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The geometric mean has from time to time been used to calculate financial indices (the averaging is over the components of the index). For example, in the past the FT 30 index used a geometric mean. [ 8 ]
This is the formula that was used for the old Financial Times stock market index (the predecessor of the FTSE 100 Index). It was inadequate for that purpose. It was inadequate for that purpose. In particular, if the price of any of the constituents were to fall to zero, the whole index would fall to zero.
This estimate is sometimes referred to as the "geometric CV" (GCV), [19] [20] due to its use of the geometric variance. Contrary to the arithmetic standard deviation, the arithmetic coefficient of variation is independent of the arithmetic mean. The parameters μ and σ can be obtained, if the arithmetic mean and the arithmetic variance are known:
The geometric average return is equivalent to the cumulative return over the whole n periods, converted into a rate of return per period. Where the individual sub-periods are each equal (say, 1 year), and there is reinvestment of returns, the annualized cumulative return is the geometric average rate of return.
The Number represents the geometric mean of the maximum that one would pay based on earnings and based on book value. Graham writes: [2] Current price should not be more than 1 1 ⁄ 2 times the book value last reported. However a multiplier of earnings below 15 could justify a correspondingly higher multiplier of assets.
In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) [1] are a family of functions for aggregating sets of numbers. These include as special cases the Pythagorean means ( arithmetic , geometric , and harmonic means ).
The arithmetic mean, or less precisely the average, of a list of n numbers x 1, x 2, . . . , x n is the sum of the numbers divided by n: + + +. The geometric mean is similar, except that it is only defined for a list of nonnegative real numbers, and uses multiplication and a root in place of addition and division:
Nomograms to graphically calculate arithmetic (1), geometric (2) and harmonic (3) means, z of x=40 and y=10 (red), and x=45 and y=5 (blue) Of all pairs of different natural numbers of the form ( a , b ) such that a < b , the smallest (as defined by least value of a + b ) for which the arithmetic, geometric and harmonic means are all also ...