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1. You want to create a price-weighted index consisting of the following three stocks.

At t = 0, you arbitrarily set the initial value of the index at 100.

stockA stockB StockC
August (t=0) Share Price $40 $60 $100
September (t=1) Share Price $44 $54 $110

(a) Given a (hypothetically) same percentage change in price – e.g., 1% - which stockwill have the greatest impact on the value of index? Why? Explain in words.

(b) Define a divisor as a constant that divides the sum of the three prices (price of A +price of B + price of C) to reach the index value. What is the value of the divisor at t =0?

(c) Compute the price-weighted index value at t = 1. What is the monthly percentagereturn on the index from t = 0 to t = 1?

Now consider a 2-for-1 stock split for stock C at t = 1. That is, each old share of stock Cbecomes 2 new shares while the price per share is halved from $110 to $55.

(d) What is the new value of the divisor?

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Collen Von
Collen VonLv2
28 Sep 2019

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Assume there are only three stocks in the market: A, B, and C. At time 0, P(A) = $10, P(B) = $20, and P(C) = $10. At time 1, P(A) = $15, P(B) = $30, P(C) = $5. The number of shares outstanding is 1 million for A, 2 million for B, and 2 million for C.

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