Question

The following three defense stocks are to be combined into a stock index in January 2019 (perhaps a portfolio manager believes these stocks are an appropriate benchmark for his or her performance):

		Price
	Shares (millions)		1/1/19			1/1/20			1/1/21
Douglas McDonnell	215		$	64		$	68		$	82
Dynamics General	455			72			64			78
International Rockwell	250			101			90			106

a. Calculate the initial value of the index if a price-weighting scheme is used.

INDEX VALUE:

b. What is the rate of return on this index for the year ending December 31, 2019? For the year ending December 31, 2020? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

2019 return		%
2020 return		%

Answer 1

We are given the stock prices of 3 different stocks for 3 different years.

a) Initial Index Value- it is the value of the index by adding the stocks and dividing by the number of stocks.

For year 2019 , Initial index value is

Share price of Douglas McDonel in 2019 - $64

Share price of Dynamics general in 2019- $72

Share price of international Rockwell in 2019- $101

Initial Index value = ($64 + $72 +$101) /3 = $79

b) Rate of return of index

For 2019

Index value on Dec 31,2019 = ($64 + $72 +$101) /3 = $79

Index value for Dec 31,2020= ($68 + $64 + $90)/3 = $74

Rate of return 2019 = ( $74 - $79) / $79 * 100 = -6.32%

For 2020

Index value on Dec 31,2020 = ($68 + $64 + $90)/3 = $74

Index value for Dec 31,2021= ($82 + $78 + $106)/3 = $88.6

Rate of return 2019 = ( $88.6 - $74) / $74 * 100 = 19.72%