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(a)univpm.it
http://www.econ.univpm.it/lucchetti