Question

The following chart provides price (P) and number of shares outstanding (Q) data for stocks A, B, and C at the end of year 0 and at the end of year1.

P0 Q0 P1 Q1

A 45 100 50 100

B 60 150 50 150

C 28 200 35 200

What are the equal-, price-, and value-weighted returns on an index comprised of A, B and C? Equal weighted return Price weighted return Value weighted return A. 1.5% B. 2.09% C. 6.48%

Answer 1

Under Price weighted method, we take the average of the prices in both the periods and then calculate the return between the two:

Stock	P0	P1
A	45	50
B	60	50
C	28	35
Sum	45+60+28= 133	50+50+35=135
Count	3	3
Average	133/3=44.33333333	135/3= 45
Return		45/44.33333333 -1 = 1.50%

Under Equal weighted method, we calculate the return from each stock, take the sum of all the returns and divide by the number of stocks as each stock gets equal weight. As the quantities have remained the same, the returns are calculated using only the prices of both the periods:

Stock	P0	P1	Return
A	45	50	50/45-1 = 11.11%
B	60	50	60/50-1 = -16.67%
C	28	35	35/28-1 = 25.00%
Sum			19.44%
Count			3
Equal weighted return			19.44/3 = 6.48%

Under value weighted method, we calculate the values for each stock for both the periods, take the sum of all the values for each period separately, and then calculate the returns using the two values as shown below:

Stock	P0	Q0	V0	P1	Q1	V1
A	45	100	45x100=4500	50	100	50x100=5000
B	60	150	60x150=9000	50	150	50x150=7500
C	28	200	28x200=5600	35	200	35x200=7000
			4500+9000+5600 = 19100			5000+7500+7000 = 19500
					Value weighted return	19500/19100-1 = 2.09%