[Gretl-users] Coefficient restrictions

[Riccardo (Jack) Lucchetti]

On Sat, 26 Apr 2008, Mixon, Wilson wrote:

> One of my former students has this problem: "The project involves 
> regressing the returns from a portfolio against the returns from several 
> market benchmarks (the S&P500, the S&P Midcap 400, the S&P Small-cap 
> 600, and treasury bills).  When the regression is restricted so that all 
> of the coefficients are non-negative and sum to 1, the coefficients will 
> identify which asset classes best explain the portfolio's returns, and 
> therefore what style the portfolio manager is using.  I figured out how 
> to get the coefficients to sum to one using linear restrictions, but I 
> can't seem to find any function or command in GRETL which will impose 
> the non-negative restriction on the regression.  Any ideas?"
>
> I don't know what to tell him. Suggestions?

Express (n-1) portfolio weights as squared parameters and the n-th one as 
1 minus all the others. Estimate via nls. Example:

nls rPORT = w1*rSP500 + w2*rSP400 + w3*rSP600
 	w1 = b1^2
 	w2 = b2^2
 	w3 = 1 - w1 - w2
 	params b1 b2
end nls


Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche

r.lucchetti at univpm.it
http://www.econ.univpm.it/lucchetti