Question

The ICAN (Index of Companies with Animal Names) is a price-weighted stock index,
comprised of the five companies shown below. None of the companies pay
dividends.

Company Name	Share Price 1/1/2022	Share Price 1/1/23
Toucan Tech	$12.40	$14.75
Manatee	$68.00	$61.75
Iguana	$101.50	$166.25
Koala	$43.33	$50.00
Penguin	$310.00	$400.00

The ICAN index on January 1, 2022 was 1784.10. On January 1, 2023, the ICAN
index rose to 2309.17. The ICAN rate of return was therefore 29.43% over this
period.

a) Calculate the ICAN divisor.

b) Suppose you purchased 500 shares of Toucan Technology, 400 shares of Manatee
Motors, 300 shares on Iguana Industries, 200 shares of Koala Cola, and 100 shares
of Penguin Pharmaceuticals. All purchases were made on January 1, 2022. Suppose
you then sold all shares on January 1, 2023. What was your portfolio rate of return
over this period?

c) Does your rate of return equal the ICAN rate of return? Why or why not. Explain
carefully

Please show work/equations not the calculator version

Answer 1

a)

Company Name	Share Price 1/1/2022	Share Price 1/1/23
Toucan Tech	$12.40	$14.75
Manatee	$68.00	$61.75
Iguana	$101.50	$166.25
Koala	$43.33	$50.00
Penguin	$310.00	$400.00
Total (SUM)	$535.23	$692.75
ICAN Index	1784.1	2309.17
Divisor (SUM / ICAN Index)	0.300	0.300

Divisor = Total of all prices / ICAN Index

We get ICAN Index divisor = 0.3

b)

Company Name	Share Price 1/1/2022	Shares purchased	Cost value (Share price* Shares purchased)	Share Price 1/1/23	Selling value
Toucan Tech	$12.40	500	$6,200.00	$14.75	$7,375.00
Manatee	$68.00	400	$27,200.00	$61.75	$24,700.00
Iguana	$101.50	300	$30,450.00	$166.25	$49,875.00
Koala	$43.33	200	$8,666.00	$50.00	$10,000.00
Penguin	$310.00	100	$31,000.00	$400.00	$40,000.00
			$103,516.00		$131,950.00

Portfolio return = (131,950-103,516)/103,516 = 0.27468

Portfolio return = 24.468%

c) No, the rate of return does not equal the ICAN rate of return.

ICAN rate of return = 29.43%

Portfolio return = 24.468%

This is because in the ICAN index, the weights of each stock is price-weighted. In the portfolio, however, the weights are given before-hand and are not price-weighted weights. Hence, there is a difference between the returns due to different weights of stock in the index and the portfolio.