Forward rates from Spot Rates (CONFUSED)

I very much confused regarding calculating forward rates from spot rates. In scheweser it just tell you (1+S2)^2=(1+s1)(1+1f1) etc where s2 spot rate for year 2 and s1 year 1. I have encourtered questions where they ask forward rate for 3 yr bond 2 years from now. Is there any easy way to understand and compute answers for these. any other book/reference will be appreciated. Thanks

The notation on these things can be cumbersome… It helps if you breakdown the formula: (1+S2)^2=(1+s1)(1+1f1) The left side of the equation is the 2 year spot rate. Because it is expressed in annual terms it must be squared to get the growth for two years. For example, if the 2 year spot rate was 5%, then the left side of the equation would be: (1+.05)^2 The right side of the equation is what makes up the two year spot rate. It makes sense if you think about it. The two year spot rate is equat to the 1 year spot rate * the 1 year forward rate. So if you had a one year bond and another one year bond a year from now (read 1f1) then you would have a synthetic two year bond. Remember when doing these problems to note the time period for the rates. Sometimes they will be in semi-annual periods. If that was the case then a two year bond would have to be mulitplied to the 4th power. Hope this helps. Try to understand the logic and solve some more complex problems with it.


I have used timelines to understand this concept. Works for me… 0–S1–1 ==> 1 yr spot rate 0------S2---------2 ==> 2 yr spot rate 0–s1–1—1f1----2 (1+s2)^2=(1+s1)(1+1f1) 0----------S3----------3 ==> 3 yr spot rate. 0–s1–1yr—1f1—2yr-----1f2----3yr 0------s2------------2yr-----1f2----3yr (1+s3)^3=(1+s1)*(1+1f1)*(1+1f2)=(1+s2)^2*(1+1f2)

What exactly are you having problems with? It will be easier to help if you explain exactly what is confusing you. I was confused by these at first too. At the most basic level 2 year bond=1 year bond * 1 year bond 1 year from now This is the same as saying (1+S2)^2=(1+s1)(1+1f1)

How abt this Given a 2-year spot rate of 4% and assuming the market expects a 3-year security two years from now to yield 5%, calculate the current 5-year spot rate. Ans 4.6%

Going by formula (1+r5)^5 = (1+r2)^2 * (1+3f2)^3 or (1+r5)^5 = 1.04^2 * 1.05^3 r5 = 1.25208^.2 - 1 = 4.5989% ===> 4.6% A 5 year security = 2 year security for 2 years * 3 year security 2 years from now for 3 years.

Looks good to me ^