# weighting

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## Weighting

When calculating an average from a given data set, the process of allowing some data points to affect the average more than others. For example, if one is calculating the average value of a stock index, one may weight the stocks with higher market capitalization greater than other stocks. Likewise, if one is determining a moving average over a given number of trading days, one may weight more recent trading days than those more distant. Weighting can lessen some of the disadvantages of taking the average of a data set instead of taking the median.

## weighting

The assigning of a measure of relative importance to each of a group of variables that are combined. If an investor has 70% of his or her invested funds in stock A, which provides a current yield of 6%, and the remaining 30% of the invested funds in stock B, which provides a current yield of 12%, the weighted current yield of both securities is (0.70)(0.06) + (0.30)(0.12), or 7.8%.
Case Study The weighting of individual securities included in an index or average can have a major impact on the market price of both the individual securities included in the index as well as on movements in the index or average itself. Although a few averages are weighted according to each component's price (for example, the Dow Jones Industrial Average), and even fewer are unweighted (the Value Line Average), most are weighted on the basis of market capitalization. That is, the index or average is calculated using a combination of each component's security price and number of outstanding shares. In May 2001 Morgan Stanley Capital International (MSCI), the world's largest indexing company, announced its intention to alter the composition of the indexes the firm calculated and published. In addition to adding and deleting companies, the firm would alter the weighting of most of the securities included in the index. At the time of the announcement MSCI was using full market capitalization to weight the components. That is, the firm was using the total number of shares outstanding, even if some of these shares were unavailable for trading. The new weighting would use "free float," or the number of shares that were actually available to investors. This change was particularly important to shareholders of companies such as Deutsche Telekom and France Telecom because the significant portion of each firm's shares was owned by its government and would not be included under the revised weighting system. The revised weighting would make each of these securities less important in the calculation. It would also likely cause a decline in the price of each security as index funds sold the stocks to rebalance their portfolios. At the same time, other stocks that assumed greater weighting under the new system could be expected to increase in price as index funds accumulated the securities for their portfolios.
References in periodicals archive ?
Observing the above and the fact that v is the root of [kappa]-disallowing gadgets for all [kappa] [member of] {n + 2,..., 2n}, we find that any proper weighting w from {0,1} satisfies xw (v) [member of] {n - 1, n, n +1}, as claimed.
We define a weighting of the edges of h(G), w : F [right arrow] {0,1} as follows.
But, from Fact 2.1, any proper weighting from {0,1} of h(G) satisfies xw (v) g {n - 1, n, n +1} for all v [member of] V.
Now note that every triangle xab, with only x having other adjacent edges (x is referred to as the top), contributes exactly 3 to xw (x) in any proper weighting w from {1 , 2}.
One can check that every proper weighting w from {1,2} of a graph adjacent to such a gadget only at x requires w(xc) = 2.
Note that in any proper weighting w from {1,2}, w(vx) [not equal to] w(vy); otherwise, since the weight contributed by gadgets to xw (x) and xw (y) is [kappa] - 3, then xw (x) = w(xv) + w(xy) + [kappa] - 3 = w(yv) + w(yx) + [kappa] - 3 = xw (y).
Fact 3.1 In f (G) the following holds: any proper weighting w from {1,2} satisfies xw (v) [[member of] {4n - 2, 4n - 1 , 4n} for every v [member of] V.

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