6.What is the market value-weighted index of the following three stocks assuming the beginning index value is 100 and a base value of $150,000?
As of December 31 | ||
Company | Stock Price | Shares Outstanding |
X | $1 | 5,000 |
Y | $20 | 2,500 |
Z | $60 | 1,000 |
A) 77.
B) 100.
C) 30.
D) 70.
7.What is the price-weighted index of the following three stocks?
As of December 31, 2001 | ||
Company | Stock Price | Shares Outstanding |
A | $50 | 10,000 |
B | $35 | 20,000 |
C | $110 | 30,000 |
A) 65.
B) 75.
C) 80.
D) 85.
8.An index was recently begun with the following two stocks:
§ Company A – 50 shares valued at $2 each.
§ Company B – 10 shares valued at $10 each.
Given that the value-weighted index was originally set at 100 and Company A's stock is currently selling for $4 per share while Company B’s stock is still at $10 per share, what is the current value of the price-weighted index and the value-weighted index?
| Price-weighted | Value-weighted |
A) 7 300
B) 8 150
C) 7 150
D) 8 300
9.James Investments is calculating an unweighted (equally-weighted) index on a four stock portfolio. Use the following information to calculate the value of the index using the geometric and arithmetic mean.
Stock | Number of Shares | Initial Cost | Current Cost |
A | 100 | 5.00 | 5.00 |
B | 1,000 | 10.00 | 12.50 |
C | 500 | 7.50 | 10.00 |
D | 1500 | 5.00 | 8.00 |
Price using geometric Price using arithmetic
A) 1.426 1.295
B) 1.277 1.379
C) 1.277 1.295
D) 1.426 1.379
答案和详解如下：
6.What is the market value-weighted index of the following three stocks assuming the beginning index value is 100 and a base value of $150,000?
As of December 31 | ||
Company | Stock Price | Shares Outstanding |
X | $1 | 5,000 |
Y | $20 | 2,500 |
Z | $60 | 1,000 |
A) 77.
B) 100.
C) 30.
D) 70.
The correct answer was A)
The market value weighted index = [(($1)(5,000) + ($20)(2,500) + ($60)(1,000))/$150,000](100)
= ($115,000/$150,000)(100)
= (0.767)(100)
= 76.67 or 77
7.What is the price-weighted index of the following three stocks?
As of December 31, 2001 | ||
Company | Stock Price | Shares Outstanding |
A | $50 | 10,000 |
B | $35 | 20,000 |
C | $110 | 30,000 |
A) 65.
B) 75.
C) 80.
D) 85.
The correct answer was A)
The price-weighted index equals [(50 + 35 + 110) / 3] = 65.
8.An index was recently begun with the following two stocks:
§ Company A – 50 shares valued at $2 each.
§ Company B – 10 shares valued at $10 each.
Given that the value-weighted index was originally set at 100 and Company A's stock is currently selling for $4 per share while Company B’s stock is still at $10 per share, what is the current value of the price-weighted index and the value-weighted index?
| Price-weighted | Value-weighted |
A) 7 300
B) 8 150
C) 7 150
D) 8 300
The correct answer was C)
Price weight = [(4) + (10)] / 2 = 7
Value weight = [(4)(50) + (10)(10)]/[(2)(50) + (10)(10)](100) = 150
9.James Investments is calculating an unweighted (equally-weighted) index on a four stock portfolio. Use the following information to calculate the value of the index using the geometric and arithmetic mean.
Stock | Number of Shares | Initial Cost | Current Cost |
A | 100 | 5.00 | 5.00 |
B | 1,000 | 10.00 | 12.50 |
C | 500 | 7.50 | 10.00 |
D | 1500 | 5.00 | 8.00 |
Price using geometric Price using arithmetic
A) 1.426 1.295
B) 1.277 1.379
C) 1.277 1.295
D) 1.426 1.379
The correct answer was C)
First calculate the return relatives and then find the mean of the relatives. The number of shares is irrelevant in this question.
Arithmetic average:
5/5 = 1; 12.5/10 = 1.25; 10/7.50 = 1.33; 8/5 = 1.60
(1 + 1.25 + 1.33 + 1.60) / 4 = 1.295
Geometric mean:
5/5 = 1; 12.5/10 = 1.25; 10/7.50 = 1.33; 8/5 = 1.60
[1 x 1.25 x 1.33 x 1.60]1/4 = 1.277
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