Index Return Question

CFA Level I
#1

Hi Guys,

Looking to get some help on this question im struggling with:

P0 Q1 P1 Q2 P2 Q2

A $80 100 $85 100 $85 100 B $40 200 $35 200 $35 200 C $80 200 $90 200 $45 400

Note: Stock C went through a stock split

A) Return on Market Value weighted index from date 0 to date 1 = (80)(100) + 40(200) +80(200) / (85)(100) + (35)(200) + (90)(200) = 4.89%

B) Return on Equally weighted index from date 0 to date 1 = (85/80) -1 + (35/40) -1 + (90/80) -1 = 6.25%

C) Return on the Price weighted index from date 1 to date 2 = So here I understand you must change the divisior due to the split -->

pw1 = (85 + 35 + 90) / 3 = $70 —> divisor for p2 = (85 + 35 + 45) / d = 70 —> d = 2.36 ----> pw2 = (85 + 35 + 45) / 2.36 = 69.9

PWI = 69.9 - 70 / 70 = 0% return. Just want some clarification that I am doing this correctly?

Now the ones I cant seem to figure out…

D) A return on the market weighted index from date 1 to date 2

E) A return on the equally weighted index from date 1 to date 2

Am I doing this the same way I did A and B, or do I need to account for the stock split?

Thanks guys!

#2

***Edited***

C) 0% You are right the price weighted returns adjust the divisor so stock splits don’t affect the index value.

D) 0% The extra shares in Security C are offset by the fact that they are worth half as much.

E) -16.7% Indicating the weakness of equal weighting, which is to say that the amount of stocks should not (in theory) change the value of the index, but does if you ignore price adjustments due to changes in the number of shares.

#3

Stock splits do not affect the value of indices: you have to account for them in price-weighted indices and equally-weighted (unweighted) indices.

#4

You are correct; equally weighted indexes require reweiging after splits. I was assuming the question referenced the index value prior to reweighing, thinking that the question would be trivial otherwise.