7. The proof is provided in the appendix to Chapter 37.

8. A concave shape means that the (upward-sloping) yield-curve is steeper in the front end than in the long end. The yield loss of moving from the two-year bond to cash is greater than the yield gain of moving from the two-year bond to the ten-year bond. Thus the yield earned from the combination of cash and tens is lower than the forgone yield from twos.