as titled, for an upward slopping spot curve, why is the forward curve lying above spot curve? and why is par curve the lowest
also how should i understand this statement
If the spot curve is downward sloping (upward sloping), increasing the initiation date (T*) will result in a forward curve that is a greater distance below (above) the spot curve. appreciated
I wrote an article on the par curve, spot curve, and forward curve that covers this: http://financialexamhelp123.com/par-curve-spot-curve-and-forward-curve/
Look at the last bit: Some Insight into these Curves.
umm, i still dont get why forward curve is necessarily above the spot curve…
bcos spot curve rates decides the forward curve rates…
so if the spot curve were rising - the forward curve would rise too and be above the spot curve.
it would be violating good ol’ math if it went any other way!
(1+s2)^2 = (1+s1) ( 1+1f1)
1f1 is the 1 year forward rate, 1 year from now. s1 and s2 are the spot rate at time period 1 and 2.
if s2 is > s1 - it is a steadily rising curve — the above makes sure that 1f1 would be above s1 and below s2 …
(and this is what I have also tried to say above).
It follows from that relationship that the steeper the yield curve the bigger the incremental one year forward rates?
We also know that’s when managers see opportunity to “ride the yield curve”. How are these tied together mathematically?
were you asking a question at the end?
take a sequence of numbers rising monotonically …
and then try to determine the 1 year forward rates that make sense, the two year forward rates to make sense and so on…
you will see what is going on.
The 5-year spot rate is a sort of average of five 1-year forward rates: one starts today, one starts in 1 year, one starts in 2 years, one starts in 3 years, and one starts in 4 years.
Think about an average of 4 numbers, then add one more number to the group. If the average of the 5 numbers is higher than the average of the first 4, what can you say about the fifth one you added? It has to be higher than the average of all 5.
So it is with spot rates and forward rates: if the 5-year spot rate is higher than the 4-year spot rate, then the fifth forward rate (starting at time 4 and ending at time 5) has to be higher than the 5-year spot rate.
The difference is that it doesn’t discount that payment back to today; instead, it discounts it back one period (six months, generally)
It is an awesome explanation. “Thank you sir”