  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.
