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However, index formulas can still be used as a basis for comparison. If you know that
the market closed at “10,952 points, up 241,” by the relative size of the increase you know
that the stocks included in the index, and presumably the rest of the market as well, had a
very good day. Also, if you know that 5 years ago the index sat at 11,275 points, you also
know that the stocks in the index, and presumably the rest of the market as well, have not
had such a great past 5 years.
Example 16.2.3 Suppose that the 1 year ago the GlobalInvestexx CleanTech 75
index stood at 21,736.14 points. Today the index stands at 24,535.72. What does this
tell you about the stocks that are tracked by this index?
Since the value of the index has risen, we can assume that the stocks that it tracks have on
average risen over the past year. In fact, we can calculate the percent increase by dividing.
24,535.72
__________21,736.14 1.1288
The index is now 112.88% of where it was a year ago, a 12.88% increase. We can take this
as an indication that the “clean tech” stocks that this index is intended to track have risen
in value by about 12.88% on average. We must be careful in interpreting this, though. This
index is a type of average; while this does indicate that stocks of clean tech companies have
risen around 12.88% on average, this does not tell us what the price change would be for
any individual stock, or for a portfolio of clean tech stocks that does not follow the weightings
used in this index.
Another type of index is a comparative index. Suppose that you earn a salary of $35,000,
living in Fort Wayne, Indiana. You get a job offer that would require you to move to Boston,
Massachusetts. You know that the cost of living in Boston is much higher than in Fort Wayne
and so you know you will need to make more money to maintain the same standard of living.
But how much more? A comparative index would provide
a way to get a handle on how the costs of living compare in
these two different locations. A comparative index would
be based on the prices of a range of different goods and ser-
vices at each location, weighted according to some formula
meant to reflect how much of a typical person’s budget
each item eats up. (For example, the cost of cable television
would count for less than the cost of food, since^3 people
spend more for food than for cable.)
Suppose that you look up a cost-of-living index for
Boston and find that it is 1,184.29. This, by itself, tells
you nothing. However, if you also know that the index
for Fort Wayne is 939.25, you can use these together by
dividing the indexes. Boston is more expensive than Fort
Wayne. How much more expensive overall? Overall, the
cost of living in Boston is 1184.29/939.25 times as much
as in Fort Wayne.
Example 16.2.4 Using the index numbers given
above, what salary would be needed in Boston to
match $35,000 in Fort Wayne.
($35,000) (
1,184.29
_____939.25 (^) ) $44,131
Comparative indexes can be helpful, but they have to be
taken with a grain of salt. The items included in an index
may not always reflect how any given person divides up
Indexes can be helpful when comparing costs of living or doing
(^3) most business in different locations. © Photodisc/Getty Images/DIL
16.2 Measures of Average 621