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Reading 42 Market Allocation question

Im seeing 2 different ways of calculating this but I think both will get the same answer and I’m hoping someone can confirm this for me.
Looking at pg 205  reading 42 market allocation is calculated as market over/under weight * rate of return of specific market allocation
but on pg 213 it is calculated as market over/under weight * (rate of return of specific market allocation - total rate of return)
I believe either will work but not seeing well defined formula…hopfully my expalation is not too confusion but its from example 4 and example 6 of reading 42.

1st example Pg 205 is an actual performance attribution where you look at sources of return .This is an overall decomposition ( essentially single period )
Second one Pg 213  is an example of multi-factor, muli-period retrn attribution . It is just an illustration of the multi-period attribution calculation , don’t take it to the bank to encash into sources of return.
It could have been any other factors in Pg 213 such as Value Manager & Growth Manager ,or Small Caps and Large Caps . You would proceed wih the bmulti-period calc exactly the same way but to get explanation for different factors.

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The first one is market allocation return component of portfolio return attribution whereas the second one is called as Pure sector/market allocation. My response in the exam will depend on the specific data provided in the input. I guess that second application will specifically require to calculate  ‘pure sector allocation return’.

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still see 1st example and part 1 of the 2nd example asking exactly the same thing on market allocation but being calculated 2 different ways.  But i also tried a few examples using both steps for calculating and come up with the same answer so just wanted to know why they used different steps and did not provide a well defined formula.

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