A price index is any single number calculated from an array of prices and quantities over a period. Since not all prices and quantities of purchases can be recorded, a representative sample is used instead. Inflation and cost indices are calculated as price indices.
There are two main methods to calculate price indices, the Paasche index (after Hermann Paasche) and the Laspeyre index (after Etienne Laspeyres.
The Paasche Index is
while the Laspeyres index computes as
where ΔP is the change in price level, p0 and q0 are the prices and quantities in the first period, p1 and q1 those in the second.
The Laspeyres index systematically overstates inflation while the Paasche index understates it. A third index, the Fisher index (after Irving Fisher), tries to get around this problem. It is calculated as the geometric mean of ΔPP and ΔPL:
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This over-weighting of the Laspeyres index, called "substitution bias", is why the Laspeyres formula produces a growth rate of GDP that is at the upper limit of possible measures.
So with a Laspeyres index producing an upper bound to measurement of economic growth and a Paasche index producing the lower bound, the Fisher, which is the geometric average of the two, follows a more stable middle path.
An important consequence of using chain indexes is that the associated volume measures are not additive.
Fisher Investments is not making a precise short-run forecast right now, but we are convinced a bull market peak has not yet arrived.
Fisher Investments finds that corporations are capitalizing on these favorable conditions by harnessing healthy cash flow and low borrowing costs to make massive share repurchases and execute value-enhancing mergers and acquisitions.
Fisher Investments attributes some of the risk aversion "fog" to a number of well-publicized storylines we think are either misguided or already reflected in prices.
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