## Related questions with answers

Boran Stockbrokers, Inc., selects four stocks for the purpose of developing its own index of stock market behavior. Prices per share for a 2007 base period, January 2009, and March 2009 follow. Base-year quantities are set on the basis of historical volumes for the four stocks.

$\begin{matrix} \text{ } & \text{ } & \text{ } & \text{ } & \text{Price per Share (\$)}\\ \text{ } & \text{ } & \text{2007} & \text{2007} & \text{January} & \text{March}\\ \text{Stock} & \text{Industry} & \text{Quantity} & \text{Base} & \text{2009} & \text{2009}\\ \hline \text{A} & \text{Oil} & \text{100} & \text{31.50} & \text{22.75} & \text{22.50}\\ \text{B} & \text{Computer} & \text{150} & \text{65.00} & \text{49.00} & \text{47.50}\\ \text{C} & \text{Steel} & \text{75} & \text{40.00} & \text{32.00} & \text{29.50}\\ \text{D} & \text{Real Estate} & \text{50} & \text{18.00} & \text{6.50} & \text{3.75}\\ \end{matrix}$

Use the 2007 base period to compute the Boran index for January 2009 and March 2009. Comment on what the index tells you about what is happening in the stock market.

Solution

Verified$\boxed{\text{Weighted Aggregate Price Index in Period $t$ : }\color{#4257b2}{I_t=\dfrac{\sum{P_{it}Q_i}}{\sum{P_{i0}Q_i}}(100)}}$

where

$P_{it}$ - unit price for item $i$ in period $t$

$P_{i0}$ - unit price for item $i$ in the base period

$Q_i$ - quantity of usage for item $i$

- {Boran index for January 2009}

$\begin{align*} I_t &=\dfrac{\sum{P_{it}Q_i}}{\sum{P_{i0}Q_i}}(100)\\ &=\dfrac{22.75(100)+49.00(150)+32.00(75)+6.50(50)}{31.50(100)+65.00(150)+40.00(75)+18.00(50)}(100)\\ &\approx\boxed{73.5} \end{align*}$

- {Boran index for March 2009}

$\begin{align*} I_t &=\dfrac{\sum{P_{it}Q_i}}{\sum{P_{i0}Q_i}}(100)\\ &=\dfrac{22.50(100)+47.50(150)+29.50(75)+3.75(50)}{31.50(100)+65.00(150)+40.00(75)+18.00(50)}(100)\\ &\approx\boxed{70.1} \end{align*}$

Thus, the stock market price decreases from January to March in 2009.

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Probability and Statistics for Engineers and Scientists

9th Edition•ISBN: 9780321629111 (9 more)Keying E. Ye, Raymond H. Myers, Ronald E. Walpole, Sharon L. Myers#### Statistics for Business and Economics

11th Edition•ISBN: 9780324783254 (2 more)David R. Anderson, Dennis J. Sweeney, Thomas A. Williams#### The Practice of Statistics for the AP Exam

5th Edition•ISBN: 9781464108730 (1 more)Daniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor#### Statistics and Probability with Applications

3rd Edition•ISBN: 9781464122163Daren S. Starnes, Josh Tabor## More related questions

- college algebra

1/4

- college algebra

1/7