Interesting Investment Problem

Published: January 27, 2012, 4:36 pm

I have an interesting investment problem.

I have an account with Scottrade and I have two different stocks that I'm investing in.

They both currently have a market value that has one of them much greater than the other.

I would like to take a fixed Total investment amount, T, and disburse it between the two stocks, A and B, in such a way the end market value of each is nearly equal.

By equal we mean, the stocks can have a few cents difference between them, but no more than a few cents.

Both of the stocks also are under a dollar and would have a commission fee of $7.00 for each trade + 0.5% of each stock's value.

Using the known information we can set up a table of the known values.

T - Total Investment amount

	Stock A	Stock B
Last Price	A_L	B_L
Ask Price	A_P	B_P
Current Shares	A_C	B_C
Buy Shares	X	Y

How much should X and Y be to make the stock values nearly equal?

Entry #2,387

Comments

time*treat - Jan 27, 2012, 5:23 pm

Why wouldn't it be
X = 1/2 ((0.95)$T-$7) / Ap, and Y = 1/2 ((0.95)$T-$7)/Bp ?
Or are you trying to get it down to the penny??

time*treat - Jan 27, 2012, 5:34 pm

Oh, edit the 0.95s to be 0.995.

JADELottery - Jan 27, 2012, 7:00 pm

time*treat,

Typical market value is given in a Last Price computation, so, the equations you've given have not factored those in.

Yes, the Asking Price is involved when it come to buying the stock, but we need to include the Last Price in the final equations.

Good try though.

JADELottery - Jan 27, 2012, 7:08 pm

We'll give the solution in another blog post either later today or tomorrow.

Also, when solving these set of equations, you'll see the underlying aspect of duality.

In that, when you solve for one, you're actually solving for both in a simultaneous symmetry solution.

The duality comes from the fact Stock A's variables are interchangeable with Stock B's variable and the reality is that in general, Stock A can be Stock A or B and Stock B can be B or A in a exclusive-or situation.

Either or, not both... hence, duality.

JADELottery - Jan 27, 2012, 7:14 pm

seems a bit of a contradiction, but it isn't.

it's only when you assign the variables does it become: either or, not both.

when you're not assigning variables or in other words, not examining the equation does the variables take on both qualities.

the duality is in the continuum and the assignment is in the instum.

Interesting Investment Problem

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