ECON 136: Financial Economics
Section 2 (Sep 4th)
Xing Huang
1
Economics Department, UC Berkeley
1 Stock Index
1.1 Review
Weights
Feature
Rebalance
Equally weighted
1
N
Equal weights
Yes
Price weighted
P
i
P
N
j
=1
P
i
Equal shares
No
Marketvalue weighted
P
i
M
i
P
N
j
=1
P
j
M
j
Propotional shares
No
1.2 Example: calculate the returns of the stock index
(revised on Ch2 problem 9, BKM 8th ed)
Consider the three stocks in the following table.
P
t
represents price at time
t
, and
Q
t
represents
shares outstanding at time
t:
P
0
Q
0
P
1
Q
1
A
90
100
95
100
B
50
200
45
200
C
100
200
110
200
Calculate the rate of return on an equally weighted index, a priceweighted index and a market
valueweighted index of the three stocks for this period.
Answer:
R
A
=
P
1
A
P
0
A
1 =
95
90
1 =
5
90
; R
B
=
1
10
; R
C
=
1
10
For equally weighted index,
w
A
=
w
B
=
w
C
=
1
3
For price weighted index,
w
A
=
90
90 + 50 + 100
=
9
24
; w
B
=
5
24
; w
C
=
10
24
1
Thank you all very much !!
1
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View Full DocumentFor marketvalue weighted index,
w
A
=
90
100
90
100 + 50
200 + 100
200
=
9
39
; w
B
=
10
39
; w
C
=
20
39
:
Therefore, we can easily get the returns for these three index as following.
R
EW
=
1
3
5
90
+
1
3
(
±
1
10
) +
1
3
1
10
=
1
48
²
2
:
08%
R
PW
=
9
24
5
90
+
5
24
(
±
1
10
) +
10
24
1
10
=
1
24
²
4
:
17%
R
V W
=
9
39
5
90
+
10
39
(
±
1
10
) +
20
39
1
10
=
1
26
²
3
:
85%
Note:
There is another simpler way to calculate
R
PW
and
R
V W
:
Because price weighted index has the same shares for all stocks, we could assume it has 1 share
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