Dear Hebbertt:

On Wed, Nov 12, 2008 at 1:44 PM, Hebbertt Soares <hsoares85@gmail.com>wrote:

> Hello UseRs,
>
> I am working with Arbitrage Pricing Theory (APT), an extension of CAPM
> proposed by Roll and Ross. One of the most troubling issues of this
> model is the estimation of its two components: the factor
> sensitivities and risk premia..
>
> Most of the literature estimate this equation in two steps, using Fama
> and Macbeth (1973) approach.
>
> However, as Burmesteir and McElroy (1988) shows this approach is
> inefficient. It would be more efficient doing a joint estimation of
> factor sensitivities  and risk premia as proposed in as Burmesteir and
> McElroy (1988) paper.
>
> This estimation would be done trough a system of nonlinear
> multivariate equations with the following structural form (suppose two
> assets and two factors):
>
> return of asset 1 - risk free rate = constant*coefficient(2) +
> coefficient(2)*factor 1 +
> coefficient(3)*coefficient(4)+coefficient(4)*factor2
>
> return of asset 2 - risk free rate = constant*coefficient(5) +
> coefficient(5)*factor 1 +
> coefficient(3)*coefficient(5)+coefficient(5)*factor2
>
> This system has N equation with K parameter, where N is the number of
> assets and K is the number of factors and the number of interaction
> among factors.
>
> The estimation can be done using SUR method.
>
> I've been looking systemfit (specially nlsystemfit function), and I
> have not been able to find a way of implementing this method in R.
>
> Does anyone in the list implemented APT joint estimation in R? How?


It should be possible to specify the formulas as for nls(). However, while
the code for the linear estimation with systemfit() is very mature and has
proven very reliable for many years, the non-linear estimation with
nlsystemfit() is still under development. Hence, you should bear in mind
that you might get wrong results :-(  You are invited to help us improving
the code of nlsystemfit ;-) (You just have to register at R-Forge and ask to
join the systemfit project)

Best wishes,
Arne

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