Question

Create an equally-weighted index for period 1, w/ initial value of 3000.

1. How many shares of A, B and C you need to purchase in order to create this index at time 1?

2. What is the value of the equally-weighted index at time 2?

3. Rebalance the index at time 2; what will be the number of shares of each A, B and C that you need to have after rebalancing and how you should trade each one of them?

Stock	P1	Q1	P2	Q2	P3	Q3
A	$70	200	$72	200	$37.5	400
B	$85	500	$81	500	$83	500
C	$105	300	$98	300	$105.5	300

Answer 1

For an equal weighted index we need to invest same amount in each of the three stocks.

Since initial value = 3000 we will have to start initially by investing 1000 in each of the stocks A, B and C.

Now the prices are given in the table and as per that we will buy

1000/70 = 14.29 shares of A

1000/85 = 11.76 shares of B

1000/705 = 9.52 shares of C

At time 2, the prices are given in the table as per that the values of each stocks are

A = $72 * 14.29 = 1028.88

B = $81 * 11.76 = 952.56

C = $98 * 9.52 = 932.96

Value of equal weighted index = 1028.88 + 952.56 + 932.96 = 2914.4

Rebalancing means going back to original goal of investing equal amounts in all stocks and creating a value of 3000

Thus again we need to invest 1000 in each stock and so as we can see from the calculations above, we need to sell A and buy B and C

For A, no of shares should be = 1000/72 = 13.89 and we currently have 14.28 shares thus we will sell 0.39 shares of A to rebalance

For B, no of shares should be = 1000/ 81 = 12.35 and we currently have 11.76 shares, thus we will buy 0.59 shares of B to rebalance

For C, no of shares should be = 1000/98 = 10.2 whereas we have 9.52 shares and thus we will buy 0.72 shares of C to rebalance