EBK STATISTICS FOR BUSINESS & ECONOMICS
EBK STATISTICS FOR BUSINESS & ECONOMICS
13th Edition
ISBN: 8220101456380
Author: Anderson
Publisher: CENGAGE L
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Chapter 20, Problem 21E
To determine

Find the price relatives for the four stocks making up the Boran index in Exercise 20.

Find the January Year 3 and March Year 3 Boran indexes by using the weighted aggregates of price relatives.

Expert Solution & Answer
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Answer to Problem 21E

The price relatives for the four stocks for January Year 3 are givrn below:

YearYear 1 BaseJanuary Year 3Price relative in Period t
Oil31.5022.7572.2
Computer654975.4
Steel403280
Real Estate186.5036.1

The price relatives for the four stocks for March Year 3 are given below:

YearYear 1 BaseMarch Year 3Price relative in Period t
Oil31.5022.5071.4
Computer6547.5073.1
Steel4029.5073.8
Real Estate183.7520.8

The Boran index for January Year 3 by using the weighted aggregates of price relatives is 73.5.

The Boran index for March Year 3 by using the weighted aggregates of price relatives is 70.10.

Explanation of Solution

Calculation:

The data shows that the price per share for Year 1, Year 2, and Year 3.

The price relatives for the four stocks for January Year 3 are obtained below:

YearYear 1 BaseJanuary Year 3Price relative in Period t=Price in period tBase period price(100)
Oil31.5022.7522.7531.50(100)=72.2
Computer65494965(100)=75.4
Steel40323240(100)=80
Real Estate186.506.5018(100)=36.1

The price relatives for the four stocks for March Year 3 are obtained below:

YearYear 1 BaseMarch Year 3Price relative in Period t=Price in period tBase period price(100)
Oil31.5022.5022.5031.50(100)=71.4
Computer6547.5047.5065(100)=73.1
Steel4029.5029.5040(100)=73.8
Real Estate183.753.7518(100)=20.8

The Boran index for January Year 3 and March Year 3 by using the weighted aggregates of price relatives is obtained below:

It=PitQiPi0Qi(100)IJanuary Year 3=22.75(100)+49(150)+32(75)+6.50(50)31.50(100)+65(150)+40(75)+18(50)(100)=12,35016,800(100)=73.5

Thus, the Boran index for January Year 3 by using the weighted aggregates of price relatives is 73.5.

The Boran index for March Year 3 by using the weighted aggregates of price relatives is obtained below:

It=PitQiPi0Qi(100)IMarch Year 3=22.50(100)+47.50(150)+29.50(75)+3.75(50)31.50(100)+65(150)+40(75)+18(50)(100)=11,77516,800(100)=70.10

Thus, the Boran index for March Year 3 by using the weighted aggregates of price relatives is 70.10.

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