And also should we understand the equation 6 given in The term structure and interest rate dynamic or we can derive forward rates from other equation
Assuming current spot rates can be used to derive spot rates in the future (forward rates today), the return on your zero-coupon bond investment should be the same for any given investment horizon irrelevant of how you sequence the investment. Meaning, whether you buy a zero-coupon bond today that matures in 5 years, or a zero-coupon bond that matures in 2-years and then invest those proceeds in a 3-year zero coupon bond (to reach your targeted 5 year investment), your returns should be the same. Now if the term structure is upward sloping, it means that the 5-year spot rate is > than the 2-year spot rate. If that’s the case, then the rate you’d need to earn on that 3-year zero coupon 2 years from today needs to be high enough to compensate for the fact that you had invested in a 2-year zero-coupon bond that earned less than what the 5-year zero-coupon offered. The further you go out in time, the greater that forward rate will need to be to equalize what you would have earned by just purchasing a zero-coupon bond of the desired investment horizon. I really hope this helped, but I have a feeling it might read a bit confusing… I’m definitely not as good at making things intuitive as some of the more seasoned AF’ers on the forum. Cross your fingers that S2000 chimes in!