What would happen if savers shunned bonds?

In the United States and the euro zone, domestic and non-resident investors are still massive buyers of bonds, despite the very low bond yields. We can imagine that the prospect of persistently negative yields on bond portfolios will end up driving savers to shun bonds and rotate in particular into listed equities and real estate. But the supply of real estate assets is very rigid and the supply of listed equities is declining in the United States (due to share buybacks) and stagnant in the euro zone: if there were an increase in investor demand for real estate and listed equities, real estate and share prices would rise very sharply due to the lack of an increase in the supply of these assets.