Comment: 22 pages, 8 figuresThis paper expands traditional stochastic volatility models by allowing for time-varying skewness without imposing it. While dynamic asymmetry may capture the likely direction of future asset returns, it comes at the risk of leading to overparameterization. Our proposed approach mitigates this concern by leveraging sparsity-inducing priors to automatically selects the skewness parameter as being dynamic, static or zero in a data-driven framework. We consider two empirical applications. First, in a bond yield application, dynamic skewness captures interest rate cycles of monetary easing and tightening being partially explained by central banks' mandates. In an currency modeling framework, our model indicates no skewness in the carry factor after accounting for stochastic volatility which supports the idea of carry crashes being the result of volatility surges instead of dynamic skewness.