We use a leveraged quantile heterogeneous autoregressive model of realized volatility to illustrate that volatility persistence and the asymmetric "leverage" effect are high volatility phenomena. More specifically, we find that (i) low volatility is not persistent, but high volatility all the more, even featuring properties of explosive processes; and (ii) asymmetry of volatility is only a high volatility phenomenon and there is no asymmetry in low volatility regimes. Our results turn out to be robust to the choice of the realized variance estimator, in particular with respect to jumps. The analysis illustrates that quantile regression can provide information that is hidden in commonly used GARCH or realized volatility models. The quantile regression results can also be linked to the weak empirical evidence of the leverage effect and the volatility feedback effect.