In the chapter, two new priors, designed directly for the tangency portfolio weights, are developed. While the first approach is based on the extension of the Laplace prior, the second procedure generalizes the spike and slab prior. The posterior distributions of the tangency portfolio weights under both priors are characterized in terms of stochastic representations. These findings are used to establish exact sampling schemes for drawing samples of tangency portfolio weights from the corresponding posterior distributions, from which both the Bayesian point and interval estimators of the tangency portfolio weights are constructed.