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Neyman allocation, also known as optimum allocation, is a method of sample size allocation in stratified sampling developed by Jerzy Neyman in 1934. This technique determines the optimal sample size for each stratum to minimize the variance of the estimated population parameter for a fixed total sample size and cost.
Sales variance is the difference between actual sales and budgeted sales. [1] It is used to measure the performance of a sales function, and/or analyze business results to better understand market conditions.
The general formula for variance decomposition or the law of total variance is: ... the population variance of a finite population of size N with values x i is given ...
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
( ()) is the market premium, the expected excess return of the market portfolio's expected return over the risk-free rate. A derivation [ 14 ] is as follows: (1) The incremental impact on risk and expected return when an additional risky asset, a , is added to the market portfolio, m , follows from the formulae for a two-asset portfolio.
But as market shares of the 20-firm industry diverge from equality the Herfindahl can exceed that of the equal-market-share 3-firm industry (e.g., if one firm has 81% of the market and the remaining 19 have 1% each, then =). A higher Herfindahl signifies a less competitive (i.e., more concentrated) industry.
Even Markowitz, himself, stated that "semi-variance is the more plausible measure of risk" than his mean-variance theory. [5] Later in 1970, several focus groups were performed where executives from eight industries were asked about their definition of risk resulting in semi-variance being a better indicator than ordinary variance. [6]
However, some firms are more sensitive to these factors than others, and this firm-specific variance is typically denoted by its beta (β), which measures its variance compared to the market for one or more economic factors. Covariance among securities result from differing responses to macroeconomic factors.