In this paper attached here, researchers analyzed data across a wide range of asset classes over the past century, spanning three different countries (the US, UK, and Japan), to identify what fares better or worse in the face of rising inflation.
Not surprisingly, the data shows that rising inflation is bad for bonds, but also shows that persistent high inflation bodes poorly for equities as well (although the transition to higher-inflation environments from lower inflation tends to provide an initial boost to stock prices). Commodities also tend to fare well in inflationary environments, but with significant variability within the commodities complex, as energy tends to perform best, precious and industrial metals perform well, but foodstuffs and agricultural tend to perform weakest (if only because governments sometimes intervene to try to quell food inflation because it can be especially disruptive to households simply being able to afford to eat). And while real estate prices may rise on a nominal basis in inflationary environments, their real returns tend to hold quite steady (not materially better nor worse) in the face of inflation.
On the other hand, the researchers find that a number of more 'dynamic' investment strategies tend to perform better in inflationary environments, with profitability and value factors roughly holding their own during inflationary periods, smaller companies performing poorly in inflationary environments, and trend-following strategies (that capitalize on the broader restructuring of investment markets transitioning from a low-inflation to higher-inflation regime) faring best.