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" ... Fourth, by buying Treasuries the Fed is effectively elbowing out all the pensions who need that duration to hedge liabilities. Now these entities will have to compete with the government to lock up debt that is at historic lows. The convexity of long Treasuries creates a vicious cycle where more demand creates even more demand. Buying Treasuries in the name of liquidity provision misses the big picture of risk management-driven demand meeting scarce Treasury availability. ... "
" ... The convexity of this bond, or the rate of change of the duration, is about 10; i.e. for a large fall in yields, the bond’s price will increase by a factor of convexity times the square of the yield change, and for a large rise in yields, the bond’s price will be cushioned by the convexity, leading to a significant amount of asymmetry. For a zero coupon bond, the convexity is super high anyway, increasing as the square of the maturity. For example, a cousin of this bond is the German bund maturing on August 15, 2029 which has a ten year maturity. The ten year zero has a convexity of “only” a tenth of the thirty year bond. ... "