Momentum risk premium is one of the most important alternative risk premia. Since it is considered a market anomaly, it is not always well understood. Many publications on this topic are therefore based on backtesting and empirical results. However, some academic studies have developed a theoretical framework that allows us to understand the behavior of such strategies. In this paper, we extend the model of Bruder and Gaussel (2011) to the multivariate case. We can find the main properties found in academic literature, and obtain new theoretical findings on the momentum risk premium. In particular, we revisit the payoff of trend-following strategies, and analyze the impact of the asset universe on the risk/return profile. We also compare empirical stylized facts with the theoretical results obtained from our model. Finally, we study the hedging properties of trend-following strategies.

Keywords: Momentum risk premium, trend-following strategy, cross-section momentum, time-series momentum, alternative risk premium, market anomaly, diversification, correlation, payoff, trading impact, hedging, skewness, Gaussian quadratic forms, Kalman filter, EWMA

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