Chapter 20, Problem 21SE

Compute the price relatives for the four stocks making up the Boran index in exercise 20. Use the weighted aggregates of price relatives to compute the January 2011 and March 2011 Boran indexes.

20. Boran Stockbrokers, Inc., selects four stocks for the purpose of developing its own index of stock market behavior. Prices per share for a 2009 base period, January 2011, and March 2011 follow. Base-year quantities are set on the basis of historical volumes for the four stocks.

Use the 2009 base period to compute the Boran index for January 2011 and March 2011. Comment on what the index tells you about what is happening in the stock market.

To determine

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

Find the January 2011 and March 2011 Boran indexes by using the weighted aggregates of price relatives.

Answer to Problem 21SE

The price relatives for the four stocks for January 2011 are obtained below:

Year	2009 Base	January 2011	$\text{Price relative in Period }t$
Oil	31.50	22.75	72.2
Computer	65	49	75.4
Steel	40	32	80
Real Estate	18	6.50	36.1

The price relatives for the four stocks for March 2011 is obtained below:

Year	2009 Base	March 2011	$\text{Price relative in Period }t$
Oil	31.50	22.50	71.4
Computer	65	47.50	73.1
Steel	40	29.50	73.8
Real Estate	18	3.75	20.8

The Boran index for January 2011 by using the weighted aggregates of price relatives is 73.5.

The Boran index for March 2011 by using the weighted aggregates of price relatives is 70.10.

Explanation of Solution

Calculation:

The data represents the price per share for the periods January 2011, March 2011 and 2009 Base. Furthermore, the values of 2009 Quantity are also given.

The price relatives for the four stocks for January 2011 are obtained below:

Year	2009 Base	January 2011	$\begin{array}{l}\text{Price relative in Period }t\\ =\frac{\text{Price in period }t}{\text{Base period price}}\left(100\right)\end{array}$
Oil	31.50	22.75	$\frac{\text{22}\text{.75}}{\text{31}\text{.50}}\left(100\right)=72.2$
Computer	65	49	$\frac{\text{49}}{\text{65}}\left(100\right)=75.4$
Steel	40	32	$\frac{\text{32}}{\text{40}}\left(100\right)=80$
Real Estate	18	6.50	$\frac{\text{6}\text{.50}}{\text{18}}\left(100\right)=36.1$

The price relatives for the four stocks for March 2011 is obtained below:

Year	2009 Base	March 2011	$\begin{array}{l}\text{Price relative in Period }t\\ =\frac{\text{Price in period }t}{\text{Base period price}}\left(100\right)\end{array}$
Oil	31.50	22.50	$\frac{\text{22}\text{.50}}{\text{31}\text{.50}}\left(100\right)=71.4$
Computer	65	47.50	$\frac{47.50}{\text{65}}\left(100\right)=73.1$
Steel	40	29.50	$\frac{\text{29}\text{.50}}{\text{40}}\left(100\right)=73.8$
Real Estate	18	3.75	$\frac{\text{3}\text{.75}}{\text{18}}\left(100\right)=20.8$

The Boran index for January 2011 and March 2011 by using the weighted aggregates of price relatives is obtained below:

$\begin{array}{c}{I}_t=\frac{{\displaystyle \sum P_{it}{Q}_i}}{{\displaystyle \sum P_{i0}{Q}_i}}\left(100\right)\\ I_{\text{January 2011}}=\frac{22.75\left(100\right)+49\left(150\right)+32\left(75\right)+6.50\left(50\right)}{31.50\left(100\right)+65\left(150\right)+40\left(75\right)+18\left(50\right)}\left(100\right)\\ =\frac{\text{12,350}}{\text{16,800}}\left(100\right)\\ =73.5\end{array}$

Thus, the Boran index for January 2011 by using the weighted aggregates of price relatives is 73.5.

The Boran index for March 2011 by using the weighted aggregates of price relatives is obtained below:

$\begin{array}{c}{I}_t=\frac{{\displaystyle \sum P_{it}{Q}_i}}{{\displaystyle \sum P_{i0}{Q}_i}}\left(100\right)\\ I_{\text{March 2011}}=\frac{22.50\left(100\right)+47.50\left(150\right)+29.50\left(75\right)+3.75\left(50\right)}{31.50\left(100\right)+65\left(150\right)+40\left(75\right)+18\left(50\right)}\left(100\right)\\ =\frac{\text{11,775}}{\text{16,800}}\left(100\right)\\ =70.10\end{array}$

Thus, the Boran index for March 2011 by using the weighted aggregates of price relatives is 70.10.