PROBLEM SET 1B
Securities’ Index Problems
1.
PriceWeighted Index Problem.
a.
Let I be a priceweighted index where the index portfolio consists of two securities,
initially identified as A and B, at time t = 0.
The market prices of A and B at t = 0 are P
0
(A) =
$50, and P
0
(B) = $30.
The initial value of the index is I
0
= 80/2 = 40.
Assume, too, that the
market prices of A and B at t = 1 are P
1
(A) = $40 and P
1
(B) = $60.
(1) Calculate I
1
, the value of the index at t = 1.
(2) Calculate the percentage change in the index from t = 0 to t = 1.
b.
Assume now that stock B splits 3 for 1 at t = 1, and that the postsplit price of B is
P
1S
(B) = $60/3 = $20.
(Notice that P
1S
(B) denotes the postsplit price of B at t = 1 whereas P
1
(B)
denotes the presplit price of B at t = 1.)
(1) Using the information from part 1a, please state the postsplit value of the index at t
= 1.
(2) Calculate the postsplit value of the index devisor.
c.
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 Spring '09
 TongYao
 Management

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