We propose a partial replication strategy to construct risk-averse enhanced index funds. Our model takes into account the parameter estimation risk by defining the asset returns and the return covariance terms as random variables. The variance of the index fund return is forced to be below a low-risk threshold with a large probability, thereby limiting … Read more
We show how we can linearize probabilistic linear constraints with binary variables when all coefficients are distributed according to either $\mathcal{N}(\mu_i,\lambda \mu_i)$, for some $\lambda >0$ and $\mu_i>0$, or $\Gamma(k_i,\theta)$ for some $\theta >0$ and $k_i>0$. The constraint can also be linearized when the coefficients are independent and identically distributed if they are, besides, either … Read more
In this paper, we study extensions of the classical Markowitz mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint which imposes that the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level. We study the deterministic equivalents … Read more