- CFA Exams
- CFA Level I Exam
- Study Session 12. Equity Investments (1)
- Reading 37. Security Market Indices
- Subject 2. Index Construction and Management
CFA Practice Question
The Board of Governors of the Nottingham Share Exchange wishes to publish an index using all three issues currently listed. They want to know how index performance might be affected by the choice of a price-weighted, a value-weighted, or an unweighted index. Advise them how the index would have changed on February 18, a day when no splits occurred, based upon the following data:
A. Price-Weighted and Value-Weighted Indices Up, Unweighted Index Unchanged
B. Price-Weighted Index Up, Value-Weighted and Unweighted Indices Down
C. Price-Weighted Index Up, Value-Weighted Index Down, Unweighted Index Up
Explanation: Price-weighted index = Sum of prices / an adjusted divisor
Since there were no splits, the divisor is constant.
(38 + 20 + 99) > (37 + 21 + 98)
157 > 156
A price-weighted index would have gone up by 0.6%.
For any beginning value, the daily change = ending capitalization / beginning capitalization.
1.00 x (38 / 37) + 5.00 x (20 / 21) + 10.00 x (99 / 98) < 1.00 + 5.00 + 10.00
1.027 + 4.762 + 10.12 < 16.000
15.891 < 16.000
A value-weighted index would have gone down by 0.7%.
[(38 / 37 - 1) + (20 / 21 - 1) + (99 / 98 - 1)] / 3 = [2.7% + (-4.7%) + 1.0%] / 3
= -1.0% / 3
An unweighted index would have gone down by 0.3%.
Since there were no splits, the divisor is constant.
(38 + 20 + 99) > (37 + 21 + 98)
157 > 156
A price-weighted index would have gone up by 0.6%.
Value-weighted index = Beginning Value x (Ending index capitalization) / (Beginning index capitalization)
For any beginning value, the daily change = ending capitalization / beginning capitalization.
1.00 x (38 / 37) + 5.00 x (20 / 21) + 10.00 x (99 / 98) < 1.00 + 5.00 + 10.00
1.027 + 4.762 + 10.12 < 16.000
15.891 < 16.000
A value-weighted index would have gone down by 0.7%.
An unweighted index is based upon the arithmetic average of percent changes for each stock.
[(38 / 37 - 1) + (20 / 21 - 1) + (99 / 98 - 1)] / 3 = [2.7% + (-4.7%) + 1.0%] / 3
= -1.0% / 3
An unweighted index would have gone down by 0.3%.
User Contributed Comments 8
| User | Comment |
|---|---|
| Yuyan | Value-weighted index: Base on price*number of outstanding shares, NOT price*capitalization. |
| utdfan | value weighted index would have increased Start ($37bn+$105bn+$980bn)= $1122bn, end ($38bn+$100bn+$990bn)= $1128bn |
| murli | Good one. Capitalization given is of op. balance, so get the no. of shares , and get market cap. based on closing price; Difference is the change. |
| sigma13 | # of shares = mkt. cap/share price |
| todolist | Determine # of shares by market cap/initial price, then use # of shares * ending price = ending value. ending value=ending market cap |
| mekc | instead of calculating all, look for the variable that can only be one thing in each answer and calc that. ie unweighted. saves time :o) |
| shiva5555 | Good question |
| Sanghamitra | end cap = (10/98)*99+(5/21)*20+(1/38)*37 = 15.89 I think the confusion here lies in that mkt cap is already given and we still make the mistake of multiplying it with sh. price. we just need to find the final market cap from no. of shares. so no. of shares (10/98) * 99(new sh. price) |