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 210 $94 $ 97 $ 111

Dynamics General 450 $36 $31 $45

International Rockwell 350 $65 $54 $68

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

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

a).

For year 2019 :
Share price of Douglas McDonel in 2019 = $94
Share price of Dynamics general in 2019 = $36
Share price of international Rockwell in 2019 = $65

Initial index value = ($94 + $36 + $65) / 3
= $195 / 3
= $65

b)

Rate of return of index:
For 2019:

Index value on Dec 31,2019 = ($94 + $36 + $65) / 3
= $195 / 3
= $65

Index value for Dec 31,2020 = ($97 + $31 + $54) / 3
= $182 / 3
= $60.67

Rate of return 2019 = ($60.67 - $65) / $65
= -6.66%

For 2020:

Index value for Dec 31,2020 = ($97 + $31 + $54) / 3
= $182 / 3
= $60.67

Index value for Dec 31,2021= ($111 + $45 + $68)/3
= $224 / 3
= $74.67

Rate of return 2020 = ($74.67 - $60.67) / $60.67
= 23.08%