Chapter 2, Problem 19PS

Requirement 1

Summary Introduction

To Calculate:

The rate of return of a price-weighted index of three stocks for the period t=0 to t=1

Introduction:

Stock exchanges are markets where securities can be bought as well as sold. New York Stock Exchange is one amongst the several markets where the investors can sell their shares or they could purchase their shares or stocks.

Stock Market Indexes are indicators of performance of the stock market.

Dow is the best known measure of the stock market performance.

Price weighted average is an average which is obtained by adding the stock prices and dividing it by a divisor.

Answer to Problem 19PS

The rate of return on the price-weighted index for the first period for the three stocks is 4.17%

Explanation of Solution

Pt represents the price of a stock at time t and Qt represents the outstanding shares at time t. Stock C is split 2 for 1 in last period.

Stock	P0	Q0	P1	Q1	P2	Q2
A	90	100	95	100	95	100
B	50	200	45	200	45	200
C	100	200	110	200	55	400

Return on the index is given by subtracting one from the value obtained when Price weighted index of period t1 divided by price weighted index of period t2.

Stock	Period 0 price	Period 1 price
A	90	95
B	50	45
C	100	110
Sum of prices	240	250
Price weighted index =	Sum/divisor	Sum/divisor
Price weighted index (PWI)	80.00	83.33
Rate of return=	(PWI 1/PWI 0 )-1
Rate of return=	4.17%

Conclusion

The rate of return on price-weighted index of the three stocks for first period is 4.17%

Requirement 2

Summary Introduction

To Calculate:

The divisor for the price weighted index in the period 2.

Introduction:

Stock exchanges are markets where securities can be bought as well as sold. New York Stock Exchange is one amongst the several markets where the investors can sell their shares or they could purchase their shares or stocks.

Stock Market Indexes are indicators of performance of the stock market.

Dow is the best known measure of the stock market performance.

Price weighted average is an average which is obtained by adding the stock prices and dividing it by a divisor.

Answer to Problem 19PS

The divisor at period 2 is 2.34

Explanation of Solution

Pt represents the price of a stock at time t and Qt represents the outstanding shares at time t. Stock C is split 2 for 1 in last period.

Stock	P0	Q0	P1	Q1	P2	Q2
A	90	100	95	100	95	100
B	50	200	45	200	45	200
C	100	200	110	200	55	400

The divisor generally changes to show the stock split. It is obtained by dividing the sum of prices of stocks in the period when the stock was split by the price-weighted index in the previous period.

Stock	Period 1 price	Period 2 price
A	95	95
B	45	45
C	110	55
Sum of prices	250	195
New divisor =	Sum of stocks prices in period 2/ PWI of Period1
New Divisor	2.34

Conclusion

The divisor in the second period is 2.34

Requirement 3

Summary Introduction

To Calculate:

The rate of return of a price-weighted index of three stocks for the period t=1 to t=2

Introduction:

Stock exchanges are markets where securities can be bought as well as sold. New York Stock Exchange is one amongst the several markets where the investors can sell their shares or they could purchase their shares or stocks.

Stock Market Indexes are indicators of performance of the stock market.

Dow is the best known measure of the stock market performance.

Price weighted average is an average which is obtained by adding the stock prices and dividing it by a divisor.

Answer to Problem 19PS

The rate of return on the price-weighted index for the second period for the three stocks is 0%

Explanation of Solution

Pt represents the price of a stock at time t and Qt represents the outstanding shares at time t. Stock C is split 2 for 1 in last period.

Stock	P0	Q0	P1	Q1	P2	Q2
A	90	100	95	100	95	100
B	50	200	45	200	45	200
C	100	200	110	200	55	400

Return on the index is given by subtracting one from the value obtained when Price weighted index of period t1 divided by price weighted index of period t2.

Stock	Period 1 price	Period 2 price
A	95	95
B	45	45
C	110	55
Sum of prices	250	195
Price weighted index =	Sum/divisor	Sum/divisor
Price weighted index (PWI)	83.33	83.33
Rate of return=	(PWI 2/PWI 1 )-1
Rate of return=	0.00%

Conclusion

The rate of return on price-weighted index of the three stocks for second period is 0%.