Question

A price-weighted index has three stocks priced at \$19, \$22, and \$33. The number of outstanding...

A price-weighted index has three stocks priced at \$19, \$22, and \$33. The number of outstanding shares for each is 100,000 shares, 200,000 shares and 220,000 shares, respectively. If prices changed to \$18, \$19, and \$39 at t=1 , what is the rate of return of the index for this period?

Initial value of index = Price of first stock * Number of shares for first stock + Price of second stock * Number of shares for second stock + Price of third stock * Number of shares for third stock.

= 19 * 100000 + 22 * 200000 + 33 * 220000

= 1900000 + 4400000 + 7260000

= \$ 13560000.

Revised value of index = Revised Price of first stock * Number of shares for first stock + Revised Price of second stock * Number of shares for second stock + Revised Price of third stock * Number of shares for third stock.

= 18 * 100000 + 19 * 200000 + 39 * 220000

= 1800000 + 3800000 + 8580000

= \$ 14180000.

Rate of return for index = (Revised value of index - Initial value of index) / Initial value of index

= (14180000 - 13560000) / 13560000

= 620000 / 13560000

= 0.0457 i.e., 4.57 % (0.0457 * 100).

Conclusion :- Rate of return for index over one year period = 4.57 % (approx)

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