Why is the long-term interest rate negative in Germany?

The first possible explication is the excess savings in Germany and in the euro zone associated with a very low fiscal deficit for the euro zone taken as a whole . But this savings surplus could be invested in the short term, and not in long-term bonds if their yield is too low. However , the yield on 3-month Treasury bills in Germany is -60 basis points, which may continue to drive investors into bonds. The second possible explication is that banks, especially German banks, are buy ing government bonds to avoid a negative interest rate (-40bp) on deposits at the central bank. The third possible explanation is that institutional investors (insurance companies, pension funds, investment fund) are forced to continue to invest in risk-free bonds. The fourth possible explanation is purchases by non-residents, which are diversifying their portfolios into euros even if interest rates are negative. To varying degrees, all these four explanations are relevant.