 This topic has 3 replies, 2 voices, and was last updated Jan214:59 am by cfachris.

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Up::14
Hi all,
I am looking for help on asset attribution of a portfolio over a period of time with some top level additions and withdrawals. If for example we had an investor deposit $1mn at the start of month 1 and this purchased four underlying assets for 40%/30%/20%/10% of the proceeds. Each asset has a 10% return in resulting in a profit of $100k and 10% portfolio return. On a weighted basis asset a would have made a 4% contribution (400k / 1mn) * 10% ; asset b 3% / asset c 2% and asset d 1%. The weighted attribution is additive for one month
in month 2 the investor adds another $1mn adding asset e, leaving opening assets as $2.1mn in the portfolio. Each asset again makes 10% which leaves us with the following at the end of month 2
asset a $440k * 10% = $44k ; $44k / $2.1mn = 2.10%
asset b $330k * 10% = $33k ; $33k / $2.1mn = 1.57%
asset c $220k * 10% = $22k ; $22k / $2.1mn = 1.05%
asset d $110k * 10% = $11k ; $11k / $2.1mn = 0.52%
asset e $1mn * 10% = $100k ; $100k / $2.1mn = 4.76%
portfolio $210k / $2.1mn = 10%
the time weighted return of the portfolio is 21% for the two months but the underlying asset returns are
asset a (100 * (1 + 4%) * (1 + 2.10%)) /100 – 1 = 6.18%
asset b (100 * (1+3%) * (1+1.57%))/100 – 1 = 4.62%
asset c (100 * (1+2%) * (1+1.05%))/100 – 1 = 3.07%
asset d (100 * (1+1%) * (1+0.52%))/1001 = 1.53%
asset e 100 * (1+4.76%))/100 – 1 = 4.76%
the sum of each of the asset ytd is 20.16% which doesnâ€™t match the portfolio twr calc of +21% and Iâ€™m trying to understand how best to break the portfolio ytd number into each sub strategy as I have come to the conclusion that because the weighted returns monthly are additive, compounding the component parts wonâ€™t equal the top number but how else would you go about breaking this down? Without the additional $1mn at the start of month 2 I think you get there by summing total $ p&l over fund initial value but it gets distorted when there is rebalancing
any help is much appreciated
thanks
j

Up::3
hey J, not sure if I’m right here, but time weighted return should have a square root in this case, as it is over 2 period, i.e. ^1/2
Time weighted return for portfolio should be (1.1 * 1.1)^(0.5) – 1 = 10%
Time weighted return for underlying assets over 2 months:
asset A: (1.04*1.021)^(0.5) – 1 = 3.05%
asset B: (1.03*1.0157)^(0.5) – 1 = 2.28%
asset C: (1.02*1.0105)^(0.5) – 1 = 1.52%
asset D: (1.01*1.0052)^(0.5) – 1 = 0.76%
asset E: (1.0475)^(0.5) – 1 = 2.35%
The total is 9.96%, probably due to rounding as I used 2 d.p. input rather than the usual 4 decimals.

Up::2
Hey Chris,
Many thanks for your time on this one, I’m still a little stuck. I think the total time weighted return over the two periods is +21%, as we made 10% in month1 and 10% in month 2, so compounded that would be 21%. If we are then trying to decompose the contribution of each of the assets to that overall return, i would need to keep 21% as the figure from which i would say asset E has contributed x%. But the sum i had so far would add up asset AE and equal a YTD overall return of only 20.16%, so i am missing nearly 1% of performance which i am not explaining. Just wondered if there was an adjustment that is needed to account for the step up in assets from month 1 to month 2 and how that keys in to the overall return.
Thanks again!
J

Up::1
OK I get that you’re compounding the 2 period returns to get 21% total return, whereas I annualized the TWRR since it is a geometric mean calculation. This bugs me as I can’t quite figure out the adjustment needed as well, although it may be something to do with the weighting adjustment is my gut feel.
I wonder if scrolling through the CIPM notes on this would help, check out page 273 onwards on the examples https://www.cfainstitute.org//media/documents/support/programs/cipm/2019cipml1v1r4.ashx


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