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Math Help - Buying stocks with regard to brokerage

  1. #1
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    Buying stocks with regard to brokerage

    Hi!

    I have a problem that doesn't seem too difficult but which is driving me crazy

    I have 1,000,000 dollars.

    I want:
    10% in stock A
    20% in stock B
    40% in stock C
    30% in stock D

    The brokerage cost is 1% of the size of the transactions.

    My question is: how much (exactly) should I buy in each stock in order to fully invest my 1,000,000 dollars?
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  2. #2
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    (Transactions) + 1%(Transactions) = (Transactions)*(1.01) = 1,000,000

    Transactions = 1,000,000/1.01 = 990,099.0099

    Convince yourself.

    990,099.01 * (.01*990,099.01) = 990.099.01 + 9,900.99 = 1,000,000

    Now break up that remaining cash with the percentages.

    You will still raise some rounding issues. The concept of "exact" is not as exact as we all would like.
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  3. #3
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    Thanks TKHunny, that did it!

    Edit:
    ...or not really
    Last edited by billiboy; October 7th 2008 at 10:58 AM.
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  4. #4
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    That really should have helped me but I still don't get my real problem to work..!

    1 have 1,000,000 dollars invested as following:

    10% in stock A
    12% in stock B
    5% in stock C
    73% in stock D

    But I want them to be invested as following:

    10% in stock A
    20% in stock B
    40% in stock C
    30% in stock D

    The brokerage cost is 1% of the size of the transactions.

    I have tried

    transaction = targetWeight*1,000,000/1.01 - currentWeight*1,000,000

    That gives me the correct weights but the wrong sum. What am I doing wrong?
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  5. #5
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    Myabe I'm missing something, but why doesn't this work...

    10% * 990,099.01 = 99,009.90
    12% * 990,099.01 = 118,811.88
    5% * 990,099.01 = 49,504.95
    73% * 990,099.01 = 722,772.28

    Total Invested: 990,099.01

    1% * 99,009.90 = 990.10
    1% * 118,811.88 = 1,188.12
    1% * 49,504.95 = 495.05
    1% * 722,772.28 = 7,227.72

    Total Transaction Cost: 9,900.99

    Total All Costs: 1,000,000.00
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  6. #6
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    Sorry for not making myself clear. The thing is that I don't start from 0. I start fully invested but want to alter my weights.

    In other words I start with:

    10% * 1,000,000 = 100,000
    12% * 1,000,000 = 120,000
    5% * 1,000,000 = 50,000
    73% * 1,000,000 = 730,000

    But want to move to 10%, 20%, 40% and 30%
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  7. #7
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    Why are you using "1,000,000"? That fails to account for transaction costs.
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  8. #8
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    Because I have 1,000,000 in the beginning (100,000 in stock A and so on)
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  9. #9
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    In other words I start with:

    A: 10% * 1,000,000 = 100,000
    B: 12% * 1,000,000 = 120,000
    C: 5% * 1,000,000 = 50,000
    D: 73% * 1,000,000 = 730,000

    But want to move to 10%, 20%, 40% and 30%

    I get it. Try this.

    Transition Ratio
    A: (0.10 / 0.10 / 0.99) - 1 = 1.0101%
    B: (0.20 / 0.12 / 0.99) - 1 = 68.3502%
    C: (0.30 / 0.05 / 0.99) - 1 = 506.0606%
    D: (0.40 / 0.73 / 0.99) - 1 = -44.6520%

    Gross Purchase
    A: 1.0101% * 100,000 = 1,010.10
    B: 68.3502% * 120,000 = 82.020.20
    C: 506.0606% * 50,000 = 253,030.30
    D: -44.6520% * 730,000 = -325,959.60

    Transaction Fees
    A: 1,010.10 * 0.01 = 10.10
    B: 82.020.20 * 0.01 = 820.20
    C: 253,030.30 * 0.01 = 2,530.30
    D: +325,959.60 * 0.01 = 3,259.60 <== Watch the sign, here. They don't pay you for selling, do they?

    New Amounts
    A: 100,000 + 1,010.10 - 10.10 = 101,020.20
    B: 120,000 + 82.020.20 - 820.20 = 202,840.40
    C: 50,000 + 253,030.30 - 2,530.30 = 305,560.61
    D: 730,000 - 325,959.60 - 3,259.60 = 407,300.00

    Total Invested
    1,016,721.21

    New Balance
    A: 101,020.20 / 1,016,721.21 = 9.9359%
    B: 202,840.40 / 1,016,721.21 = 19.9504%
    C: 305,560.61 / 1,016,721.21 = 30.0535%
    D: 407,300.00 / 1,016,721.21 = 40.0601%

    I can see that you may be troubled that the total investment has increased, even after we paid fees of almost $7000. That's okay. You can just scale things for a better second approximation.

    Spreadsheets are wonderful things.
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  10. #10
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    Thanks, I appreciate the time you've put into this. I'm using Excel so I agree that spreadsheets are nice

    The thing with increasing total investment isn't unproblematic however. I can scale the new balance, but I can't scale the transactions so I can't find out what transactions I should make. The sum of the gross purchases minus the transaction costs should be 0 but it becomes something else however I scale them!
    Last edited by billiboy; October 8th 2008 at 12:49 PM.
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  11. #11
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    Darn it, I still haven't got it to work. Somebody else want to give it a try?
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