When building an ERC portfolio given covariance $S$, I am familiar with the approach in optimalPortfolio. It takes the risks of a given weight vector $(w_i * (S w)_i)$, divides it by total risk to get the vector of current budget $Rb = (w_i * (S w)_i) / w^T S w$ and it minimizes the objective $\sum (Rb - b)^2$ where $b$ is your target budget (e.g. the vector of $1/n$ if you want ERC)

That is very intuitive, however, when reading this article Equal Risk Contribution Portfolios it mentions on page 4 near the bottom:

Finally, the investor must think carefully about her various and possibly conflicting goals when deciding on a portfolio layer. It’s typical to see both the MV and ERC portfolios written with a “fully invested” constraint, i.e.∑iwi= 1.This requirement may or may not make sense; for a long-short futures portfolio, for example, it is not appropriate.

And subsequently it says the portfolio objective for the ERC becomes

$$\text{max}_w \sum \log w_i \text{ subject to } w^T S w \leq 1$$

Why might it be saying "fully invested" for long short futures portfolio not appropriate? Why the need for this second formulation (is it equivalent?), what is the limitation with the former specification?


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