# Deriving Spot rates - Forward rates

Please, could someone comes up with a simple way to derive all these spot and forward rates ? I just get confused, especially when the sequence of rates is not “linear”, I mean when you have to reconstitute all the rates from rates of rate of rates…

Are you talking about spot-forward or vice versa rate conversion or something else?

yep sir

Well for objective exam it’s pretty easy if you really want to get a approximate values for the rate and solve the question. For sport rates from forward rate, you can calculate by simply taking arithmatic mean of all forward rates, but don’t forget to consider that rates are annual. For Forward rates from spot rates, you can calculate by subtracting the spot rates: Lets say 1F0=5% 1F1=6% 1F2=7%, sport rate for the three years S3 will be 5+6+7/3=6% second examaple: 2F0=5% 1F2=7 spot rate for the three years will be 2*5+7/3…remember these are annual rates so if you are using for 2 years, you have to multiply by 2. For SR to FR, S1=5% S2=6% S3=7% S4=8%, 1F1=2*6-5=7% 2F2=(4*8-2*6)/2=10% Do you get an idea? If you want to calculate exact rates you have the formulas.

Let’s say 5Y spot = 6% 3Y spot = 5% 2Y Fwd rate 8Y from today = 6.5% 2Y Fwd 5Y from today = 4% 3Y Fwd rate 7Y from today = 5.5% what is the 8Y spot rate ? A basic simple way to resolve it. I understand the answer, but just want to figure out if there is any way to solve it quickly and simply. Thanks

There are these videos from Elan on youtube which are very interesting, but just want to get a better and easy understanding http://www.youtube.com/results?search_query=elan+guides&aq=f

What is the answer? approx 5.2%? I would approach like this first get 1year forward rate 7 years from now by doing this: 1F7=3*3F7-2*2F8=3*5.5-2*6.5=3.5 Then calculate 8 year spot rate by: (5*S5+2*2F5+1F7)/8=5*6+2*4+3.5=5.1875 ~ 5.2%

But this is one the toughest questions I solved about rate conversion, although I am not sure if I got it correct

(1+ 5 yr spot)^5 * (1+2-yr forward 5 years from now)^2 * (1 + 3-yr forward rate 7 years from now) MUST EQUAL (1 + 8 year spot rate)^8 * (1 + 2-yr forward rate 8 years from now)^2 Use those arrows/semi circles like the elan video does

will let you know the answer tonight