One of the core issues with alternative risk premia is not just determining whether they exist but how they will move through time. If alternative risk premia are time varying and associated with specific macro factors, it may be possible to tilt exposures based on current or future market conditions or avoid carry risk premia during those periods when expected returns will be lower.
What can we say about carry alternative risk premia returns, one of the most basic of risk premia? We don't have significant amounts of live trading data across all asset classes from bank or money management providers, so we have to rely on evidence-based analysis. We can look at research concerning carry and make judgments on relative performance across asset classes and under different market conditions. Judgments based on academic evidence are not definitive, but they do provide a good guide on what to expect.
The best overview paper is this area is simple-named "Carry" by Koijen, Moskowitz, Pedersen, and Vrugt. Foremost, this paper provides a universal definition of carry and apply it across all the major asset classes. It brings together in one framework the research of many authors. As defined, carry is the stand-alone return not associated with a change in expected prices. Given this simple definition, carry strategies are just the combination of being long high carry assets and short low carry assets within an asset class. This simple definition can be applied to currencies, equities, fixed income, commodities, credit, and options.
While carry is available in all major asset classes, these risk premia are not highly correlated to each other. There is benefit with building a diversified basket of carry trades.