I disagree the CFA answer. My calculations below.
Any idea guys, if I wrong or right?
12,4 12,00 12,39
EW return CW return PW return
cap weighted return is:
(sum of ending market caps / sum of beg market caps) - 1
price weighted you use the initial prices as weights and equal weighted you take sum of prices
this confused me as well. I don’t understand why if you weight the stock based on market cap you don’t derive performance from the price performance if no rebalancing was done.
What???
Equal weighting : 1/n where n=5 => equivalent to mean return = 12.4%
Price weighting : w1 = price(stock1 on 1/1/2009)/sum(prices on 1/1/2009) = 2.35/56.41=4.17%.This the initial weight on the 1/1/2009 for stock 1. This lead to a return contribution of 4.17%*7.7%=0.32%. Doing this for all stocks lead to 12.39%
Cap Weighting : w1=mkt cap stock 1 on 1/1/2009 / sum(market caps on 1/1/2009) = 48.5/157 = 30.89%. This the initial weight on the 1/1/2009 for stock 1. This lead to a return contribution of 30.89% * 7.7% = 2.38%. Doing this for all the stocks lead to 12.00%.
Edit:
I think I’ve found the issue. Regarding the market cap, if one divide for each stocks, the original market cap by its price, doing this for both year, one can notice that the number of shares outstanding has changed. And it has notably changed in favor of the stock with the largest return (the one at 17.9%) but also the others (+/-, it depends). So the final answer provided is false as it is totally upward biased. An example in figures:
Stock 2 price 2009 = 5.77 => Mkt cap 2009 = 32.7 => shares outstanded 2009 = 32.7/5.5=5.67 (rounded)
Stock 2 price 2010 = 6.8 => Mkt cap 2010 = 41.2 => shares outstanded 2010 = 42.1/6.8=6.06 (rounded) >>5.67
If you consider the price change => 6.8/5.77-1=17.9% => OK
If you consider the mkt cap change => 41.2/32.7-1=26% => KO
As they assume “no splits or something else”, the number of shares outstanded should have not changed. So I think there is an error here.
Any comments please feel free. Again, I may be wrong but that’s crazy for me.
I posted the same question a few days back. Yes I also found this quite confusing. While the weighting mechanism for each method should be different, the same return should be used for each stock under each method correct?
Of course.
We can use different weightings systems, no matter. Once weightings are compute at time zero, on a buy & hold basis, assuming no dividend, splits and so on, the return of a portfolio at time 1 will be the sum of the (weights at time 0 * returns for the period) for eich stocks in the portfolio.
I’m really surprised that nobody asked for this issue before. I may be wrong but I’m still searching for…
Anyone??
UP! Nobody? Really?? So you guys are comfortable with the original answer? Can’t believe it…
UP
Last UP
Ok I hope we will not have any question on this tomorrow 
Good luck!!
so what exactly are you debating? i thought this to be a simple free point. Question was pretty plain straight fwd
I need a TLDR summary
“TLDR summary”?
We are debating the official answer that states the largest return, on this sample, was the one with capitalization weighted method.
Indeed its seems this answer is false. Just have a deep look at what we wrote above.