1. ## 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?

2. (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.

3. Thanks TKHunny, that did it!

Edit:
...or not really

4. 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?

5. 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

6. 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.

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%

7. Why are you using "1,000,000"? That fails to account for transaction costs.

8. Because I have 1,000,000 in the beginning (100,000 in stock A and so on)

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.