa. A description of a data collection should include both a measure of central tendency, such as the mean, and a measure of dispersion.
Suppose two companies each pay an average annual salary of USD50,000. In one company, most incomes are clustered close to the average, whereas in the second, they are spread out with many people earning very little and some earning a lot. It would be useful to have a measure of dispersion that can help discover such disparities between data sets
Another reason why measurements of dispersion are significant in finance is because investment risk is generally measured using some measure of variability. When investors are considering investing in a security, they are interested in the likely (anticipated) return on that investment as well as in the risk that the return could differ from the expected return (its variability). A risk-averse investor assessing two investments that have equal expected returns but substantially different amounts of fluctuation (risk) around those expected returns often favors the asset with the lowest variability.
Two popular metrics of dispersion of a data collection are the range and the standard deviation.
Range
The range is the difference between the highest and lowest values in a data set. It is the easiest measure of dispersion to compute and understand, but it is particularly sensitive to outliers. To compute the range in a data set:
Find the lowest value (Min) and the maximum value (Max)
Calculate the difference between the Max and the Min
Range = Max – Min
Clearly, the range is affected by extreme values and, if there are outliers, it indicates little about the distribution of the data between those extremes.
If there are a significant number of observations listed in order of size, the range can be partitioned into 100 equal-sized intervals. Dividing points between intervals are termed percentiles. The 50th percentile is the median and divides the observations so that 50% are higher and 50% are lower than the median. The 20th percentile is the value below which 20% of observations in the series fall. Accordingly, the dispersion of the observations can be characterized in terms of percentiles. Observations can also be separated into various equal-sized intervals. Commonly used intervals include quartiles (the observations are divided into four equal-sized intervals) and deciles (the observations are divided into 10 equal-sized intervals).
Standard Deviation
A commonly used metric of dispersion is standard deviation. It quantifies the variability or volatility of a data set around the average value (the arithmetic mean) of that data collection. Although, as said before, you are not responsible for any computations, you may find it beneficial to look at the formula for how standard deviation is computed.
Whereas measures of central tendency are used to estimate representative or center values of a data collection, measurements of dispersion are crucial for describing the spread of the data or its variation around a central value. Two data sets may have the same mean or median but radically different amounts of variability or vice versa. A description of a data collection should include both a measure of central tendency, such as the mean, and a measure of dispersion.
Suppose two companies each pay an average annual salary of USD50,000. In one company, most incomes are clustered close to the average, whereas in the second, they are spread out with many people earning very little and some earning a lot. It would be useful to have a measure of dispersion that can help discover such disparities between data sets
Another reason why measurements of dispersion are significant in finance is because investment risk is generally measured using some measure of variability. When investors are considering investing in a security, they are interested in the likely (anticipated) return on that investment as well as in the risk that the return could differ from the expected return (its variability). A risk-averse investor assessing two investments that have equal expected returns but substantially different amounts of fluctuation (risk) around those expected returns often favors the asset with the lowest variability.
Two popular metrics of dispersion of a data collection are the range and the standard deviation.
Range
The range is the difference between the highest and lowest values in a data set. It is the easiest measure of dispersion to compute and understand, but it is particularly sensitive to outliers. To compute the range in a data set:
Find the lowest value (Min) and the maximum value (Max)
Calculate the difference between the Max and the Min
Range = Max – Min
Clearly, the range is affected by extreme values and, if there are outliers, it indicates little about the distribution of the data between those extremes.
If there are a significant number of observations listed in order of size, the range can be partitioned into 100 equal-sized intervals. Dividing points between intervals are termed percentiles. The 50th percentile is the median and divides the observations so that 50% are higher and 50% are lower than the median. The 20th percentile is the value below which 20% of observations in the series fall. Accordingly, the dispersion of the observations can be characterized in terms of percentiles. Observations can also be separated into various equal-sized intervals. Commonly used intervals include quartiles (the observations are divided into four equal-sized intervals) and deciles (the observations are divided into 10 equal-sized intervals).
Standard Deviation
A commonly used metric of dispersion is standard deviation. It quantifies the variability or volatility of a data set around the average value (the arithmetic mean) of that data collection. Although, as said before, you are not responsible for any computations, you may find it beneficial to look at the formula for how standard deviation is computed.
The disparities between the observed values of X and the mean value of X capture the variability of X. These discrepancies are squared and totaled. Note that, because the differences are squared, what matters is the size of the difference, not the sign of the difference. The sum is then divided by the number of observations. Finally, the square root of this value is calculated to determine the standard deviation.
Variance
The value before the square root is used when calculating standard deviation is known as the variance, which is another measure of dispersion. The standard deviation is the square root of the variance. The standard deviation and the variance capture the same thing – how far out from the mean the data are. The advantage of the standard deviation is that it is expressed in the same unit as the mean. For example, if the mean is stated as minutes of journey time, the standard deviation will also be expressed as minutes, however the variance will be expressed as minutes squared, making the standard deviation an easier measure than range to use and compare with the mean.
Calculating Standard Deviation
To explain the calculation of the standard deviation, let us return to the example presented in Lesson 5 of a three-year investment that yields 8% or 0.08 the first year, 3% or 0.03 the second year, and 7% or 0.07 the third year. The arithmetic mean return is 6% or 0.06. The standard deviation is roughly 2.16%.
Variance
The value before the square root is used when calculating standard deviation is known as the variance, which is another measure of dispersion. The standard deviation is the square root of the variance. The standard deviation and the variance capture the same thing – how far out from the mean the data are. The advantage of the standard deviation is that it is expressed in the same unit as the mean. For example, if the mean is stated as minutes of journey time, the standard deviation will also be expressed as minutes, however the variance will be expressed as minutes squared, making the standard deviation an easier measure than range to use and compare with the mean.
Calculating Standard Deviation
To explain the calculation of the standard deviation, let us return to the example presented in Lesson 5 of a three-year investment that yields 8% or 0.08 the first year, 3% or 0.03 the second year, and 7% or 0.07 the third year. The arithmetic mean return is 6% or 0.06. The standard deviation is roughly 2.16%.
Larger levels of standard deviation compared to the mean imply greater variety in a data set. Also, by utilizing standard deviation, you may predict how likely it is that any given observation will occur depending on its distance from the mean.
Example: Comparison of Investments
The next example compares the returns on the investment sample we have been using to the returns on another investment over the same period using mean and standard deviation.
An investment receives returns over a 10-year period with the following characteristics:
Number of observations = 10
Mean = 6.3%
Standard deviation = 7.1%
Another investment over the same time period has the following characteristics:
Number of observations = 10
Mean = 6.5%
Standard deviation = 2.6%
Based on mean and standard deviation, the second investment is better than the first investment. It has a higher mean return and lower standard deviation, hence less variability (which suggests less risk) in its returns.
Larger levels of standard deviation compared to the mean imply greater variety in a data set. Also, by utilizing standard deviation, you may predict how likely it is that any given observation will occur depending on its distance from the mean.
Example: Comparison of Investments
The next example compares the returns on the investment sample we have been using to the returns on another investment over the same period using mean and standard deviation.
An investment receives returns over a 10-year period with the following characteristics:
Number of observations = 10
Mean = 6.3%
Standard deviation = 7.1%
Another investment over the same time period has the following characteristics:
Number of observations = 10
Mean = 6.5%
Standard deviation = 2.6%
Based on mean and standard deviation, the second investment is better than the first investment. It has a higher mean return and lower standard deviation, hence less variability (which suggests less risk) in its returns.
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Investment - Normal Distribution
The arithmetic mean and standard deviation are two useful techniques of representing numerous distributions of data. A distribution is just a group of values, representing their actual or hypothesized frequency of occurrence.
Analysing Data
Sometimes it is beneficial to look at a picture of the distribution to comprehend it. The form of the distribution has a bearing on how you perceive the summary measurements of the distribution. This data can be shown pictorially using a histogram — a bar chart with bars that are proportional to the frequency of occurrence of each group of observations — as illustrated in the following illustrations.
For a fully symmetrical distribution, such as a normal distribution the mean, median, and mode will be identical.
Normal Distribution Representation
A normal distribution is represented in a graph by a bell curve, an example of which is shown below. The shape of the curve is symmetrical, with a single central peak at the mean of the data and the graph falling off evenly on either side of the mean; 50% of the distribution is to the left of the mean, and 50% lies to the right of the mean. The shape of a normal distribution depends on the mean and the standard deviation.
The mean of the distribution dictates the placement of the centre of the curve, and the standard deviation determines the height and width of the curve. When the standard deviation is big, the curve is short and wide; when the standard deviation is small, the curve is tall and narrow.
The arithmetic mean and standard deviation are two useful techniques of representing numerous distributions of data. A distribution is just a group of values, representing their actual or hypothesized frequency of occurrence.
Analysing Data
Sometimes it is beneficial to look at a picture of the distribution to comprehend it. The form of the distribution has a bearing on how you perceive the summary measurements of the distribution. This data can be shown pictorially using a histogram — a bar chart with bars that are proportional to the frequency of occurrence of each group of observations — as illustrated in the following illustrations.
For a fully symmetrical distribution, such as a normal distribution the mean, median, and mode will be identical.
Normal Distribution Representation
A normal distribution is represented in a graph by a bell curve, an example of which is shown below. The shape of the curve is symmetrical, with a single central peak at the mean of the data and the graph falling off evenly on either side of the mean; 50% of the distribution is to the left of the mean, and 50% lies to the right of the mean. The shape of a normal distribution depends on the mean and the standard deviation.
The mean of the distribution dictates the placement of the centre of the curve, and the standard deviation determines the height and width of the curve. When the standard deviation is big, the curve is short and wide; when the standard deviation is small, the curve is tall and narrow.
A normal distribution has special importance in statistics because many variables have the approximate shape of a normal distribution — for example, height, blood pressure, and lengths of items created by machines. This distribution is often useful as a description of data when there are a large number of observations.
Observation of a Normal Distribution
A normal distribution is a distribution of a continuous random variable (i.e., a variable that can take on an unlimited number of values). The vertical axis for the normal distribution represents the probability or likelihood of occurrence. By contrast, on the histograms for the companies showed before, the vertical axis was frequency of occurrence.
The mean (and median) is the centre of the distribution and has the highest likelihood of occurring. Half of the observations are on one side of the mean and half on the other. Approximately two-thirds of the observations are within one standard deviation of the mean, and 95% of observations are within two standard deviations of the mean.
Standard Deviation and Normal Distribution
The whole area under the curve or bell is 100% of the distribution. The area under the curve that is within one standard deviation of the mean is around 68% of all the data. In other words, given a mean of 0 and a standard deviation of 1, around 68% of the observations lie between –1 and +1, and 32% of the observations are more than one standard deviation from the mean. The area under the curve that is within 2 standard deviations of the mean is around 95% of the data.
Given a mean of 0 and a standard deviation of 1, around 95% of the observations lie between –2 and +2, and 5% of the observations are more than two standard deviations from the mean. The area under the curve that is within three standard deviations of the mean represents around 99% of the observations. Given a mean of 0 and a standard deviation of 1, nearly 99% of the observations fall between –3 and +3, and less than 1% of the observations occur more than three standard deviations away from the mean.
The observations that are more than a specific number of standard deviations from the mean can be regarded as residing in the tails of the distribution. Assuming that returns on a portfolio of stocks are normally distributed, the chance of significant losses (a return more than three standard deviations lower than the mean return) is quite small. The chance of the return being in the left tail more than two standard deviations from the mean (which would be a significant loss under usual circumstances) is just 2.5%.
In other words, out of 200 days, 5 days are projected to contain observations that are greater than two standard deviations from the mean. But during financial crises, losses made by banks and other financial organizations over short periods have been many standard deviations below the mean.
Bell-Shaped Distributions with Fat and Thin Tails
Observation of a Normal Distribution
A normal distribution is a distribution of a continuous random variable (i.e., a variable that can take on an unlimited number of values). The vertical axis for the normal distribution represents the probability or likelihood of occurrence. By contrast, on the histograms for the companies showed before, the vertical axis was frequency of occurrence.
The mean (and median) is the centre of the distribution and has the highest likelihood of occurring. Half of the observations are on one side of the mean and half on the other. Approximately two-thirds of the observations are within one standard deviation of the mean, and 95% of observations are within two standard deviations of the mean.
Standard Deviation and Normal Distribution
The whole area under the curve or bell is 100% of the distribution. The area under the curve that is within one standard deviation of the mean is around 68% of all the data. In other words, given a mean of 0 and a standard deviation of 1, around 68% of the observations lie between –1 and +1, and 32% of the observations are more than one standard deviation from the mean. The area under the curve that is within 2 standard deviations of the mean is around 95% of the data.
Given a mean of 0 and a standard deviation of 1, around 95% of the observations lie between –2 and +2, and 5% of the observations are more than two standard deviations from the mean. The area under the curve that is within three standard deviations of the mean represents around 99% of the observations. Given a mean of 0 and a standard deviation of 1, nearly 99% of the observations fall between –3 and +3, and less than 1% of the observations occur more than three standard deviations away from the mean.
The observations that are more than a specific number of standard deviations from the mean can be regarded as residing in the tails of the distribution. Assuming that returns on a portfolio of stocks are normally distributed, the chance of significant losses (a return more than three standard deviations lower than the mean return) is quite small. The chance of the return being in the left tail more than two standard deviations from the mean (which would be a significant loss under usual circumstances) is just 2.5%.
In other words, out of 200 days, 5 days are projected to contain observations that are greater than two standard deviations from the mean. But during financial crises, losses made by banks and other financial organizations over short periods have been many standard deviations below the mean.
Bell-Shaped Distributions with Fat and Thin Tails
In the display, the curve with the solid line illustrates the normal distribution. The curve with the green dotted line is an example of a distribution with thinner tails than the normal distribution, indicating a lower risk of extreme outcomes. By contrast, the curve with the blue dotted line is an example of a distribution with fatter tails than the normal distribution, indicating increased possibility of extreme outcomes.
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Investment - Correlation
Another approach of using and interpreting data is detecting relationships between data sets. The degree of a relationship between two variables, such as growth in gross domestic product (GDP) and stock market returns, can be quantified by employing correlation. Essentially, two variables are linked when a change in one variable helps predict a change in another one.
When both variables fluctuate in the same direction, the variables are positively linked. If we take the example of traders at an investment bank, salary and age are positively connected if salaries increase as age increases. If the variables move in the opposite direction, then they are negatively linked.
For example, the size of a transaction and the fees stated as a percentage of the transaction are negatively connected if the greater the transaction, the smaller the associated fees. When there is no evident tendency for one variable to move in a particular direction (up or down) relative to changes in the other variable, then the variables are near to being uncorrelated. In practice, it is difficult to identify two variables that have absolutely no relationship.
Correlation Coefficient
Correlation is assessed by the correlation coefficient, which has a scale of –1 to +1. When two variables move exactly in step with each other in the same direction — if one goes up and the other goes up in the same proportion — the variables are said to be fully positively linked. In that situation, the correlation coefficient is at its maximum of +1. When the two variables move exactly in step 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.
Degree of Correlation
Correlation evaluates both the direction of the association between two variables (negative or positive) and the strength of that relationship (that is, the closer to +1 or –1, the stronger the relationship). In practice, it is unusual to find variables that are fully positively or perfectly negatively associated. The greater the association between two variables — the higher the degree of correlation — the more reliably one variable may be predicted given the other value.
For example, there may be a substantial link between stock market index returns and predicted economic growth. In that instance, if economic growth in the future is predicted to be high, then returns on the stock market index are likely to be high too.
It is vital, however, to recognize that correlation does not imply causality. For example, traditionally in the United States, stock market returns and snowfall are both greater in January, and from that you may presume a correlation. But obviously, snowfall does not create an increase in stock market returns, and an increase in stock market returns surely does not cause snowfall.
There are occasions in which a correlation implies some causal relationship. For example, a substantial association has been discovered between power generation and job growth. It may follow that the more workers there are, the more power is consumed, but it does not necessarily follow that an increase in power generation will create jobs.
Correlation and Portfolio Diversification
Correlation is significant in investing because the rise or fall in value of a variable may assist anticipate the growth or fall in value of a security. It is also essential because when two or more securities that are not perfectly positively correlated are pooled together in a portfolio, there is generally a reduction in risk (measured by the portfolio’s standard deviation of returns). The process of blending assets in a portfolio to lessen risk is known as diversification.
An extreme example of an undiversified portfolio is someone holding only one security. This technique is dangerous because it is not rare for a single security to fall down in value by a big amount for a period of time, sometimes permanently. It is significantly less usual for a diversified portfolio of 20 or more different assets to go down by a large amount, even if they are selected at random.
If the assets are selected from a variety of sectors, industries, firm sizes, asset classes, and marketplaces, it is much less likely. One caution is that the benefits of diversity are considerably decreased in periods of financial crises. In such periods, the correlation between returns on different securities (and other asset classes) tends to climb towards +1.
Another approach of using and interpreting data is detecting relationships between data sets. The degree of a relationship between two variables, such as growth in gross domestic product (GDP) and stock market returns, can be quantified by employing correlation. Essentially, two variables are linked when a change in one variable helps predict a change in another one.
When both variables fluctuate in the same direction, the variables are positively linked. If we take the example of traders at an investment bank, salary and age are positively connected if salaries increase as age increases. If the variables move in the opposite direction, then they are negatively linked.
For example, the size of a transaction and the fees stated as a percentage of the transaction are negatively connected if the greater the transaction, the smaller the associated fees. When there is no evident tendency for one variable to move in a particular direction (up or down) relative to changes in the other variable, then the variables are near to being uncorrelated. In practice, it is difficult to identify two variables that have absolutely no relationship.
Correlation Coefficient
Correlation is assessed by the correlation coefficient, which has a scale of –1 to +1. When two variables move exactly in step with each other in the same direction — if one goes up and the other goes up in the same proportion — the variables are said to be fully positively linked. In that situation, the correlation coefficient is at its maximum of +1. When the two variables move exactly in step 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.
Degree of Correlation
Correlation evaluates both the direction of the association between two variables (negative or positive) and the strength of that relationship (that is, the closer to +1 or –1, the stronger the relationship). In practice, it is unusual to find variables that are fully positively or perfectly negatively associated. The greater the association between two variables — the higher the degree of correlation — the more reliably one variable may be predicted given the other value.
For example, there may be a substantial link between stock market index returns and predicted economic growth. In that instance, if economic growth in the future is predicted to be high, then returns on the stock market index are likely to be high too.
It is vital, however, to recognize that correlation does not imply causality. For example, traditionally in the United States, stock market returns and snowfall are both greater in January, and from that you may presume a correlation. But obviously, snowfall does not create an increase in stock market returns, and an increase in stock market returns surely does not cause snowfall.
There are occasions in which a correlation implies some causal relationship. For example, a substantial association has been discovered between power generation and job growth. It may follow that the more workers there are, the more power is consumed, but it does not necessarily follow that an increase in power generation will create jobs.
Correlation and Portfolio Diversification
Correlation is significant in investing because the rise or fall in value of a variable may assist anticipate the growth or fall in value of a security. It is also essential because when two or more securities that are not perfectly positively correlated are pooled together in a portfolio, there is generally a reduction in risk (measured by the portfolio’s standard deviation of returns). The process of blending assets in a portfolio to lessen risk is known as diversification.
An extreme example of an undiversified portfolio is someone holding only one security. This technique is dangerous because it is not rare for a single security to fall down in value by a big amount for a period of time, sometimes permanently. It is significantly less usual for a diversified portfolio of 20 or more different assets to go down by a large amount, even if they are selected at random.
If the assets are selected from a variety of sectors, industries, firm sizes, asset classes, and marketplaces, it is much less likely. One caution is that the benefits of diversity are considerably decreased in periods of financial crises. In such periods, the correlation between returns on different securities (and other asset classes) tends to climb towards +1.
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Investment - Introduction to Investment Instruments
When we invest, we must understand the risks we are incurring with our money as well as the level of return we need or expect. This understanding may help us individually in accomplishing our own financial goals, but it also has professional value. You might be working for a company that generates or distributes investment instruments, or that offers investment management or trading services that need an understanding of investment instruments.
The four primary categories of investment instruments are:
Equity securities (stocks)
Debt securities (bonds)
Alternative investments
Derivatives
These investment tools exist because they respond to the needs of users of capital as well as to investors’ needs. Users of capital include individuals, companies, and governments that need to raise capital for a number of reasons. Individuals, for instance, might need to borrow to finance a property purchase or their child’s schooling. Companies require cash to fund and grow their operations, and governments borrow when their tax receipts are insufficient to fulfill their expenditure commitments.
Each investment instrument has different characteristics that affect the risks to investors and the rewards they can expect to obtain. Debt securities represent loans made by investors to issuing firms and/or governments in order to receive interest revenue. Equity securities are issued by corporations and generally signify ownership in the issuing company; investors buy equity securities in exchange for sharing in the company’s future profits. Equity and debt securities are the building blocks of many investors’ portfolios; investing in stocks and bonds, either directly or indirectly, is how most investors participate in the financial markets.
Alternative investments are roughly described as investments outside typical publicly traded equities and debt securities, such as real estate, commodities, private equity, and hedge funds. Alternative investments can help investors boost profits and decrease risk in a portfolio of investments. Derivatives, which are contracts that draw their value from the performance of an underlying asset, exist to help both investors and borrowers manage future risks, such as fluctuations in stock or commodity prices, interest rates, exchange rates, or non-financial events, such as weather.
When we invest, we must understand the risks we are incurring with our money as well as the level of return we need or expect. This understanding may help us individually in accomplishing our own financial goals, but it also has professional value. You might be working for a company that generates or distributes investment instruments, or that offers investment management or trading services that need an understanding of investment instruments.
The four primary categories of investment instruments are:
Equity securities (stocks)
Debt securities (bonds)
Alternative investments
Derivatives
These investment tools exist because they respond to the needs of users of capital as well as to investors’ needs. Users of capital include individuals, companies, and governments that need to raise capital for a number of reasons. Individuals, for instance, might need to borrow to finance a property purchase or their child’s schooling. Companies require cash to fund and grow their operations, and governments borrow when their tax receipts are insufficient to fulfill their expenditure commitments.
Each investment instrument has different characteristics that affect the risks to investors and the rewards they can expect to obtain. Debt securities represent loans made by investors to issuing firms and/or governments in order to receive interest revenue. Equity securities are issued by corporations and generally signify ownership in the issuing company; investors buy equity securities in exchange for sharing in the company’s future profits. Equity and debt securities are the building blocks of many investors’ portfolios; investing in stocks and bonds, either directly or indirectly, is how most investors participate in the financial markets.
Alternative investments are roughly described as investments outside typical publicly traded equities and debt securities, such as real estate, commodities, private equity, and hedge funds. Alternative investments can help investors boost profits and decrease risk in a portfolio of investments. Derivatives, which are contracts that draw their value from the performance of an underlying asset, exist to help both investors and borrowers manage future risks, such as fluctuations in stock or commodity prices, interest rates, exchange rates, or non-financial events, such as weather.
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Investment - Introduction to Equity Securities
Companies may issue numerous types of equity securities. The types of equity instruments, or equity-like securities, that firms generally issue include common stock (sometimes called common shares or ordinary shares) and preferred stock (or preferred shares). Another sort of equity asset, depositary receipts, are not issued by a firm, but they provide the holder an equity interest in the company. Let’s review the features of equity securities.
Features of Equity Securities
Each sort of equity security has unique properties, as detailed in the table below. Most equity instruments are issued without a maturity date (infinite life), may or may not have a stated par value (or face value), come with cash flow rights, and come with voting rights if they are common shares.
Shareholders having voting rights collectively elect a group of persons, called the board of directors, whose role it is to supervise the company’s business activities on behalf of its shareholders because shareholders do not often engage in the day-to-day management decisions of major corporations.
The board of directors is responsible for appointing the company’s senior management (e.g., chief executive officer and chief operating officer), who handle the company’s day-to-day business operations. But choices of considerable importance, such as the decision to acquire another company, normally require the majority approval of shareholders with voting rights.
Features of Equity Securities
Life Most equity instruments are issued with an unlimited life, while some may be issued with a maturity date.
Par Value
Equity securities may or may not be issued with a par value, which is the security’s stated value, or face value.
Voting Rights
Some equity securities, such as common shares, allow their holders the power to vote on specific subjects.
Cash Flow Rights
Equity shares offer their holders the right to distributions, such as dividends, paid by the corporation. Preferred shares give an explicit annual dividend rate.
Equity securities come with cash flow rights – the right to receive payments, such as dividends, made by the corporation. In the case of the corporation being liquidated, assets are allocated following a priority of claims.
Common Stock
Common stock is the principal type of equity investment issued by firms. A common share signifies an ownership position in a firm. Common shares normally have an endless life; in other words, they are issued without maturity dates.
Common stock may or may not be issued with a par value. When common shares are issued with par values, firms generally set their par value extremely low, such as 1 penny per share in the United States. It is crucial to remember that the par value of a common share may have no connection to its market value, even at the time of issue. For instance, a common share having a par value of 1 cent may be issued to a shareholder for USD50.
Common shares comprise the biggest component of equity securities by market value. Large corporations often have numerous common owners, each of whom normally holds a very small part of the company’s total shares. Private corporations are often significantly smaller than public companies, and their shares typically do not trade on stock exchanges.
Investors may own common stock of public or private companies.
Shares of public corporations often trade on stock exchanges that facilitate trading of shares between buyers and sellers. The ability to sell common shares of public firms on stock exchanges affords shareholders the benefit of liquidity - the opportunity to trade when they want to trade and at a reasonable price.
Companies may pay out a portion of their profits each year to their shareholders as dividends; the rights to such payments are the shareholders’ cash flow rights. Dividends are normally issued by the board of directors and vary according to the company’s performance, its reinvestment needs, and the management’s attitude on paying dividends. As owners of the underlying corporation, common shareholders participate in the performance of the company and have a residual claim on the company’s liquidated assets after all liabilities (debts) and other claims with higher seniority have been paid.
In terms of voting rights, many corporations have a single class of common stock and follow the rule of ‘one share, one vote’. But some corporations may issue several classes of common stock that give varying cash flow and voting rights. In general, an arrangement in which a corporation sells two classes of common stock (e.g., Class A and Class B) typically provides one class of shareholders — generally the company’s founding members — with superior voting and/or cash flow rights.
The reason for having numerous share classes is frequently that the company’s original owner wants to keep control, as measured by voting power, while also offering cash flow rights to attract shareholders.
In financial markets, the firms issuing common shares are often categorized by two key company characteristics:
Firm size, as defined by market capitalization (total market value of the company’s common stock)
Investment style (value or growth)
With respect to size, corporations are often classed as either small-cap (market capitalisation under USD2 billion), mid-sized (market cap between USD2 billion and USD10 billion), or large-cap (market cap larger than USD10 billion). In terms of style, value stocks tend to be linked with older, established companies with predicted low growth in future revenues and earnings. In contrast, growth firms tend to be younger organizations with predicted stronger growth in future revenues and earnings.
Preferred Stock
Companies may also issue preferred stock (also known as preferred shares or preference shares). These shares are named preferred because owners of preferred stock get dividends before common stockholders. If the company ceases operations, they also have a larger claim on the company’s assets compared with common shareholders. In other words, preferred stockholders receive preferential treatment in some areas. But preferred shareholders are often not entitled to voting rights.
Preferred shares provide an annual set dividend to investors. The annual dividend amount is equal to the product of the stated dividend rate and the stated par value. The annual dividend is normally paid in two payments
(semiannually) or in four payments (quarterly). Unlike the par values for common stock that are often close to nothing, the par values of preferred shares are substantial sums because they are a determinant of the annual dividend payment.
The par value of a preferred share also often symbolizes the amount the shareholder would be entitled to receive after a liquidation, as long as there are sufficient assets to fulfill the claim.
Although the annual dividend rate is explicitly mentioned, there is no legal duty of the firm to pay it in a particular year. For example, the board of a corporation with bad performance in a particular year may chose not to pay preferred dividends. Preferred shares differ with respect to the policy on missed dividends, depending on whether the preferred stock is cumulative or non-cumulative. Cumulative preferred stock demands that the corporation pay in full any missed dividends to preferred owners before paying dividends to common shareholders. In comparison, non-cumulative preferred stock does not demand that missed dividends be paid before dividends are paid to common shareholders.
Preferred share conditions may provide the issuing firm with the opportunity to purchase back, or redeem, the preferred stock from shareholders at a pre-specified price, referred to as the redemption price. In general, the pre-specified redemption price is equal to the par value.
Some corporations have more than a single issue of preferred stock. Multiple preferred stock offerings are referred to by series. Each preferred stock series issued by a corporation normally carries its own yearly dividend rate, and they may differ with respect to other attributes as well.
Depositary Receipts
A depositary receipt is a security reflecting an economic stake in a foreign corporation, and trades like a common share on a local stock exchange.
For investors buying shares of foreign companies, the transaction costs involved with obtaining depositary receipts are much lower than the costs of directly purchasing the stock on a foreign country’s stock exchange. Depositary receipts are issued by financial institutions, not by the corporation, and do not raise money for the company.
A custodian financial institution located in the domestic country buys the shares in the foreign country, holds them in custody, issues depositary receipts against the shares held, and sells the depositary receipts to domestic investors who can trade them on the local stock exchange. Consequently, depositary receipts permit trading of a firm’s stock in nations other than the one where the company is listed. In essence, depository receipts make the process of investing in international corporations easier for local market investors.
Depositary receipts are typically referred to as global depositary receipts (GDRs) but may be designated by different names in different nations. In the United States, GDRs are known as American Depositary Receipts (ADRs) or American depositary shares.
The following are other properties of depositary receipts:
Generally similar globally but may vary somewhat because of differing legislation
Have no maturity date like the shares they are based on (i.e., they have an unlimited existence)
May or may not offer their owners any voting rights even if they effectively represent common stock ownership; in such situations, the custodian financial institution may maintain the voting rights linked with the shares
Companies may issue numerous types of equity securities. The types of equity instruments, or equity-like securities, that firms generally issue include common stock (sometimes called common shares or ordinary shares) and preferred stock (or preferred shares). Another sort of equity asset, depositary receipts, are not issued by a firm, but they provide the holder an equity interest in the company. Let’s review the features of equity securities.
Features of Equity Securities
Each sort of equity security has unique properties, as detailed in the table below. Most equity instruments are issued without a maturity date (infinite life), may or may not have a stated par value (or face value), come with cash flow rights, and come with voting rights if they are common shares.
Shareholders having voting rights collectively elect a group of persons, called the board of directors, whose role it is to supervise the company’s business activities on behalf of its shareholders because shareholders do not often engage in the day-to-day management decisions of major corporations.
The board of directors is responsible for appointing the company’s senior management (e.g., chief executive officer and chief operating officer), who handle the company’s day-to-day business operations. But choices of considerable importance, such as the decision to acquire another company, normally require the majority approval of shareholders with voting rights.
Features of Equity Securities
Life Most equity instruments are issued with an unlimited life, while some may be issued with a maturity date.
Par Value
Equity securities may or may not be issued with a par value, which is the security’s stated value, or face value.
Voting Rights
Some equity securities, such as common shares, allow their holders the power to vote on specific subjects.
Cash Flow Rights
Equity shares offer their holders the right to distributions, such as dividends, paid by the corporation. Preferred shares give an explicit annual dividend rate.
Equity securities come with cash flow rights – the right to receive payments, such as dividends, made by the corporation. In the case of the corporation being liquidated, assets are allocated following a priority of claims.
Common Stock
Common stock is the principal type of equity investment issued by firms. A common share signifies an ownership position in a firm. Common shares normally have an endless life; in other words, they are issued without maturity dates.
Common stock may or may not be issued with a par value. When common shares are issued with par values, firms generally set their par value extremely low, such as 1 penny per share in the United States. It is crucial to remember that the par value of a common share may have no connection to its market value, even at the time of issue. For instance, a common share having a par value of 1 cent may be issued to a shareholder for USD50.
Common shares comprise the biggest component of equity securities by market value. Large corporations often have numerous common owners, each of whom normally holds a very small part of the company’s total shares. Private corporations are often significantly smaller than public companies, and their shares typically do not trade on stock exchanges.
Investors may own common stock of public or private companies.
Shares of public corporations often trade on stock exchanges that facilitate trading of shares between buyers and sellers. The ability to sell common shares of public firms on stock exchanges affords shareholders the benefit of liquidity - the opportunity to trade when they want to trade and at a reasonable price.
Companies may pay out a portion of their profits each year to their shareholders as dividends; the rights to such payments are the shareholders’ cash flow rights. Dividends are normally issued by the board of directors and vary according to the company’s performance, its reinvestment needs, and the management’s attitude on paying dividends. As owners of the underlying corporation, common shareholders participate in the performance of the company and have a residual claim on the company’s liquidated assets after all liabilities (debts) and other claims with higher seniority have been paid.
In terms of voting rights, many corporations have a single class of common stock and follow the rule of ‘one share, one vote’. But some corporations may issue several classes of common stock that give varying cash flow and voting rights. In general, an arrangement in which a corporation sells two classes of common stock (e.g., Class A and Class B) typically provides one class of shareholders — generally the company’s founding members — with superior voting and/or cash flow rights.
The reason for having numerous share classes is frequently that the company’s original owner wants to keep control, as measured by voting power, while also offering cash flow rights to attract shareholders.
In financial markets, the firms issuing common shares are often categorized by two key company characteristics:
Firm size, as defined by market capitalization (total market value of the company’s common stock)
Investment style (value or growth)
With respect to size, corporations are often classed as either small-cap (market capitalisation under USD2 billion), mid-sized (market cap between USD2 billion and USD10 billion), or large-cap (market cap larger than USD10 billion). In terms of style, value stocks tend to be linked with older, established companies with predicted low growth in future revenues and earnings. In contrast, growth firms tend to be younger organizations with predicted stronger growth in future revenues and earnings.
Preferred Stock
Companies may also issue preferred stock (also known as preferred shares or preference shares). These shares are named preferred because owners of preferred stock get dividends before common stockholders. If the company ceases operations, they also have a larger claim on the company’s assets compared with common shareholders. In other words, preferred stockholders receive preferential treatment in some areas. But preferred shareholders are often not entitled to voting rights.
Preferred shares provide an annual set dividend to investors. The annual dividend amount is equal to the product of the stated dividend rate and the stated par value. The annual dividend is normally paid in two payments
(semiannually) or in four payments (quarterly). Unlike the par values for common stock that are often close to nothing, the par values of preferred shares are substantial sums because they are a determinant of the annual dividend payment.
The par value of a preferred share also often symbolizes the amount the shareholder would be entitled to receive after a liquidation, as long as there are sufficient assets to fulfill the claim.
Although the annual dividend rate is explicitly mentioned, there is no legal duty of the firm to pay it in a particular year. For example, the board of a corporation with bad performance in a particular year may chose not to pay preferred dividends. Preferred shares differ with respect to the policy on missed dividends, depending on whether the preferred stock is cumulative or non-cumulative. Cumulative preferred stock demands that the corporation pay in full any missed dividends to preferred owners before paying dividends to common shareholders. In comparison, non-cumulative preferred stock does not demand that missed dividends be paid before dividends are paid to common shareholders.
Preferred share conditions may provide the issuing firm with the opportunity to purchase back, or redeem, the preferred stock from shareholders at a pre-specified price, referred to as the redemption price. In general, the pre-specified redemption price is equal to the par value.
Some corporations have more than a single issue of preferred stock. Multiple preferred stock offerings are referred to by series. Each preferred stock series issued by a corporation normally carries its own yearly dividend rate, and they may differ with respect to other attributes as well.
Depositary Receipts
A depositary receipt is a security reflecting an economic stake in a foreign corporation, and trades like a common share on a local stock exchange.
For investors buying shares of foreign companies, the transaction costs involved with obtaining depositary receipts are much lower than the costs of directly purchasing the stock on a foreign country’s stock exchange. Depositary receipts are issued by financial institutions, not by the corporation, and do not raise money for the company.
A custodian financial institution located in the domestic country buys the shares in the foreign country, holds them in custody, issues depositary receipts against the shares held, and sells the depositary receipts to domestic investors who can trade them on the local stock exchange. Consequently, depositary receipts permit trading of a firm’s stock in nations other than the one where the company is listed. In essence, depository receipts make the process of investing in international corporations easier for local market investors.
Depositary receipts are typically referred to as global depositary receipts (GDRs) but may be designated by different names in different nations. In the United States, GDRs are known as American Depositary Receipts (ADRs) or American depositary shares.
The following are other properties of depositary receipts:
Generally similar globally but may vary somewhat because of differing legislation
Have no maturity date like the shares they are based on (i.e., they have an unlimited existence)
May or may not offer their owners any voting rights even if they effectively represent common stock ownership; in such situations, the custodian financial institution may maintain the voting rights linked with the shares
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Investment - Valuation of Common Shares
Valuing common shares is a hard process because of their endless life and the difficulties of projecting future corporate success.
There are three fundamental ways to evaluating common shares:
Discounted cash flow valuation
Relative valuation
Asset-based valuation
Analysts usually utilize more than one approach to evaluate the value of a common share. Once an estimate of value has been calculated, it can be compared with the current price of the share, provided that the share is publicly traded, to determine if the share is overvalued, undervalued, or appropriately valued. This formula is utilized when investors decide to buy or sell a share.
Discounted Cash Flow Valuation
The example below illustrates the use of the discounted cash flow (DCF) approach, utilizing projections of dividends and a future selling price, for a common share of Vodafone. In summary, the DCF valuation approach estimates the value of a security as the present value of all future cash flows that the investor anticipates to receive from the security.
Common shareholders anticipate to earn two forms of cash flows from investing in equity securities: dividends and the revenues from selling their shares at a later period. The DCF valuation approach applied to common shares focuses on a consideration of the characteristics of the company issuing the shares, such as the company’s ability to create earnings, the expected growth rate of earnings, and the level of risk associated with the company’s business environment.
Example: Discounted Cash Flow Approach
Consider an investor calculating the value of Vodafone shares.
The investor anticipates Vodafone to generate annual dividends of 8.00, 8.50, and 9.00 pence per share over the next three years, respectively. Furthermore, the investor expects that the stock price of Vodafone will trade at 150.00 pence per share at the end of three years.
Note that, using the DCF valuation approach, the estimated selling price of Vodafone stock of 150.00 pence per share in three years indicates the present value of cash flows to investors expected to be generated by the company beyond the three years.
The investor evaluates all risks and believes that a discount rate of 8% is fair. In other words, the investor intends to earn at least an annual rate of return of 8% by investing in Vodafone.
Valuing common shares is a hard process because of their endless life and the difficulties of projecting future corporate success.
There are three fundamental ways to evaluating common shares:
Discounted cash flow valuation
Relative valuation
Asset-based valuation
Analysts usually utilize more than one approach to evaluate the value of a common share. Once an estimate of value has been calculated, it can be compared with the current price of the share, provided that the share is publicly traded, to determine if the share is overvalued, undervalued, or appropriately valued. This formula is utilized when investors decide to buy or sell a share.
Discounted Cash Flow Valuation
The example below illustrates the use of the discounted cash flow (DCF) approach, utilizing projections of dividends and a future selling price, for a common share of Vodafone. In summary, the DCF valuation approach estimates the value of a security as the present value of all future cash flows that the investor anticipates to receive from the security.
Common shareholders anticipate to earn two forms of cash flows from investing in equity securities: dividends and the revenues from selling their shares at a later period. The DCF valuation approach applied to common shares focuses on a consideration of the characteristics of the company issuing the shares, such as the company’s ability to create earnings, the expected growth rate of earnings, and the level of risk associated with the company’s business environment.
Example: Discounted Cash Flow Approach
Consider an investor calculating the value of Vodafone shares.
The investor anticipates Vodafone to generate annual dividends of 8.00, 8.50, and 9.00 pence per share over the next three years, respectively. Furthermore, the investor expects that the stock price of Vodafone will trade at 150.00 pence per share at the end of three years.
Note that, using the DCF valuation approach, the estimated selling price of Vodafone stock of 150.00 pence per share in three years indicates the present value of cash flows to investors expected to be generated by the company beyond the three years.
The investor evaluates all risks and believes that a discount rate of 8% is fair. In other words, the investor intends to earn at least an annual rate of return of 8% by investing in Vodafone.
The estimated value of a Vodafone share using the DCF valuation approach is equal to the present value of the cash flows the investor expects to receive from the equity investment. The investor computes the current value of the expected cash flows as follows:
So, the investor’s projected worth of Vodafone on a per-share basis is 140.91 pence.
If shares of Vodafone are currently priced at less than 140.91 pence, the investor may assume that the stock is undervalued and opt to buy it.
Alternatively, if the stock is priced at more than 140.91 pence, the investor may infer that the stock is overvalued and opt not to buy.
In other instances, such as when a firm is considering buying another company, a company’s worth can also be assessed using the DCF approach as the present value of predicted future free cash flows. The DCF approach can also be used to value preferred shares. Valuing preferred shares is often easier than for common shares because the expected dividends are fixed and do not alter over time.
Relative Valuation
The relative valuation approach assesses the value of a common share as the multiple of some measure, such as earnings per share (EPS) or sales per share. The multiple is derived based on price and the appropriate measure for publicly traded, comparable equity securities. The main premise of the relative valuation approach is that common shares of companies with similar risk and return characteristics should have similar values.
Relative valuation relies on the utilization of price multiples of comparable, publicly traded companies or an industry average. The relative valuation approach implicitly argues that common shares of companies with similar risk and return characteristics should have similar price multiples.
One multiple widely employed in relative valuation is the price-to-earnings ratio (P/E), which is the ratio of a company’s stock price to its EPS. For instance, a publicly traded firm that earns annual earnings per share of USD1.00 and is trading at USD12 per share has a P/E (or price-to-earnings multiple) of 12. The following example explains the relative valuing approach.
Example: Relative Valuation
An investor is calculating the value of an airline’s common shares on a per-share basis. The airline in question generates annual EPS of EUR2.00.
The investor sees that the average price-to-earnings multiple or P/E for the industry is 9. Using relative valuation, the investor estimates the value of the airline’s stock on a per-share basis to be EUR18.00 (= €2.00 × 9).
One concern with the use of the relative valuation approach is that price multiples alter with investor mood. Companies trade at greater price multiples when investors are hopeful and at lower price multiples when investors are pessimistic.
Asset-Based Valuation
The asset-based valuation approach determines the value of common stock by evaluating the company’s net asset value, which is equal to the difference between the market value of a company’s total assets and its outstanding liabilities. In other words, the asset-based valuation approach evaluates the value of common shares by determining a company’s net asset value. The asset-based valuation approach implicitly implies that the company is dissolved, sells all its assets, and then pays off all its creditors. The residual value after paying off all liabilities is the value to the shareholders.
The difference between total assets and total liabilities on a company’s balance sheet indicates shareholders’ equity, or the book value of equity. But the values of some assets on the balance sheet are based on historical cost (the cost when they were obtained), and the real market values of these assets may be significantly different. For instance, the value of land on a company’s balance sheet, normally carried at historical cost, may be considerably different from its current market value. As a result, assessing the worth of the equity of a corporation using asset values derived directly from the balance sheet may yield a false estimate. To improve the accuracy of the value estimation, current market values can be estimated instead.
Also, some assets may not be reported on the balance sheet due of financial reporting restrictions. For instance, some internally produced intangible assets, such as a brand or reputation, may not be reported in financial reports. It is crucial that analysts utilizing asset-based valuation estimate fair values for all of a company’s assets, which can be tough to achieve.
In the following task, categorize each object into the correct category.
So, the investor’s projected worth of Vodafone on a per-share basis is 140.91 pence.
If shares of Vodafone are currently priced at less than 140.91 pence, the investor may assume that the stock is undervalued and opt to buy it.
Alternatively, if the stock is priced at more than 140.91 pence, the investor may infer that the stock is overvalued and opt not to buy.
In other instances, such as when a firm is considering buying another company, a company’s worth can also be assessed using the DCF approach as the present value of predicted future free cash flows. The DCF approach can also be used to value preferred shares. Valuing preferred shares is often easier than for common shares because the expected dividends are fixed and do not alter over time.
Relative Valuation
The relative valuation approach assesses the value of a common share as the multiple of some measure, such as earnings per share (EPS) or sales per share. The multiple is derived based on price and the appropriate measure for publicly traded, comparable equity securities. The main premise of the relative valuation approach is that common shares of companies with similar risk and return characteristics should have similar values.
Relative valuation relies on the utilization of price multiples of comparable, publicly traded companies or an industry average. The relative valuation approach implicitly argues that common shares of companies with similar risk and return characteristics should have similar price multiples.
One multiple widely employed in relative valuation is the price-to-earnings ratio (P/E), which is the ratio of a company’s stock price to its EPS. For instance, a publicly traded firm that earns annual earnings per share of USD1.00 and is trading at USD12 per share has a P/E (or price-to-earnings multiple) of 12. The following example explains the relative valuing approach.
Example: Relative Valuation
An investor is calculating the value of an airline’s common shares on a per-share basis. The airline in question generates annual EPS of EUR2.00.
The investor sees that the average price-to-earnings multiple or P/E for the industry is 9. Using relative valuation, the investor estimates the value of the airline’s stock on a per-share basis to be EUR18.00 (= €2.00 × 9).
One concern with the use of the relative valuation approach is that price multiples alter with investor mood. Companies trade at greater price multiples when investors are hopeful and at lower price multiples when investors are pessimistic.
Asset-Based Valuation
The asset-based valuation approach determines the value of common stock by evaluating the company’s net asset value, which is equal to the difference between the market value of a company’s total assets and its outstanding liabilities. In other words, the asset-based valuation approach evaluates the value of common shares by determining a company’s net asset value. The asset-based valuation approach implicitly implies that the company is dissolved, sells all its assets, and then pays off all its creditors. The residual value after paying off all liabilities is the value to the shareholders.
The difference between total assets and total liabilities on a company’s balance sheet indicates shareholders’ equity, or the book value of equity. But the values of some assets on the balance sheet are based on historical cost (the cost when they were obtained), and the real market values of these assets may be significantly different. For instance, the value of land on a company’s balance sheet, normally carried at historical cost, may be considerably different from its current market value. As a result, assessing the worth of the equity of a corporation using asset values derived directly from the balance sheet may yield a false estimate. To improve the accuracy of the value estimation, current market values can be estimated instead.
Also, some assets may not be reported on the balance sheet due of financial reporting restrictions. For instance, some internally produced intangible assets, such as a brand or reputation, may not be reported in financial reports. It is crucial that analysts utilizing asset-based valuation estimate fair values for all of a company’s assets, which can be tough to achieve.
In the following task, categorize each object into the correct category.
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Investment - Risks of Investing in Equity Securities
There are two primary hazards inherent with equities investing:
Specific risk, also referred to as unsystematic risk
Market risk, commonly referred to as systematic risk
Specific risk (unsystematic risk) refers to the risk that a specific firm may have bad performance owing to a number of variables (e.g., increasing competition, operational issues, higher regulatory supervision), resulting in its equity shares falling in value.
In the case of preferred shares, the risk of loss is missing dividend payments that may not be made by the corporation. In the case of common stock, the risk of loss is high because common shareholders are the last in line to receive cash flows after creditors (which are described in the following module) and preferred shareholders.
The second important risk inherent in equities investing is general market risk, or systematic risk. Market risk is the risk of loss from stock shares dropping in value due to reasons external to the company, such as adverse changes in macroeconomic conditions (e.g., recessionary periods or high inflationary periods).
Investors can generally eliminate company-specific risk by diversification – holding portfolios of diverse stocks whose stock price movements display minimal (or negative) correlation.
Of course, certain equities are perceived riskier than others, as reflected in their larger stock price volatility. In financial markets, a stock’s amount of systematic risk is assessed by beta. Beta is a measure of the stock price volatility of a particular stock relative to the price volatility of the market as a whole.
Beta of 1.0 implies that the stock’s price tends to move in accordance with the general market. Stocks with betas larger than 1.0 are judged riskier (and those with less than 1.0 are deemed safer) than the average stock in the market — that is, in terms of their price volatility compared to the market’s volatility.
1.0 Stock’s price moves in accordance with the entire market; considered an average-risk equity security. >1.0 Stock’s price fluctuations are more volatile than the general market; considered an above average-risk equity security. <1.0 Stock’s price movements are less volatile than the overall market; considered a below average-risk equity security.
Return Expectations Models
To construct their return expectations, equity investors, particularly prospective buyers of preferred shares, will typically analyze a company’s dividend yield. A preferred or common stock’s dividend yield is the estimated annual dividend to be paid over the following year divided by the price. A stock’s dividend yield provides potential owners with an estimate of the annualised return from dividend income solely, without consideration for the effect of any capital gain or loss resulting from changes in the stock’s price over time.
Another approach used by equity investors to determine a stock’s expected annualised return is based on the capital asset pricing model (CAPM), which asserts that a stock’s expected return equals the sum of the risk-free interest rate plus the product of the stock’s beta and the equity risk premium (ERP):
CAPM: E(ri) = rf + βi(ERP)
The equity (market) risk premium is the extra annual return that an equity investor anticipates to earn above a risk-free asset on an average-risk equities investment. It is generally evaluated using historical data on the difference in average returns between a broad equity index and the risk-free asset.
So, if a particular stock is considered riskier than the average stock as measured by beta, it will have a beta greater than 1.0 and investors should expect to earn a higher risk premium compared to the risk-free asset (and if safer, it will have a beta of less than 1.0 and earn a lower risk premium).
For example, say that the current risk-free rate is 2.0% and the market risk premium has been calculated to be 6.0%.
Consider two stocks, one with a beta of 0.75 and another with a beta of 1.50.
An investor employing the CAPM to predict expected returns for the two equities would estimate them to be 6.5% (= 2% + 0.75 x 6%) and 11% (= 2% + 1.50 x 6%), respectively.
In conclusion, the risk–return profile of owning preferred shares is very different from the profile of owning common shares.
Owners of preferred shares know in advance the expected return they will receive each year from income because the annual dividend amount is explicitly known. Although it is certainly possible that the dividend may not be paid during years of poor company performance and missed dividends may not ever be received in the case of non-cumulative preferred stock, it is also the case that the annual dividend payment does not increase during years of good company performance.
Consequently, the prices of preferred shares do not display as much volatility as common share prices because the predicted dividend amount does not vary with corporate performance. Some investors are attracted to this set return and the generally low-volatility investment profile of preferred shares.
In contrast, common stockholders are not assured any set dividend amount each year. In periods of good company performance, the common share price is likely to climb due to increasing earnings and dividends, and vice versa for poor company performance. Relative to preferred shares, the upside price potential for common stockholders can be much higher, but the downside price potential can also be significantly lower. Some investors are attracted to the significant upside potential given by common shares, even with the increased possibility for loss.
There are two primary hazards inherent with equities investing:
Specific risk, also referred to as unsystematic risk
Market risk, commonly referred to as systematic risk
Specific risk (unsystematic risk) refers to the risk that a specific firm may have bad performance owing to a number of variables (e.g., increasing competition, operational issues, higher regulatory supervision), resulting in its equity shares falling in value.
In the case of preferred shares, the risk of loss is missing dividend payments that may not be made by the corporation. In the case of common stock, the risk of loss is high because common shareholders are the last in line to receive cash flows after creditors (which are described in the following module) and preferred shareholders.
The second important risk inherent in equities investing is general market risk, or systematic risk. Market risk is the risk of loss from stock shares dropping in value due to reasons external to the company, such as adverse changes in macroeconomic conditions (e.g., recessionary periods or high inflationary periods).
Investors can generally eliminate company-specific risk by diversification – holding portfolios of diverse stocks whose stock price movements display minimal (or negative) correlation.
Of course, certain equities are perceived riskier than others, as reflected in their larger stock price volatility. In financial markets, a stock’s amount of systematic risk is assessed by beta. Beta is a measure of the stock price volatility of a particular stock relative to the price volatility of the market as a whole.
Beta of 1.0 implies that the stock’s price tends to move in accordance with the general market. Stocks with betas larger than 1.0 are judged riskier (and those with less than 1.0 are deemed safer) than the average stock in the market — that is, in terms of their price volatility compared to the market’s volatility.
1.0 Stock’s price moves in accordance with the entire market; considered an average-risk equity security. >1.0 Stock’s price fluctuations are more volatile than the general market; considered an above average-risk equity security. <1.0 Stock’s price movements are less volatile than the overall market; considered a below average-risk equity security.
Return Expectations Models
To construct their return expectations, equity investors, particularly prospective buyers of preferred shares, will typically analyze a company’s dividend yield. A preferred or common stock’s dividend yield is the estimated annual dividend to be paid over the following year divided by the price. A stock’s dividend yield provides potential owners with an estimate of the annualised return from dividend income solely, without consideration for the effect of any capital gain or loss resulting from changes in the stock’s price over time.
Another approach used by equity investors to determine a stock’s expected annualised return is based on the capital asset pricing model (CAPM), which asserts that a stock’s expected return equals the sum of the risk-free interest rate plus the product of the stock’s beta and the equity risk premium (ERP):
CAPM: E(ri) = rf + βi(ERP)
The equity (market) risk premium is the extra annual return that an equity investor anticipates to earn above a risk-free asset on an average-risk equities investment. It is generally evaluated using historical data on the difference in average returns between a broad equity index and the risk-free asset.
So, if a particular stock is considered riskier than the average stock as measured by beta, it will have a beta greater than 1.0 and investors should expect to earn a higher risk premium compared to the risk-free asset (and if safer, it will have a beta of less than 1.0 and earn a lower risk premium).
For example, say that the current risk-free rate is 2.0% and the market risk premium has been calculated to be 6.0%.
Consider two stocks, one with a beta of 0.75 and another with a beta of 1.50.
An investor employing the CAPM to predict expected returns for the two equities would estimate them to be 6.5% (= 2% + 0.75 x 6%) and 11% (= 2% + 1.50 x 6%), respectively.
In conclusion, the risk–return profile of owning preferred shares is very different from the profile of owning common shares.
Owners of preferred shares know in advance the expected return they will receive each year from income because the annual dividend amount is explicitly known. Although it is certainly possible that the dividend may not be paid during years of poor company performance and missed dividends may not ever be received in the case of non-cumulative preferred stock, it is also the case that the annual dividend payment does not increase during years of good company performance.
Consequently, the prices of preferred shares do not display as much volatility as common share prices because the predicted dividend amount does not vary with corporate performance. Some investors are attracted to this set return and the generally low-volatility investment profile of preferred shares.
In contrast, common stockholders are not assured any set dividend amount each year. In periods of good company performance, the common share price is likely to climb due to increasing earnings and dividends, and vice versa for poor company performance. Relative to preferred shares, the upside price potential for common stockholders can be much higher, but the downside price potential can also be significantly lower. Some investors are attracted to the significant upside potential given by common shares, even with the increased possibility for loss.
- Published on
Investment - Company Actions That Affect Equity Outstanding
Companies undertake big changes as they expand, evolve, mature, or merge with another company. Some of these adjustments result in changes to the number of common shares outstanding — that is, the number of common shares currently held by shareholders. The following table outlines several business acts that can alter equity outstanding. Each of the activities and their effects are detailed in the following sections.
Company Actions That Affect Equity Outstanding
Initial Public Offering (IPO)-Company sells shares to public investors for the first time (private company becomes a public company).
Seasoned Equity Offering (SEO) -Selling shares to the public after the IPO in a secondary (or seasoned) offering.
Share repurchase - Company buys back existing shares from shareholders.
Stock dividend or stock split - Company issues new shares to current shareholders without getting any money in exchange.
Spinoff = firm forms a new firm by spinning off some existing company assets.
Initial Public Offering
The major distinction between a private company and a publicly listed firm is that the shares of a private company are available only to chosen investors and are not exchanged on a public exchange. A private firm becomes a publicly listed company through an initial public offering (IPO), which is the first time that it offers new shares to investors in a public market.
Private corporations become publicly traded companies for a number of reasons. First, it provides the company more visibility, which makes it easier to raise cash to fund expansion prospects. It also helps attract talented people, build brand awareness, and gain credibility with trading partners. In addition, it provides better liquidity for stockholders who want to sell their shares or buy additional shares. At or after the IPO, some of the initial shareholders may choose to sell some of their shares. The fact that the shares now trade in a public market makes the shares more liquid and hence easier to sell.
A downside of becoming a public business is additional regulatory and transparency responsibilities.
Seasoned Equity Offering
After an IPO, publicly listed corporations may sell further shares to raise more funds for expansion. The selling of new shares by a publicly traded firm after an IPO is referred to as a seasoned or secondary equity offering. A typical seasoned equity offering raises the number of shares outstanding by 5%–20%. For a current investor who does not buy additional shares in the seasoned stock offering, the increase in shares outstanding dilutes their ownership percentage.
Another reason why a corporation may issue new shares is to fund a purchase of another company. For larger purchases, the acquiring business may pay for the transaction by issuing new shares. The amount of new shares issued depends on the purchase price and the ratio of the two companies’ stock values. An acquisition in which the firm utilizes its stock to finance the transaction results in an increase in the acquiring company’s shares outstanding. For current shareholders in the acquiring company, the extra shares outstanding effectively dilutes their ownership proportion.
Share Repurchases
Companies may choose to return funds to shareholders by repurchasing shares rather than paying dividends. The share repurchase will boost the company’s earnings per share since net income will be split by a reduced number of shares following the repurchase. Repurchased shares are either cancelled or maintained and reported as treasury stock in the shareholders’ equity account on the company’s balance sheet. Treasury shares are not included in the number of shares outstanding.
To buy back shares, a firm can buy shares on the open market just like other investors or it can issue a formal offer to buyback directly to shareholders. Shareholders may opt to sell their shares or to remain involved in the company. For an existing investor who does not sell shares, the drop in the number of shares outstanding effectively raises that person’s ownership percentage.
Stock Splits and Stock Dividends
Companies may, on occasion, execute stock splits or give stock dividends.
A stock split is when a corporation exchanges one existing common share with a specific number of common shares.
A stock dividend is a dividend in which a firm distributes more shares to its common shareholders.
Stock splits and stock dividends both increase the number of shares outstanding, but they do not modify any single shareholder’s proportion of ownership.
When a corporation splits its stock or issues a stock dividend, the number of shares outstanding grows, and more shares are issued equally to existing shareholders depending on their present ownership percentages. Because no new money is received for the new shares, the overall worth of the company should not change. So, the price of each share will decline. But the value of any single shareholder’s total shares should not alter.
Example: Effects of a Stock Split and a Stock Dividend
Consider an investor who owns 900 shares of a business with 24,000 shares outstanding and a current share price of EUR75.00.
Stock Split
Suppose the company announces a three-for-two stock split, which means for every two shares the investor now has, they would receive three shares in replacement. So, the investor with 900 shares will get 1,350 shares after the stock split.
(900/2) x 3 = 1,350 shares
Stock Dividend
Suppose instead the firm declares a 50% stock dividend – that is, for every share investors already own, they will receive an additional 0.5 shares. In other words, the investor with 900 shares will have 1,350 shares after the stock dividend.
900 × 1.5 = 1,350 shares
A stock split or stock dividend does not modify each shareholder’s proportional ownership of the company. Shareholders do not invest any additional money for the increased number of shares, and the stock split or stock dividend does not have any influence on the company’s activities. The overall value of the company’s shares and an investor’s shares are unchanged by the stock split or stock dividend.
Given that stock splits and stock dividends do not have any influence on company operations or value, why do you think companies take these actions? One rationale is that as a firm works well and its assets and income increase, the stock price is likely to climb. At some point, the stock price may reach so high that shares become unaffordable to some investors and liquidity reduces. A stock split or stock dividend will have the effect of lowering a company’s stock price, making the shares more affordable to a larger group of investors, so enhancing liquidity.
It is vital to remember that the affordability of a company’s shares is distinct from whether the stock is undervalued or overvalued. A corporation with a stock price of USD500 per share may be unaffordable to some investors but may still be considered undervalued when the price per share is compared with the projected value per share. Similarly, a company with a stock price of USD5 per share may be accessible to most investors yet still be overvalued.
Companies with very low stock values may undertake a reverse stock split to boost their stock price. In this situation, the corporation reduces the number of shares outstanding. The fundamental reason for a reverse stock split is because a firm may face the possibility of having its shares delisted from a public exchange if its stock price falls below a certain threshold stipulated by the exchange.
After the reverse stock split, stockholders will still possess the same proportion of the shares they initially had. In other words, a reverse stock split reduces the number of shares outstanding but, again, does not impact a shareholder’s proportional ownership of the company. After a reverse stock split, the stock price should increase by the same multiple as the reverse stock split. The following example describes a 1-for-8 reverse stock split by General Electric.
Spinoffs A company may create a new company from an existing subsidiary or package of existing assets in a procedure referred to as a spinoff.
Shares of the new entity are dispersed to the parent company’s existing shareholders. After the spinoff, the value of the shares of the parent firm initially drops since the assets of the parent company are reduced by the amount assigned to the new company. But stockholders receive the shares of the newly established firm to compensate them for the fall in value.
For the parent business’s current shareholders, the total value of the shares of both companies should approximately equal the pre-spinoff value of the shares in the parent company. The logic for a spinoff is that the market may provide a better worth to two distinct, but more specialised, companies compared with the value allocated to these entities while they were part of the parent company.
Companies undertake big changes as they expand, evolve, mature, or merge with another company. Some of these adjustments result in changes to the number of common shares outstanding — that is, the number of common shares currently held by shareholders. The following table outlines several business acts that can alter equity outstanding. Each of the activities and their effects are detailed in the following sections.
Company Actions That Affect Equity Outstanding
Initial Public Offering (IPO)-Company sells shares to public investors for the first time (private company becomes a public company).
Seasoned Equity Offering (SEO) -Selling shares to the public after the IPO in a secondary (or seasoned) offering.
Share repurchase - Company buys back existing shares from shareholders.
Stock dividend or stock split - Company issues new shares to current shareholders without getting any money in exchange.
Spinoff = firm forms a new firm by spinning off some existing company assets.
Initial Public Offering
The major distinction between a private company and a publicly listed firm is that the shares of a private company are available only to chosen investors and are not exchanged on a public exchange. A private firm becomes a publicly listed company through an initial public offering (IPO), which is the first time that it offers new shares to investors in a public market.
Private corporations become publicly traded companies for a number of reasons. First, it provides the company more visibility, which makes it easier to raise cash to fund expansion prospects. It also helps attract talented people, build brand awareness, and gain credibility with trading partners. In addition, it provides better liquidity for stockholders who want to sell their shares or buy additional shares. At or after the IPO, some of the initial shareholders may choose to sell some of their shares. The fact that the shares now trade in a public market makes the shares more liquid and hence easier to sell.
A downside of becoming a public business is additional regulatory and transparency responsibilities.
Seasoned Equity Offering
After an IPO, publicly listed corporations may sell further shares to raise more funds for expansion. The selling of new shares by a publicly traded firm after an IPO is referred to as a seasoned or secondary equity offering. A typical seasoned equity offering raises the number of shares outstanding by 5%–20%. For a current investor who does not buy additional shares in the seasoned stock offering, the increase in shares outstanding dilutes their ownership percentage.
Another reason why a corporation may issue new shares is to fund a purchase of another company. For larger purchases, the acquiring business may pay for the transaction by issuing new shares. The amount of new shares issued depends on the purchase price and the ratio of the two companies’ stock values. An acquisition in which the firm utilizes its stock to finance the transaction results in an increase in the acquiring company’s shares outstanding. For current shareholders in the acquiring company, the extra shares outstanding effectively dilutes their ownership proportion.
Share Repurchases
Companies may choose to return funds to shareholders by repurchasing shares rather than paying dividends. The share repurchase will boost the company’s earnings per share since net income will be split by a reduced number of shares following the repurchase. Repurchased shares are either cancelled or maintained and reported as treasury stock in the shareholders’ equity account on the company’s balance sheet. Treasury shares are not included in the number of shares outstanding.
To buy back shares, a firm can buy shares on the open market just like other investors or it can issue a formal offer to buyback directly to shareholders. Shareholders may opt to sell their shares or to remain involved in the company. For an existing investor who does not sell shares, the drop in the number of shares outstanding effectively raises that person’s ownership percentage.
Stock Splits and Stock Dividends
Companies may, on occasion, execute stock splits or give stock dividends.
A stock split is when a corporation exchanges one existing common share with a specific number of common shares.
A stock dividend is a dividend in which a firm distributes more shares to its common shareholders.
Stock splits and stock dividends both increase the number of shares outstanding, but they do not modify any single shareholder’s proportion of ownership.
When a corporation splits its stock or issues a stock dividend, the number of shares outstanding grows, and more shares are issued equally to existing shareholders depending on their present ownership percentages. Because no new money is received for the new shares, the overall worth of the company should not change. So, the price of each share will decline. But the value of any single shareholder’s total shares should not alter.
Example: Effects of a Stock Split and a Stock Dividend
Consider an investor who owns 900 shares of a business with 24,000 shares outstanding and a current share price of EUR75.00.
Stock Split
Suppose the company announces a three-for-two stock split, which means for every two shares the investor now has, they would receive three shares in replacement. So, the investor with 900 shares will get 1,350 shares after the stock split.
(900/2) x 3 = 1,350 shares
Stock Dividend
Suppose instead the firm declares a 50% stock dividend – that is, for every share investors already own, they will receive an additional 0.5 shares. In other words, the investor with 900 shares will have 1,350 shares after the stock dividend.
900 × 1.5 = 1,350 shares
A stock split or stock dividend does not modify each shareholder’s proportional ownership of the company. Shareholders do not invest any additional money for the increased number of shares, and the stock split or stock dividend does not have any influence on the company’s activities. The overall value of the company’s shares and an investor’s shares are unchanged by the stock split or stock dividend.
Given that stock splits and stock dividends do not have any influence on company operations or value, why do you think companies take these actions? One rationale is that as a firm works well and its assets and income increase, the stock price is likely to climb. At some point, the stock price may reach so high that shares become unaffordable to some investors and liquidity reduces. A stock split or stock dividend will have the effect of lowering a company’s stock price, making the shares more affordable to a larger group of investors, so enhancing liquidity.
It is vital to remember that the affordability of a company’s shares is distinct from whether the stock is undervalued or overvalued. A corporation with a stock price of USD500 per share may be unaffordable to some investors but may still be considered undervalued when the price per share is compared with the projected value per share. Similarly, a company with a stock price of USD5 per share may be accessible to most investors yet still be overvalued.
Companies with very low stock values may undertake a reverse stock split to boost their stock price. In this situation, the corporation reduces the number of shares outstanding. The fundamental reason for a reverse stock split is because a firm may face the possibility of having its shares delisted from a public exchange if its stock price falls below a certain threshold stipulated by the exchange.
After the reverse stock split, stockholders will still possess the same proportion of the shares they initially had. In other words, a reverse stock split reduces the number of shares outstanding but, again, does not impact a shareholder’s proportional ownership of the company. After a reverse stock split, the stock price should increase by the same multiple as the reverse stock split. The following example describes a 1-for-8 reverse stock split by General Electric.
Spinoffs A company may create a new company from an existing subsidiary or package of existing assets in a procedure referred to as a spinoff.
Shares of the new entity are dispersed to the parent company’s existing shareholders. After the spinoff, the value of the shares of the parent firm initially drops since the assets of the parent company are reduced by the amount assigned to the new company. But stockholders receive the shares of the newly established firm to compensate them for the fall in value.
For the parent business’s current shareholders, the total value of the shares of both companies should approximately equal the pre-spinoff value of the shares in the parent company. The logic for a spinoff is that the market may provide a better worth to two distinct, but more specialised, companies compared with the value allocated to these entities while they were part of the parent company.