Trend-following strategies take long positions in assets with positive past returns and short positions in assets with negative past returns. They are typically constructed using futures contracts across all asset classes, with weights that are inversely proportional to volatility, and have historically exhibited great diversification features especially during dramatic market downturns. However, following an impressive performance in 2008, the trend-following strategy has failed to generate strong returns in the post-crisis period, 2009-2013. This period has been characterised by a large degree of co-movement even across asset classes, with the investable universe being roughly split into the so-called Risk-On and Risk-Off subclasses. We examine whether the inverse-volatility weighting scheme, which effectively ignores pairwise correlations, can turn out to be suboptimal in an environment of increasing correlations. By extending the conventionally long-only risk-parity (equal risk contribution) allocation, we construct a long-short trend-following strategy that makes use of risk-parity principles. Not only do we significantly enhance the performance of the strategy, but we also show that this enhancement is mainly driven by the performance of the more sophisticated weighting scheme in extreme average correlation regimes.