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December 14th, 2013, 09:49 AM   #1
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Can't get my head around this asset allocation formula

I have a small spreadsheet to figure out asset allocation for a retirement account. There are a total of ten index funds and I have assigned a percentage of the total value of all funds that each fund should be. For example:

Total is $1,000
Fund 1 = 10% (or $100)
Fund 2 = 5% (or $50)
Fund 3 = 7.5% (or $75)
etc.

Once a year, I will rebalance all funds to match the percentages by selling funds that hold too much and redistributing to the funds that have too little. This is very simple to calculate; just total everything up and multiply by the target percentage. However, on a monthly basis I want to add money to the funds and keep the balances as close as possible to the target percentages but (and this is where I'm having trouble) without selling any of the funds that are over the target percentages. For example:

Current total is $1,000
I'm going to add $500
Fund 1 goal is 10%; current is actually 5% (it's 5% under)
Fund 2 goal is 5%; current is actually 4% (it's 1% under)
Fund 3 goal is 7.5%; current is actually 9% (it's 1.5% over)

In this case, I would want a formula that tells me how to divvy up the $500 contribution so that after the contribution were made, the percentage Fund 1 and Fund 2 were under are as equal as possible (e.g. both 2.3% under). In most cases, I would need to ignore funds that were over their target percentage (since I'm not selling), but if a contribution were big enough and that fund was just a little over the target, it might need a portion of the contribution as well.

Any ideas on how to solve this? And I apologize if my explanation is unclear. Thanks!!!
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December 15th, 2013, 01:53 AM   #2
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Re: Can't get my head around this asset allocation formula

Code:
 100    10          50    5      +100      150   10
  50     5          40    4       +35       75    5
  75     7.5        90    9       +36      126    8.4
 775    77.5       820   82      +329     1149   76.6
=====================================================
1000   100        1000  100      +500     1500  100
Added 4th (775): to keep "picture" clear!

COLUMN 1,2 : theoretical set-up
COLUMN 3,4 : actual at purchase date
COLUMN 5 : 500 purchase breakdown
COLUMN 6,7: after purchase

NOTES:
1st 2 invs't back to original percentages
500 - 135 = 365 left:
3rd invs't gets 9/91 * 365 = 36 : the 9:82 percentages used
4th invs't gets 82/91 * 365 = 329

The percentages of 3rd and 4th drop after the purchase,
but NOT the size of each...

Am I "seeing" this mess :P properly ?
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