We consider a portfolio allocation problem for trend following (TF) strategies on multiple correlated assets. Under simplifying assumptions of a Gaussian market and linear TF strategies, we derive analytical formulas for the mean and variance of the portfolio return. We construct then the optimal portfolio that maximizes risk-adjusted return by accounting for inter-asset correlations. The dynamic allocation problem for $n$ assets is shown to be equivalent to the classical static allocation problem for $n^2$ virtual assets that include lead-lag corrections in positions of TF strategies. The respective roles of asset auto-correlations and inter-asset correlations are investigated in depth for the two-asset case and a sector model. In contrast to the principle of diversification suggesting to treat uncorrelated assets, we show that inter-asset correlations allow one to estimate apparent trends more reliably and to adjust the TF positions more efficiently. If properly accounted for, inter-asset correlations are not deteriorative but beneficial for portfolio management that can open new profit opportunities for trend followers.
