Volatility of a stock may incur a risk premium, leading to a positive correlation between volatility and returns. On the other hand the leverage effect, whereby negative returns increase volatility, acts in the opposite direction. We propose a reformulation and extension of the ARCH in Mean model, in which the logarithm of scale is driven by the score of the conditional distribution. This EGARCH-M model is shown to be theoretically tractable as well as practically useful. By employing a two component extension we are able to distinguish between the long and short run effects of returns on volatility. The EGARCH formulation allows more flexibility in the asymmetry of the response (leverage) and this enables us to find that the short-term response is, in some cases, close to being anti-asymmetric. The long and short run volatility components are shown to have very different effects on returns, with the long-run component yielding the risk premium. A model in which the returns have a skewed t distribution is shown to fit well to daily and weekly data on some of the major stock market indices.Asymmetric price transmission, cost pass-through, electricity markets, price theory, rockets and feathers