Question

Please include work and formulas

2). Consider the following information for three stocks Time -0 Time -1 Total shares outstanding 100 200 200 Number of shares outstanding for B and C changed due to reverse and regular stock splits, Price per share S90 S50 $100 Price per share S108 $90 $55 Total shares outstanding 100 100* 400* Stock respectively a) Calculate the value-weighted, equal-weighted, and price weighted index weights of stocks A, B and C at time 0 b) Calculate the holding period return on stocks A, B, and C from time 0 to time 1. c) Calculate the value-weighted, equal-weighted, and price-weighted index returns on a portfolio of stocks A, B, and C in the first quarter of 2004?

Answer 1

a)

Value weighted:

In a value weighted index, each stock is weighted based on their market capitalization, where market capitalization is the price of a stock multiplied by total shares outstanding. The calculation and formulas are as shown below:

Equal weighted:

In an equal weighted index, each stock gets an equal importance or weight. In case of 3 stocks, each stock will get a weight of 0.33 (1/3).

Price weighted:

In this kind, each stock is weighted according to their price. Calculations are as shown:

Price weight of a stock is calculated as the price of that stock divided by the sum of prices of all 3 stocks.

b)

Holding period return is simple the percentage change in total market cap of the portfolio. Calculations are as shown.

Holding period return is simply calculated using the formula:

$holding\:period\:return=\frac{market\; cap_{period\:1}-market\; cap_{period\:0}}{market\; cap_{period\:0}}$

c)

I am assuming that first quarter of 2004 refers to the same data.

Index returns are calculated simply by computing the index values for both periods and then calculating the percentage change. The formula to calculate index values in all three cases is:

$Index =w_{A}P_{A}+w_{B}P_{B}+w_{C}P_{C}$

where

• w's are weights of each stock
• P's are prices

Value weighted:

Formula implementation in excel:

Price weighted:

Formula implementation in excel:

Equal weighted:

Formula implementation in excel: