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This is from the book The Long Good Buy by Peter C. Oppenheimer. I’d recommend giving it a read if ya got the time.

“ The move to a negative correlation between bond and equity prices has proved to be more sustained than ever, as lower bond yields are viewed as a reflection of lower structural growth and potential deflation (as per Japan).

Inflation is the biggest risk for investors in fixed income securities because, although government bonds offer a fixed nominal return over a specific maturity, they offer no protection against surprises in inflation. For equities, their cash flows are linked to inflation and therefore offer some protection in the event of rising prices. Of course, the opposite is the case in periods of deflation.

In these circumstances, a fixed nominal return is highly prized, whereas equities - whose cash flows and dividends would fall in line with inflation - are more exposed and require a higher prospective return (lower valuation or higher ERP) to compensate for the risk. This is why in economies that are more prone to deflation, such as Japan and (more recently) Europe, rising interest rates and bond yields have often been seen as positive for equity investors.

This seems to be one of the main reasons why the ERP in many markets appears so high currently relative to the past. Another way to think about this is that future returns are more certain for bond investors (there is less perceived risk that inflation will eat away at the fixed nominal returns) and so equities need a higher relative yield to continue to attract investors.

To summarise, there is a constant tug of war between the bond yield and growth expectations that influences the relationship between bond and equity returns.”