# forward/spot rate computation

i’m struggling pretty bad with the forward rate/spot rate computation… specifically the comrpehensive problems that go with reading 66… i get what forward and spot rates are but how neccessary is it to have the calculations down path? They are consuming a lot of my time and I don’t know if it’s a waste to keep trying to get it, for some reason i’m just not conceptually getting how the forward to spot and spot to forward equations are working… i see how they’re doing it, just don’t get why it’s working. I did these in college and just memorized formulas and how to do it at the time but it took forever, never really understood it

I am unsure as to what your specific concerns are but as a basis, the foundation of equating spot and forward rates is the concept of arbitrage in my opinion.i.e You should be indifferent to investing your money for one year or for six months and reinvesting after six months as long as the returns are the same. Else an opportunity for arbitrage arises. Thus the equation X (1+ z1) (1+f) = X (1+z2)^2 (Pardon the scripting)

First try to understand the concept of forward rates and spot rates then indulge yourself in the calculation so that it might help you out in understanding. If the spot rate for 2 year investment is 6% and for 1 year investment is 4% then it implies that if you reinvest the investment after 1 year, it should be invested at a rate which must equate it to a 2 year investment at 6%, which in this case roughly is 8%. 100(1+4%)(1+f)=100(1+6%)^2 104(1+f)=112.36 1+f = 112.36/104 1+f = 1.0804 f = 1.0804 - 1 f = 0.0804 or 8.04% This f here is written 1f1 and interpreted as 1 year investment 1 year from now. The 1 year spot rate S1 is equal to 1f0 which is 1 year investment from now (Time zero). The first subscript tells the length of time and the 2nd subscript tells the time from when the length(period) will start. If its 2f3 it would be 2 years investment 3 years from now and it would be a spot rate of 5th Year, S5.