Buying stocks with regard to brokerage

• Oct 6th 2008, 10:48 AM
billiboy
Buying stocks with regard to brokerage
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?
• Oct 6th 2008, 11:17 AM
TKHunny
(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.
• Oct 7th 2008, 09:32 AM
billiboy
Thanks TKHunny, that did it!

Edit:
...or not really
• Oct 7th 2008, 10:57 AM
billiboy
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?
• Oct 7th 2008, 06:08 PM
TKHunny
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
• Oct 8th 2008, 02:04 AM
billiboy
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%
• Oct 8th 2008, 04:12 AM
TKHunny
Why are you using "1,000,000"? That fails to account for transaction costs.
• Oct 8th 2008, 08:10 AM
billiboy
Because I have 1,000,000 in the beginning (100,000 in stock A and so on)
• Oct 8th 2008, 09:30 AM
TKHunny

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.