An analyst collects the following information regarding spot rates:
1-year rate = 4%.
2-year rate = 5%.
3-year rate = 6%.
4-year rate = 7%.
The 2-year forward rate two years from today is closest to: … we are searching then 2y2y
((1.07)4/(1.05)^2)0.5 … my question is why would we at the end make it the squared root … if we were searching 3y3y … suppose that the 6-year rate was 9% … then 3y3y would be ((1.09)4/(1.06)2)1/3 ??? and also other question the 3 because they is a 3 year rate … (not because it is 3 years from now, right?)
Think of it this way. The key concept behind forward rates is that they are the implied rates that make an investor indifferent between investing at the long (in this case, 4-year) spot rate or investing at the short (2-year) spot rate followed by the “leftover” forward rate (in this case, the two-year forward in two years).
Indifferent means that the two approaches would result in the same terminal wealth. So, if you invested $1 at the 4-year spot, at the end of 4 years, you’d have 1.074 = $1.3108. Likewise, if you invested for 2 years at the 2-year spot of 5%, you’d have 1.052 = 1.1025.
The 2-year forward is the rate that would turn 1.1025 into 1.3108 in two years. time. Using the FV formula
1.1025 x (1+r)2 = 1.3108 ==> (1+r)2 = 1.3108/1.1025 ==> r + (1.3108/1.1025)0.50 - 1
Now just substitute 1.074 for 1.3108 and 1.052 for 1.1025, and you have your answer.
Hey S2000, thank you. Didnt understand that last part with subscripts. Let me do you another question please. The 1/ 3 … that 3 comes from a) rate 3 years from now ; b) 3 year rate. Thank you