Wavelet timescales and conditional relationship between higher-order systematic co-moments and portfolio returns

This paper investigates the association between portfolio returns and higher-order systematic co-moments at different timescales obtained through wavelet multi-scaling, a technique that decomposes a given return series into timescales enabling investigation at different return intervals. In Australian industry portfolios, the relative risk positions indicated by systematic co-moments at some timescales are different from those revealed in daily returns. A strong positive (negative) linear association between beta and portfolio return and co-kurtosis and portfolio return in the up (down) market is observed in daily returns and at different timescales. The beta risk is priced in the up and down markets. Co-kurtosis is not priced when the beta is in the pricing model. Co-skewness appears to be priced at a relatively high timescale and this is observed only after the up and down separation of market returns.