CFA CFA Level 1 Complications with equal weighted index.

# Complications with equal weighted index.

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So , price weighted index is a bit more intuitive , because it matches the returns on a portfolio , that has bought the same number of shares of each stock in it.
Ex : Stock A – \$3 , Stock B – \$7 , Stock C-\$8 , Price W. Index = (3+7+8)/3 = 6. one can clearly see that that it seems as if we have bought 1 share of each stock , while calculating PWI.

Equal weighted index confuses me because it seems to more like an “index return” than an index, ((calculated as the “arithmetic average return” of the stocks)). An index return is the percentage change in the index value(could be calculated using price index or return index).

Also the fact that it mimics a portfolio , with equal \$ amount invested in each stock , is not that intuitive.

Do we calculate an Equal Weighted index like this ?

Stock A – \$3 , Stock B – \$7 , Stock C-\$8 , for the 1st period , in the second period the price of the stocks change to Stock A – \$4 , Stock B – \$5 , Stock C-\$10.
EWI = (return on A + return on B + return on C) / 3 (unlike the Price Weighted Index , I can’t really imagine How I have invested equal dollar amount in each stock )

return on A = 33.33%
return on B = -25.57%
return on C = 25.00%
EWI = ((.3333+(-.2557)+.2500)/3)*100=10.92

Also it says that the matching portfolio would have to adjusted periodically as prices change so that the “value of all security positions are made equal each period”. This doesn’t makes sense to me either.What are the adjustments and why are they needed?

• Maroon5
Participant
• CFA Level 1
5

@karanv_10111 – you are right in the price weighted index example.

For equal weighted index, your calculation is correct if it assumes using arithmetic mean method. This should how much % return you’d get as if you invested \$1 into each stock (though technically you can’t buy a fraction of a stock).

You can also calculate the return of an equal weighted index using geometric mean (if stated), which is [(1.3333*0.7153*1.25)^(1/3)]-1 = 6%

• Maroon5
Participant
• CFA Level 1
4
• Maroon5
Participant
• CFA Level 1
3

@karanv_10111 – I forgot to add that:

Only the equal weighted index needs to be rebalanced periodically, because for price and value weighted ones, the price/value movement does the rebalancing automatically since it is reflected in the index value instantly. This is not the case for equal weighted index. So if you start out investing \$1 in each 3 stocks above, after the price changes, your portfolio is no longer equally weighted as the \$ amount you invest in each stock changes, hence the need to rebalance. I hope this makes sense.

• 1

@Marron5 by value you mean market capitalization?