Multi-scale variation, path risk and long-term portfolio management

Mean-variance analysis is constrained to weight the frequency bands in a return time series equally. A more flexible approach allows the user to assign preference weightings to short or longer run frequencies. Wavelet analysis provides further flexibility, removing the need to assume asset returns are stationary and encompassing alternative return concepts. The resulting portfolio choice methodology establishes a reward-energy efficient frontier that allows the user to trade off expected reward against path risk, reflecting preferences as between long or short run variation. The approach leads to dynamic analogues of mean-variance such as band pass portfolios that are more sensitive to variability at designated scales.