# 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.

<sales-pitch>

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.

</sales-pitch>

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 "Mean-Variance 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

.

**Follow-Ups**:**Re: 10 to 20 item optimizer?***From:*dave

**References**:**Re: 10 to 20 item optimizer?***From:*Mike Williams

**Re: 10 to 20 item optimizer?***From:*Schmidt

**Re: 10 to 20 item optimizer?***From:*dave

**Re: 10 to 20 item optimizer?***From:*S. I. Becker

**Re: 10 to 20 item optimizer?***From:*dave

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