Question

Considering four stocks in the following table. Pt represents a price at the end of day t, and Qt represents the number of shares outstanding at the end of day t. At the beginning of day 2, stock C splits ten-for-one; and stock D splits one-for-two.

	P0	Q0	P1	Q1	P2	Q2
A	81.52	1000	85.32	1000	90.16	1000
B	48.12	2000	45.24	2000	47.52	2000
C	611.23	2000	632.25	2000	60.45	20000
D	16.26	3000	17.16	3000	34.11	1500

A. Calculate the rate of return on a price-weighted index of the four stocks for the first day ( t =0 to t =1).

B. Calculate the rate of return on a value-weighted index of the four stocks for the first day ( t =0 to t =1).

C. What must happen to the divisor for the price-weighted index at the beginning of day 2?  

D. Calculate the rate of return on a price-weighted index of the four stocks for the second day ( t =1 to t =2).

Answer 1

Part A

To calculate the return on price weighted index, we first need to find the sum of beginning price and ending price. Second step is to calculate the return by using the formula (Ending - beginning)/Beginning

Since it is a price weighted index, we are not concerned about the number of shares but just the price of each share.

So to calculate the rate of return on a price-weighted index of the four stocks for the first day ( t =0 to t =1).

			P0	P1
		A	81.52	85.32
		B	48.12	45.24
		C	611.23	632.25
		D	16.26	17.16
Step 1	Find sum	A+B+C+D	757.13	779.97
Step 2	Return	(totalP1- total P0)/total P0	That is	(779.97-757.13)/757.13
			equals	0.03016655
			That is	3.02%

PART B

Calculate the rate of return on a value-weighted index of the four stocks for the first day ( t =0 to t =1).

For value weighted index, we take the market capitalization which means the total dollar amount, which can be calculated as (No: of shares * Share price). Then take the sum of beginning value and sum of ending value. The return is calculated as (Ending - Beginning)/Beginning

					Column A
			P0	P1	No: of share	P0 * ColumnA	P1*Column A
		A	81.52	85.32	1000	81520	85320
		B	48.12	45.24	2000	96240	90480
		C	611.23	632.25	2000	1222460	1264500
		D	16.26	17.16	3000	48780	51480
Step 1	Find sum	A+B+C+D				1449000	1491780
Step 2	Return	(totalP1- total P0)/total P0	That is			(1491780 - 1449000)/1449000
			equals			0.02952381
			That is			2.90%

PART C

To compute this, the key concept to remember is that the price of the index should remain the same before or after the split.

		Price before split	Price after split at beginning of the day
	A	85.32	85.32
	B	45.24	45.24
	C	632.25	63.225	632.25/10 for 10 way split
	D	17.16	34.32	17.16*2 one for two split
Sum of prices of stocks in portfolio	TOTAL	779.97	228.105
Number of stocks in portfolio	DIVISOR	4	??
TOTAL/Divisor	Index value	194.9925	194.9925	The index value remains same before and after

Since the index value has to remain as 194.9925, the new divisor can be calculated as 228.105/194.9925 = 1.17

New divisor = 1.17

PART D

Calculate the rate of return on a price-weighted index of the four stocks for the second day ( t =1 to t =2).

This can be calculated same as PART A

			P1	P2
		A	85.32	90.16
		B	45.24	47.52
		C	632.25	60.45
		D	17.16	34.11
Step 1	Find sum	A+B+C+D	779.97	232.24
Step 2	Return	(totalP1- total P0)/total P0	That is	(232.24 - 779.97)/232.24
			equals	-0.702244958
			That is	negative 70% return