Re: 10 to 20 item optimizer?
 From: "S. I. Becker" <stewart@xxxxxxxxxxxxx>
 Date: Wed, 07 Feb 2007 09:55:10 +0000
dave wrote:
"S. I. Becker" <stewart@xxxxxxxxxxxxx> wrote in message
news:OyidyIfSHHA.5068@xxxxxxxxxxxxxxxxxxxxxxx
dave wrote:wayyes you are right on.
My equation is z=E((x1+y1)*(x2+y2)*(x3+y3)*(x4+y4)*(x5*y5)....)
x's are known
y's are unknown
z is my target of about.12
with a couple of simple constraits
y>=0
sum of all y=1
yeah there are math tricks to do this and solver knows them
there are libraries for this too but do way more than I need and cost
else?more than I haveA few questions:
1) What is E(...) ? Mathematical/statistical Expectation? Something2) Are you sure that those + and * signs are the right way round? If1. with E, I was trying to infer that the sum of the whole equation
they aren't then the simplex algorithm may well do the job for you.
What expression(s) do you want to _optimize_ (i.e. minimise / maximise),
and what expressions(s) do you want to _constrain_ (have less
than/greater than/equal to a given value)?
As I understand the terminology, you have only given constraints in your
example above:
Constraints 1 to n:
y_i >= 0
Constraint n+1:
Sum over i (y_i) = 1
Constraint n+2:
.12 [ = z ] = E(Product over i (x_i + y_i))
Wanting to help, but needing more information,
Stewart
Aha! so E := Sigma (but you had summation signs in there already). But now I know what you mean, so that's sorted. <g>
2. you are correct in my haste I have + and * wrong, y are weights and
multiplied by the return(x)
I would like to maximize the sum of the equation
((x1*y1)+(x2*y2)+(x3*+y3)+(x4*y4)+(x5*y5)....)
So this is linear optimisation on linear constraints.
I am essentially trying to embed a portfolio optimizer into my data charting
software for my own use.
<salespitch>
Why not buy the one I write: http://www.occamsrazor.com/ ? It has a COM automation interface for access from VB, or it plugs directly into Excel for charting purposes.
</salespitch>
So I need to have the sum of all weights of course = 1 and then no more
than 5% for any one weight
for right now they are my only constraints
x is monthly return and y is weight
Its very similar to markowitz optimization but I care less about deviation
and more about downside deviation or sortino but I want to take one step at
a time
If you don't care about the risk part of the equation, then you want the simplex algorithm:
http://en.wikipedia.org/wiki/Simplex_algorithm
Also google for "Simplex algorithm" Many universities have it in "linear programming" courses, and some have their lecture slides on the web.
If you have Markowitz's book "MeanVariance Analysis in Portfolio Choice and Capital Markets," the simplex algorithm is described in chapter 8, with particular reference to maximising return subject to linear constraints on your portfolio.
Stewart
.
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