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From: Jess on 6 Aug 2010 16:08
Hello,

following is an objective function that i want to minimize;

To find; MIN ( (1/T) * sum (p (w'*r - m)) )
w,m
s.t. w'*e = 1, (e is a vector of ones)

here 'p' is a convex symmetric function which follows p (anything) = | anything | or modulus. 'r' is vector of returns from time t= 1,2,......T.

The difficulty for me in doing this lies from the fact that 2 variables;
'w' (the weights of the portfolio) and 'm' (the estimator of portfolio risk) has to be optimized from a single objective function.
I tried to use fmincon, but got stuck because I couldn't fit in two variables to minimize.

So if anybody can give in any ideas, it would be great. any more information needed and I will be happy to provide. Cheers!

Jess
From: Jess on 6 Aug 2010 16:37
"Jess " <fe09jt(a)mail.wbs.ac.uk> wrote in message <i3hq37$mqs$1(a)fred.mathworks.com>...
> Hello,
>
> following is an objective function that i want to minimize;
>
> To find; MIN ( (1/T) * sum (p (w'*r - m)) )
> w,m
> s.t. w'*e = 1, (e is a vector of ones)
>
> here 'p' is a convex symmetric function which follows p (anything) = | anything | or modulus. 'r' is vector of returns from time t= 1,2,......T.
>
> The difficulty for me in doing this lies from the fact that 2 variables;
> 'w' (the weights of the portfolio) and 'm' (the estimator of portfolio risk) has to be optimized from a single objective function.
> I tried to use fmincon, but got stuck because I couldn't fit in two variables to minimize.
>
> So if anybody can give in any ideas, it would be great. any more information needed and I will be happy to provide. Cheers!
>
> Jess

just a clarification; 'm' is the estimator of portfolio return not risk as i had wrongly mentioned. The estimator of portfolio risk is the whole objective function itself, which has to be minimized..
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