RE: [Gretl-users] Coefficient restrictions
Wilson-- I would suggest to your former student that even with the
re-parameterization this model (restricting coefficients to be positive and
sum to one) is not the best approach to determining an asset style. For
one, shorting an asset class is a legitimate style, as is a Beta > 1.
I imagine the problem that is trying to be solved is the multi-collinearity
of the three explanatory variables. For this I suggest creating 2 extra
series that are almost independent of the S&P 500 return: z400= rSP400-
rSP500 and z600= rSP600 - rSP500. And then run two regressions with
b1*rsp500 + b2*z400 and b1*rsp500 + b2*z600 as the RHS.
This allows them to test whether either b2 is significant and the manager
has significant risk exposure to an asset class other than large cap stocks
(either positive or negative). If both b2's are significant, they could
then explore further by strategies such as creating z600b= rsp600-rsp400 and
running the RHS as b1*rsp500 + b2*z400 + b3* z600b, but I would first check
for the individual significance of rsp400 and rsp600, given the general
dominance of large caps movements (as measured by the SP 500) in market
returns.
Also, a potential side issue is that rPORT may include dividend
re-investment while SP500, 400, and 600 return calculations typically do not
include dividend effects.
-----Original Message-----
From: gretl-users-bounces(a)lists.wfu.edu
[mailto:gretl-users-bounces@lists.wfu.edu] On Behalf Of Riccardo (Jack)
Lucchetti
Sent: Saturday, April 26, 2008 11:27 AM
To: Gretl list
Subject: Re: [Gretl-users] Coefficient restrictions
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