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Hi!
I have a problem that doesn't seem too difficult but which is driving me crazy (Thinking)
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?
(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.
Thanks TKHunny, that did it!
Edit:
...or not really
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?
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
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%
Why are you using "1,000,000"? That fails to account for transaction costs.
Because I have 1,000,000 in the beginning (100,000 in stock A and so on)
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.
Thanks, I appreciate the time you've put into this. I'm using Excel so I agree that spreadsheets are nice (Wink)
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!
Darn it, I still haven't got it to work. Somebody else want to give it a try?