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CAGR
Compound annual growth rate (CAGR) is a business, economics and investing term representing the mean annualized growth rate for compounding values over a given time period. CAGR smoothes the effect of volatility of periodic values that can render arithmetic means less meaningful. It is particularly useful to compare growth rates of various data values, such as revenue growth of companies, or of economic values, over time. Equation For annual values, CAGR is defined as: :\mathrm(t_0,t_n) = \left( \frac \right)^\frac - 1 where V(t_0) is the initial value, V(t_n) is the end value, and t_n - t_0 is the number of years. CAGR can also be used to calculate mean annualized growth rates on quarterly or monthly values. The numerator of the exponent would be the value of 4 in the case of quarterly, and 12 in the case of monthly, with the denominator being the number of corresponding periods involved. In practice, CAGR calculations are often performed in Microsoft Excel. A convenient ...
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Volatility (finance)
In finance, volatility (usually denoted by "sigma, σ") is the Variability (statistics), degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Volatility terminology Volatility as described here refers to the actual volatility, more specifically: * actual current volatility of a financial instrument for a specified period (for example 30 days or 90 days), based on historical prices over the specified period with the last observation the most recent price. * actual historical volatility which refers to the volatility of a financial instrument over a specified period but with the last observation on a date in the past **near synonymous is realized volatility, the square root of the realized variance, in turn c ...
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Annual Growth %
Annual growth rate (AGR) is the change in the value of a measurement over the period of a year. Economics Annual growth rate is a useful tool to identify trends in investments. According to a survey of nearly 200 senior marketing managers conducted by The Marketing Accountability Standards Board, 69% of subjects responded that they consider average annual growth rate to be a useful measurement.Farris, Paul W.; Neil T. Bendle; Phillip E. Pfeifer; David J. Reibstein (2010). ''Marketing Metrics: The Definitive Guide to Measuring Marketing Performance.'' Upper Saddle River, New Jersey: Pearson Education, Inc. . The Marketing Accountability Standards Board (MASB) The Marketing Accountability Standards Board (MASB), authorized by the Marketing Accountability Foundation (MAF),MASB''Marketing Accountability Foundation (MAF)''. ited 8 December 2010is an independent, private sector, self-governing organizat ... endorses the definitions, purposes, and constructs of classes of measures th ...
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Geometric Mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean of numbers is the Nth root, th root of their product (mathematics), product, i.e., for a collection of numbers , the geometric mean is defined as : \sqrt[n]. When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function , :\sqrt[n] = \exp \left( \frac \right). The geometric mean of two numbers is the square root of their product, for example with numbers and the geometric mean is \textstyle \sqrt = The geometric mean o ...
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Mean
A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose. The ''arithmetic mean'', also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar. If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the '' sample mean'' (\bar) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted \mu or \mu_x. Outside probability and statistics, a wide rang ...
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Arithmetic Mean
In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the ''mean'' or ''average'' is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a Survey (statistics), survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps to distinguish it from other types of means, such as geometric mean, geometric and harmonic mean, harmonic. Arithmetic means are also frequently used in economics, anthropology, history, and almost every other academic field to some extent. For example, per capita income is the arithmetic average of the income of a nation's Human population, population. While the arithmetic mean is often used to report central tendency, central tendencies, it is not a robust statistic: it is greatly influenced by outliers (Value (mathematics), values much larger or smaller than ...
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Investment Fund
An investment fund is a way of investment, investing money alongside other investors in order to benefit from the inherent advantages of working as part of a group such as reducing the risks of the investment by a significant percentage. These advantages include an ability to: * hire professional investment managers, who may offer better returns and more adequate risk management; * benefit from economies of scale, i.e., lower transaction costs; * increase the asset diversification (finance), diversification to reduce some unsystematic risk. It remains unclear whether professional active investment managers can reliably enhance risk adjusted returns by an amount that exceeds fees and expenses of investment management. Terminology varies with country but investment funds are often referred to as investment pools, collective investment vehicles, collective investment schemes, managed funds, or simply funds. The regulatory term is undertaking for collective investment in transferable ...
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Market Share
Market share is the percentage of the total revenue or sales in a Market (economics), market that a company's business makes up. For example, if there are 50,000 units sold per year in a given industry, a company whose sales were 5,000 of those units would have a 10percent share in that market. "Marketers need to be able to translate sales targets into market share because this will demonstrate whether forecasts are to be attained by growing with the market or by capturing share from competitors. The latter will almost always be more difficult to achieve. Market share is closely monitored for signs of change in the competitive landscape, and it frequently drives strategic or tactical action."Farris, Paul W.; Neil T. Bendle; Phillip E. Pfeifer; David J. Reibstein (2010). ''Marketing Metrics: The Definitive Guide to Measuring Marketing Performance.'' Upper Saddle River, New Jersey: Pearson Education, Inc. . The Marketing Accountability Standards Board (MASB) endorses the definitio ...
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Customer Satisfaction
Customer satisfaction is a term frequently used in marketing to evaluate customer experience. It is a measure of how products and services supplied by a company meet or surpass customer expectation. Customer satisfaction is defined as "the number of customers, or percentage of total customers, whose reported experience with a firm, its products, or its services (ratings) exceeds specified Contentment, satisfaction goals".. Enhancing customer satisfaction and fostering customer loyalty are pivotal for businesses, given the significant importance of improving the balance between customer Attitude (psychology), attitudes before and after the consumption process. Expectation confirmation theory, Expectancy disconfirmation theory is the most widely accepted theoretical framework for explaining customer satisfaction. However, other frameworks, such as equity theory, attribution theory, Contrast theory of meaning, contrast theory, assimilation theory, and various others, are also used to ...
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Gross Domestic Product
Gross domestic product (GDP) is a monetary measure of the total market value of all the final goods and services produced and rendered in a specific time period by a country or countries. GDP is often used to measure the economic performance of a country or region. Several national and international economic organizations maintain definitions of GDP, such as the OECD and the International Monetary Fund. GDP is often used as a metric for international comparisons as well as a broad measure of economic progress. It is often considered to be the world's most powerful statistical indicator of national development and progress. The GDP can be divided by the total population to obtain the average GDP per capita. Total GDP can also be broken down into the contribution of each industry or sector of the economy. Nominal GDP is useful when comparing national economies on the international market according to the exchange rate. To compare economies over time inflation can be adjus ...
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Rate Of Return
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms (e.g., dollars) or as a percentage of the amount invested. The latter is also called the holding period return. A loss instead of a profit is described as a '' negative return'', assuming the amount invested is greater than zero. To compare returns over time periods of different lengths on an equal basis, it is useful to convert each return into a return over a period of time of a standard length. The result of the conversion is called the rate of return. Typically, the period of time is a year, in which case the rate of return is also called the annualized return, and the conversion process, described below, is called ''annualiz ...
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Continuous Compounding
Compound interest is interest accumulated from a principal sum and previously accumulated interest. It is the result of reinvesting or retaining interest that would otherwise be paid out, or of the accumulation of debts from a borrower. Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period. Compounded interest depends on the simple interest rate applied and the frequency at which the interest is compounded. Compounding frequency The ''compounding frequency'' is the number of times per given unit of time the accumulated interest is capitalized, on a regular basis. The frequency could be yearly, half-yearly, quarterly, monthly, weekly, daily, continuously, or not at all until maturity. For example, monthly capitalization with interest expressed as an annual rate means that the compounding frequency is 12, with time periods measured in months. Annual equivalent rate To help consum ...
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Exponential Growth
Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present size. For example, when it is 3 times as big as it is now, it will be growing 3 times as fast as it is now. In more technical language, its instantaneous rate of change (that is, the derivative) of a quantity with respect to an independent variable is proportional to the quantity itself. Often the independent variable is time. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). Exponential growth is the inverse of logarithmic growth. Not all cases of growth at an always increasing rate are instances of exponential growth. For example the function f(x) = x^3 grows at an ever increasing rate, but is much slower than growing exponentially. For example, w ...
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