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Consider the following three stocks constitute an index
Consider the following three stocks constitute an index. P represents price at time t and Q represents no. of shares outstanding at time t. Q. 1,000,000 ? B Po 1.25 500 10 Q 1,000,000 200 100 P 1.18 580 9 200 ? 100 a) Compute rate of return of each stock at time I. (3 marks) b) Compute percentage change of the index value at time I given it is (i) value-weighted index and (ii) price-weighted index. (3 marks) c) Describe how stock split affects the process to calculate index value under value-weighted and price-weighted scheme respectively. No numerical examples or explanations is allowed. (4 marks)
Expert Solution
Ans: Note 1
|
Stocks |
P0 |
Q0 |
P1 |
Q1 |
|
A |
1.25 |
1000000 |
1.18 |
1000000 |
|
B |
500 |
200 |
580 |
200 |
|
C |
10 |
100 |
9 |
100 |
Ans a)
|
Rate of return for stock A =yr 1 |
|||
|
p1q1 |
{-p0q0} |
[/p0q0] |
Ans(%) |
|
1180000 |
-1250000 |
1250000 |
-5.6 |
|
Rate of return for stock B =Yr1 |
|||
|
p1q1 |
{-p0q0} |
[/p0q0] |
Ans(%) |
|
116000 |
-100000 |
100000 |
16 |
|
Rate of return for stock B =yr1 |
|||
|
p1q1 |
{-p0q0} |
[/p0q0] |
Ans(%) |
|
900 |
-1000 |
1000 |
-10 |
Ans b) i)
|
Market Value Weighted Index |
||||||
|
Stocks |
P0 |
Q0 |
P1 |
Q1 |
P0*Q0 |
P1*Q1 |
|
A |
1.25 |
1000000 |
1.18 |
1000000 |
1250000 |
1180000 |
|
B |
500 |
200 |
580 |
200 |
100000 |
116000 |
|
C |
10 |
100 |
9 |
100 |
1000 |
900 |
|
Total |
1351000 |
1296900 |
||||
|
1st period rate of return = Total of(P1*Q1-P0*Q0)/Total of P0*Q0 |
||||||
|
= |
1296900 |
minus |
1351000 |
divide |
1296900 |
|
|
= |
-0.04004 |
-4.00444 |
B II)
|
Rate of return on price weighted Index from t=0 to t=1 |
||||
|
Stocks |
P0 |
P1 |
P2 |
|
|
A |
1.25 |
1.18 |
0 |
|
|
B |
500 |
580 |
0 |
|
|
C |
10 |
9 |
0 |
|
|
Total |
511.25 |
590.18 |
0 |
|
|
Avg Price |
170.4167 |
196.7267 |
0 |
|
|
Price Weighted Return from t0 to t1 = |
(P1-P0)/P0 |
0.15438631 |
15.438631 |
C) When market value is taken , stock split does not affect the calculations since Price * no of stock = M.V
No of stock increases as a result of split and price is halfed , hence net result on M.V. is same . So indeed value remains same.
But , When price – wt is taken , stock split does affect the calculations since as a result of split and price is halfed , hence Divisor changes . We take total of Stock prices of Pt and divide with total of P(t-1) . So indeed value changes.
Ans: Note 1
|
Stocks |
P0 |
Q0 |
P1 |
Q1 |
|
A |
1.25 |
1000000 |
1.18 |
1000000 |
|
B |
500 |
200 |
580 |
200 |
|
C |
10 |
100 |
9 |
100 |
Ans a)
|
Rate of return for stock A =yr 1 |
|||
|
p1q1 |
{-p0q0} |
[/p0q0] |
Ans(%) |
|
1180000 |
-1250000 |
1250000 |
-5.6 |
|
Rate of return for stock B =Yr1 |
|||
|
p1q1 |
{-p0q0} |
[/p0q0] |
Ans(%) |
|
116000 |
-100000 |
100000 |
16 |
|
Rate of return for stock B =yr1 |
|||
|
p1q1 |
{-p0q0} |
[/p0q0] |
Ans(%) |
|
900 |
-1000 |
1000 |
-10 |
Ans b) i)
|
Market Value Weighted Index |
||||||
|
Stocks |
P0 |
Q0 |
P1 |
Q1 |
P0*Q0 |
P1*Q1 |
|
A |
1.25 |
1000000 |
1.18 |
1000000 |
1250000 |
1180000 |
|
B |
500 |
200 |
580 |
200 |
100000 |
116000 |
|
C |
10 |
100 |
9 |
100 |
1000 |
900 |
|
Total |
1351000 |
1296900 |
||||
|
1st period rate of return = Total of(P1*Q1-P0*Q0)/Total of P0*Q0 |
||||||
|
= |
1296900 |
minus |
1351000 |
divide |
1296900 |
|
|
= |
-0.04004 |
-4.00444 |
B II)
|
Rate of return on price weighted Index from t=0 to t=1 |
||||
|
Stocks |
P0 |
P1 |
P2 |
|
|
A |
1.25 |
1.18 |
0 |
|
|
B |
500 |
580 |
0 |
|
|
C |
10 |
9 |
0 |
|
|
Total |
511.25 |
590.18 |
0 |
|
|
Avg Price |
170.4167 |
196.7267 |
0 |
|
|
Price Weighted Return from t0 to t1 = |
(P1-P0)/P0 |
0.15438631 |
15.438631 |
C) When market value is taken , stock split does not affect the calculations since Price * no of stock = M.V
No of stock increases as a result of split and price is halfed , hence net result on M.V. is same . So indeed value remains same.
But , When price – wt is taken , stock split does affect the calculations since as a result of split and price is halfed , hence Divisor changes . We take total of Stock prices of Pt and divide with total of P(t-1) . So indeed value changes.
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