Question

Use the following information to answer questions 7 - 8.

**PLEASE SHOW ALL WORK***

Stock	P1	P2	P3	Shares Outstanding
A	$45	$47.50	$49	250
B	$60	$58.75	$60	425
C	$15	$15.30	$17.45	700

7. (1 point) What is the rate of return on a price-weighted index between day 1 and day 2? What is rate of return on a price-weighted index between day 2 and day 3?

8. (1 point) Construct a value-weighted index with an initial value of 2,000. What is the rate of return on the index between day 1 and day 2 and between day 2 and day 3? What is the value of the index after each day?

Answer 1

Q7.

Under Price weighted method, we don't consider the number of shares outstanding to calculate the return. We simply take the average price of the index for two days and calculate the return. Below screen shot shows the same calculation. For day 1 the sum of the prices of the three stocks is 45+60+15=120 and as there are 3 stocks, the average price is 120/3 = 40. Similarly the average price in day 2 is 40.512 and in day 3 it is 42.15

Rate of return on a price-weighted index between day 1 and day 2 = ((40.517/40) - 1) x 100 = 1.292%

Rate of return on a price-weighted index between day 3 and day 2 = ((42.15/40.517) - 1) x 100 = 4.031%

8. Under Value weighted method, we consider the number of shares outstanding to calculate the return. We multiply the number of shares outstanding for each stock with its price and sum these products to arrive at the value of the index. Below screen shot shows the same calculation.

Value of the index after Day 1: (250 x 45)+(425 x 60)+ (700 x 15)=$47250.00

Value of the index after Day 2: (250 x 47.50)+(425 x 58.75)+ (700 x 15.30)=$47553.75

Value of the index after Day 1: (250 x 49)+(425 x 60)+ (700 x 17.45)=$49965.00

Rate of return on a value-weighted index between day 1 and day 2 = ((47553.75/47250) - 1) x 100 = 0.6429%

Rate of return on a value-weighted index between day 3 and day 2 = ((49965/47553.75) - 1) x 100 = 5.0706%

To construct a value-weighted index with an initial value of 2,000 we would need to use solver in excel. basically there can be multiple solutions as it depends on the prices of the three stock. Using the given number of shares outstanding for each stock, we would have to come up with the value of 2000 for the index.

So if prices are 0.40, 2, 150 then the index value will be 2000 but there can be several such price combinations.