Hi! Can someone please explain the following statement to me? I don’t quite understand why.
The returns on a price-weighted index can be matched by purchasing a portfolio with an equal number of shares of each stock in the index.
Thanks alot!! 
Suppose that you have three stocks with share prices of $10, $20, and $70, respectively. In a price-weighted index, the weights would be 10% (= $10 / ($10 + $20 + $70)), 20% (= $20 / ($10 + $20 + $70)), and 70% (= $70 / ($10 + $20 + $70)) respectively.
If you bought one share of each stock, the weight of the first in your portfolio would be 10% (= $10 / ($10 + $20 + $70)), the weight of the second would be 20% (= $20 / ($10 + $20 + $70)), and the weight of the third would be 70% (= $70 / ($10 + $20 + $70)).
In the index, if the first stock went up 10%, the second went down 1%, and the third went up by 2%, then the index return would be 10%(10%) + 20%(–1%) + 70%(2%) = 2.2%.
In the portfolio, the first stock would be worth $11.00, the second $19.80, and the third $71.40, for a total of $102.20. ($102.20 – $100.00) / $100.00 = 2.2%.