Stochastic volatility models do two jobs at once: they produce a smile and generate a dynamics for implied volatilities. For general stochastic volatility models, working at order one in the volatility of volatility we establish the structural connection between both aspects of a model.

The derivation calls for the introduction of the Skew Stickiness Ratio, a dimensionless number that quantifies the amount by which the ATM volatility moves when the spot moves, in units of the ATM skew. We derive lower and higher bounds for the SSR and relate the SSR to the decay of the ATM skew as a function of maturity, which leads to a natural partition of stochastic volatility models into two classes.

We then consider the historical joint dynamics of spot and implied volatilites, assess whether our generic results hold in practice and introduce the notion of realized skew.