Hello Everyone,
Material says that if the forward rates are greater than spot rates/curve then forward rates pull spot rates up…what’s the logic/reason behind this ? Also same applies when situation is vice versa!
The forward curve must be above the spot curve if the spot curve is upwards sloping. And the oppoisite is true. Because in order for the no arbitrage theory to hold, the future rate that satisfies the upward yield curve must be higher than the spot rate for the same period.
For example, if:
S1 = 3%
S2 = 4%
then
F(1,1) must be = (1.04^2)/1.03 - 1 = 5%
Spot rates are a geometric average of forward rates. For example, the 3-year spot rate is the geometric average of 0f1, 1f1, and 2f1. So if the forward rates are above the spot rates, the spot rates will be increasing.
I wrote an article on this that may be of some help: http://financialexamhelp123.com/calculating-spot-rates-from-forward-rates/
The article on the par curve, spot curve, and forward curve has a graph at the bottom that you may find useful: http://financialexamhelp123.com/par-curve-spot-curve-and-forward-curve/