Abstract
In this paper, we pay our attention to geometric parameters and their applications in economics and finance. We discuss the multiplicative models in which a geometric mean and a geometric standard deviation are more natural than arithmetic ones. We give two examples from Warsaw Stock Exchange in 1995--2009 and from a bid of 52-week treasury bills in 1992--2009 in Poland as an illustrative example. For distributions having applications in finance and insurance we give their multiplicative parameters as well as their estimations. We consider, among others, heavy-tailed distributions such as lognormal and Pareto distribution, applied to modelling of large losses.
Highlights
Two measures frequently used in descriptive statistics are the arithmetic mean and the standard deviation
The geometric mean is used less often, while the geometric standard deviation connected with the geometric mean is used even more rarely
In which the geometric mean and the geometric standard deviation are more natural than their arithmetic counterparts
Summary
Two measures frequently used in descriptive statistics are the arithmetic mean and the standard deviation. Arithmetic and geometric means are somewhat controversial measurements of the past and future investment returns Critical remarks on this topic are given in the paper (Missiakoulis et al 2007). Unlike in the results discussed above, the issue concerning multiplicative parameters, including a geometric mean, is extended with interpretations and applications of multiplicative variance as a measure of dispersion. Such a measure, as we justify in more detail is a better and more natural measure of deviation between random variables and their geometric mean. These examples indicate the real benefits of applying the geometric parameters instead of arithmetic ones in real situations in economics and finance
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