I have read this topic several times but every time i don’t really get it. when i try question i sort of guess. can some help me to really get this conversion?
It is basically finding the geometric mean of the spot rate over a given period of time. If the 2 year spot rate is 7% and the 1 year spot rate is 6%, then the 1 year spot rate 1 year from now would have to equal: (1.07)^2 = (1.06)*(?) then solve for the ?. Same goes for all other similar questions. Put all in the same time frame and solve the geometic average of each. Was tricky for me also before I had someone explain a little more clearly.
Also helps to draw out a timeline if you have trouble visualizing it.
the only way to understand this is to read chapter 68 slowly and carefully and to keep going back into the chapter when you dont understand a particular line. in short, spot rate = the rate at which anything should be discounted at present. forward rate = the rate at which you can discount it for future additionally forward rate for period t is simply a package of spot rates.
when he says 2 yr spot rate is 7, he means if you invested something today, and held it for 2 yrs, you’d get a return of 7 percent yearly. but that 7 percent annually is same as getting 6 % for the first year, and then 8% for the second year… okay this is s imple example hence the average worked out but thats not how you should think about it. think about it in terms of geometric averages. what you’ve done is simply found a forward rate for 1 year, 1 year from now. now if someone gave you 2 forward rates, for 1 year from now, and another 1, for 1 year starting 1 yr from now, and asked you to compute the spot rate you could easily do it. so 6% for first, year, 8% for second year, hence spot rate for 2 yr must be 7%