Question

In the following table, Pt represents the price at time t and Qt represents shares outstanding at time t. If the equally weighted index of the three stocks at t=0 was 300, what is the index at t=1? Please show calculations.

	P0	Q0	P1	Q1
A	88	100	93	100
B	45	200	40	200
C	96	200	48	400

Answer 1

For calculating an index, we use following formula

Index Value = $\sum$ (Market Cap of securities in index) / Index Divisor

Index Divisor remains constant. It changes in case securities are added/dropped from the index

AT t = 0

А в с Price Shares Market Cap = Price * Shares I 881 100=B3* C3 no

SUMIE X v fx =D3/$D$6 AA B C D Price Weighting = Market Cap of Shares Market Cap = Price * Shares security / Total Market Cap 8800] = D3 / $D$6 45200 9000 24% 96200 19200 500 37000 100% 52% Total

Price	Shares	Market Cap = Price * Shares	Weighting = Market Cap of security / Total Market Cap
88	100	8800	24%
45	200	9000	24%
96	200	19200	52%
Total	500	37000	100%

Hence,

Index Value = $\sum$ (Market Cap of securities in index) / Index Divisor

300 = 37000 / Index Divisor

Index Divisor = 37000 / 300 = 123.333333

Now,

Using this for T = 1

AA в с Price Weighting = Market Cap of Shares Market Cap = Price * Shares security / Total Market Cap 100 9300| 25% 2001 8000/=D4 / $D$6 400 192001 53% 700 36500) 100% 93 40 48 Total

E4 ® =D4/$D$6 fx C A B D E F Price Weighting = Market Cap of Shares Market Cap = Price * Shares security / Total Market Cap 100 9300 25% 200 8000 22% 400 19200 53% 700 36500 100% 93 48 Total

Hence,

Index Value = $\sum$ (Market Cap of securities in index) / Index Divisor

Index Value = 36500 / 123.33333

Index Value = 295.9459459 = 295.95