CFA CFA Level 3 Asset allocation

Asset allocation

• Author
Posts
• 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%))/100-1 = 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

• cfachris
Participant
• CFA Level 3
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.

• 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 A-E 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

• cfachris
Participant
• CFA Level 3
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/2019-cipm-l1v1r4.ashx