What is the closed form solution for the following inverse Markowitz problem?
Given a mean-variance optimized fully invested portfolio $X$, a risk aversion parameter $\lambda$ and a var-covar matrix $C$. What is the formula for the (implied) returns $\mu_{impl}$ that must have been used to build the portfolio $X$?
I have a working paper (Kritzman et. al. 2008) claiming a closed form solution $\mu_{impl}$ that depends on the "expected returns" $\mu$ which seems a bit circular and is perhaps a typo.
$$ \mu_{impl} = \lambda C X^T + \frac{-\lambda + 1 C^{-1} \mu^{T}}{1 C^{-1} 1^T} 1^T $$