Investments
Investments
11th Edition
ISBN: 9781259277177
Author: Zvi Bodie Professor, Alex Kane, Alan J. Marcus Professor
Publisher: McGraw-Hill Education
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Chapter 2, Problem 11PS

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.

Requirement 1

Expert Solution
Check Mark

Answer to Problem 11PS

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.

Requirement 2

Expert Solution
Check Mark

Answer to Problem 11PS

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.

Requirement 3

Expert Solution
Check Mark

Answer to Problem 11PS

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%.

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