The economic value of richer return forecasts depends on investors’ ability to translate distributional information into portfolio decisions. We examine this relationship in currency markets, where observable interest-rate differentials discipline currency expected excess re-turns under the maintained no-predictability restriction for exchange-rate changes. We com-bine a multivariate model with time-varying volatility, skewness, and kurtosis (and associated co-moments) with Bayesian online Sequential Monte Carlo estimation, incorporating param-eter uncertainty directly into dynamic portfolio choice. In an out-of-sample exercise spanning the period 2006-2025, we consider a US investor allocating across nine major currencies. We compare mean-variance allocations with rules that additionally incorporate skewness and kurtosis under four mandates governing gross exposure, net directional exposure, and short selling. The economic value of distributional information depends critically on the investment mandate through which it can be implemented. The largest and most statistically robust gains arise when investors can adjust total exposure, while smaller and more heterogeneous gains remain under more restrictive mandates. The benchmark-relative results remain eco-nomically meaningful after proportional transaction costs, although their magnitude depends on the investment constraints and trading intensity.
 

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