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The Brinson model performance attribution can be described as "arithmetic attribution" in the sense that it describes the difference between the portfolio return and the benchmark return. For example, if the portfolio return was 21%, and the benchmark return was 10%, arithmetic attribution would explain 11% of value added. [11]
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. [1] Arithmetic geometry is centered around Diophantine geometry , the study of rational points of algebraic varieties .
The daily price change of the Value Line Arithmetic Composite Index is calculated by adding the daily percent change of all the stocks, and then dividing by the total number of stocks. While the Kansas City Board of Trade (KCBT) made use of the indices since 1982, it shifted exchange distribution to NYSE’s Global Index Feed on August 30, 2013.
The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound annual growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant ...
Quantitatively, the volatility tax is the difference between the arithmetic and geometric average (or “ensemble average” and “time average”) returns of an asset or portfolio. It thus represents the degree of “non-ergodicity” of the geometric average.
Using martingale pricing, the value of the European Asian call with geometric averaging is given by: = [() +] = / In order to find , we must find such that: () After some algebra, we find that: At this point the stochastic integral is the sticking point for finding a solution to this problem.
In mathematics, the QM-AM-GM-HM inequalities, also known as the mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean square). Suppose that ,, …, are positive real numbers. Then
The geometric mean of two positive numbers is never greater than the arithmetic mean. [3] So the geometric means are an increasing sequence g 0 ≤ g 1 ≤ g 2 ≤ ...; the arithmetic means are a decreasing sequence a 0 ≥ a 1 ≥ a 2 ≥ ...; and g n ≤ M(x, y) ≤ a n for any n. These are strict inequalities if x ≠ y.