Transcript MANAGEMENT FUNCTIONS - 精品课程平台

Chapter 10
Index analysis
The concept and classification of index
• A statistical indicator providing a
representation of the value of the
securities which constitute it. Indices
often serve as barometers for a given
market or industry and benchmarks
against which financial or economic
performance is measured.
Some commonly used statistical indexs
INDIVIDUAL INDEX
QUANTITY
INDEX
VALUE
INDEX
Price Relatives
• Price relatives are helpful in understanding
and interpreting changing economic and
business conditions over time.
Price Relatives
• A price relative shows how the current price per unit
for a given item compares to a base period price per
unit for the same item.
• A price relative expresses the unit price in each
period as a percentage of the unit price in the base
period.
• A base period is a given starting point in time.
Price in period t
Price relative in period t =
( 100)
Base period price
Example: Besco Products
• Price Relatives
The prices Besco paid for newspaper and television ads in
1992 and 1997 are shown below. Using 1992 as the base year,
compute a 1997 price index for newspaper and television ad prices.
Newspaper
Television
1992
1997
$14,794
$29,412
11,469 23,904
Example: Besco Products
• Price Relatives
Newspaper
Television
29,412
I1997 
(100)  199
14,794
Television advertising cost increased at a
greater rate.
Aggregate Price Indexes
• An aggregate price index is developed for the specific purpose
of measuring the combined change of a group of items.
• An unweighted aggregate price index in period t,
denoted by It , is given by
 Pit
It 
(100)
 Pi 0
where
Pit = unit price for item i in period t
Pi 0 = unit price for item i in the base
period
Aggregate Price Indexes
• With a weighted aggregate index each item in the group is
weighted according to its importance, which typically is the
quantity of usage.
• Letting Qi = quantity for item i, the weighted aggregate price
index in period t is given by
 Pit Q i
It 
(100)
 Pi 0 Q i
where the sums are over all items in the group.
Aggregate Price Indexes
• When the fixed quantity weights are
determined from the base-year usage, the
index is called a Laspeyres index.
• When the weights are based on period t
usage the index is a Paasche index.
Example: City of Newton
• Aggregate Price Indexes
Data on energy consumption and expenditures by sector for
the city of Newton are given below. Construct an aggregate
price index for energy expenditures in 2000 using 1985 as the
base year.
Sector
Residential
Commercial
Industrial
Transport.
Quantity (BTU) Unit Price ($/BTU)
1985
2000
1985
2000
9,473
8,804
$2.12
$10.92
5,416
6,015
1.97
11.32
21,287
17,832
.79
5.13
15,293
20,262
2.32
6.16
Example: City of Newton
• Unweighted Aggregate Price Index
I2000 = 10.92 + 11.32 + 5.13 + 6.16 (100) = 466
2.12 + 1.97 + .79 + 2.32
• Weighted Aggregate Index (Laspeyres Method)
I2000 = 10.92(9473) + . . . + 6.16(15293) (100) = 443
2.12(9473) + . . . + 2.32(15293)
• Weighted Aggregate Index (Paasche Method)
I2000 = 10.92(8804) + . . . + 6.16(20262) (100) = 415
2.12(8804) + . . . + 2.32(20262)
The Paasche value being less than the Laspeyres
indicates usage has increased faster in the lowerpriced sectors.
Some Important Price Indexes
• Consumer Price Index (CPI)
–
–
–
–
–
Primary measure of the cost of living in US.
Based on 400 items including food, housing,
clothing, transportation, and medical items.
Weighted aggregate price index with fixed
weights derived from a usage survey.
Published monthly by the US Bureau of Labor
Statistics.
Its base period is 1982-1984 with an index of
100.
Some Important Price Indexes
• Producer Price Index (PPI)
–
–
–
–
–
Measures the monthly changes in prices in
primary markets in the US.
Used as a leading indicator of the future
trend of consumer prices and the cost of
living.
Covers raw, manufactured, and processed
goods at each level of processing.
Includes the output of manufacturing,
agriculture, forestry, fishing, mining, gas
and electricity, and public utilities.
Weighted average of price relatives using
the Laspeyres method.
Some Important Price Indexes
• Dow Jones Averages
–
–
–
–
Indexes designed to show price trends and
movements on the New York Stock
Exchange.
The Dow Jones Industrial Average (DJIA)
is based on common stock prices of 30
industrial firms.
The DJIA is not expressed as a percentage
of base-year prices.
Another average is computed for 20
transportation stocks, and another for 15
utility stocks.
Deflating a Series by Price Indexes
• In order to correctly interpret business
activity over time, when it is expressed
in dollar amounts, we should adjust the
data for the price-increase effect.
• Removing the price-increase effect from
a time series is called deflating the
series.
• Deflating actual hourly wages results in
real wages or the purchasing power of
wages.
Example: McNeer Cleaners
• Deflating a Series by Price Indexes
McNeer Cleaners, with 46 branch
locations, has had the total sales revenues
shown on the next slide for the last five
years. Deflate the sales revenue figures
on the basis of 1982-1984 constant dollars.
Is the increase in sales due entirely to the
price-increase effect?
Example: McNeer Cleaners
Deflating a Series by Price Indexes
Year Total Sales ($1000) CPI
1996
1997
1998
1999
2000
8,446
9,062
9, 830
10,724
11,690
156.9
160.5
163.0
166.6
172.6
Example: McNeer Cleaners
• Deflating a Series by Price Indexes
Deflated
Annual
Year Sales ($1000)
Change(%)
1996
(8,446/156.9)(100) = 5,383
1997
(9,062/160.5)(100) = 5,646
+4.9
1998
(9,830/163.0)(100) = 6,031
+6.8
1999
(10,724/166.6)(100) = 6,437
2000 (11,690/172.6)(100) = 6,773
+5.2
+6.7
After adjusting revenue for the price-increase
effect, revenue is still increasing at an average rate of
5.9% per year.
Price Indexes: Other
Considerations
• Selection of Items
– When the class of items is very large, a
representative group (usually not a random
sample) must be used.
– The group of items in the aggregate index must be
periodically reviewed and revised if it is not
representative of the class of items in mind.
• Selection of a Base Period
– As a rule, the base period should not be too far
from the current period.
– The base period for most indexes is adjusted
periodically to a more recent period of time.
Price Indexes: Other
Considerations
• Quality Changes
–
–
–
A basic assumption of price indexes is that the
prices are identified for the same items each
period.
Is a product that has undergone a major
quality change the same product it was?
A substantial quality improvement also may
cause an increase in the price of a product.
Quantity Indexes
• An index that measures changes in quantity levels over
time is called a quantity index.
• Probably the best known quantity index is the Index of
Industrial Production.
• A weighted aggregate quantity index is computed in
much the same way as a weighted aggregate price index.
• A weighted aggregate quantity index for period t is given
by
 Q it w i
It 
(100)
 Qi0 w i
Average index
• Arithmetic mean index
• Harmonic mean index
Arithmetic mean index
p
q
1.Individualindex calculationip  p1 ,iq  q1 。
0
0
2.Collectingtheinformention of weight numberp0q0
3.Accordingto theweight arithmeticaverage, we get
p
 i p p0 q0  p10 p0q0  p1q0
Ip 



L
p
q
p
q
p
p
q

 0 0
 0 0
0 0
q1
 iq p0q0  q0 p0q0  q1 p0
Iq 


p
q
 p0q0
 q0 p0
 0 0
 Lq
xf
(x   )
f
Harmonic mean index
p1
q1
1.Individualindex calculation。ip  p ,iq  q 。
0
0
2.Collect the information of theweight numberp1q1。
3.Accordingto theformof theaverageof theweightedharmonic,we get
p1q1

I p  p q   p1q1   p1q1
p0
1 1

 p1q1  p0q1

ip
p1
 Pp
p1q1
q1 p1
p1q1



Iq  p q  q


P
q
p
q

0 1
 1 1  0  p1q1
iq
q1
m
(H   m )

x
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