Systematic risk and volatility skew

The impact of systematic risk on volatility skew is assessed in a CAPM-GARCH framework under which the relationship between asset price and market index adheres to the CAPM with each residual following an asymmetric GARCH process. From numerical analysis, we demonstrate that (1) the relation between beta and implied volatilities presents a beta smile; (2) beta can determine the shape of implied volatility curve, but systematic risk proportion (SRP) cannot; and (3) the degree of negative skewness and positive kurtosis is proportional to the SRP; however, a higher SRP does not always lead to a higher level of implied volatility.