I cannot figure out an easy way to calculate these. For instance, “find the 2 year spot rate beginning in 4 years from now” etc. blah blah. Can anyone explain this?
You have 2 choices: invest at 6 year spot OR invest at 4 year spot and reinvest at then current 2 year spot. Either way, you should have the same amount of money at the end of 6 years. You know what the 4 year and 6 year spot rates are; the only unknown is the 2 year forward rate 4 years from now,
(1 + s4)4(1 + 2f4)2 = (1 + s6)6
(1 + 2f4)2 = (1 + s6)6 / (1 + s4)4
1 + 2f4 = [(1 + s6)6 / (1 + s4)4]½
2f4 = [(1 + s6)6 / (1 + s4)4]½ − 1
Thanks all. I will stare at this stuff for a bit. Hopefully it clicks.
Another way that helped it click for me was thinking about how you’d price / value an FRA (derivative, not accounting). If you’re given a problem where you have to value a 6x9 FRA, you’re taking the 9 month rate / 6 month rate. Apply the same concept here (same formulas even - see the last formula in Magician’s post above. Look familiar?): 4 yr x 6 yr (you’re basically solving for equivalent of what rate you’d pay for 2 yr loan in 4 yrs). If you can remember that formula, and have two of three variables (much like you’ll have for FRA questions in derivatives), you can easily solve for the third. The one key difference is how you calculate interest compounding. FRA use simple interest while forward rates use compounded interest
It depends on the nature of the forward rates. If they’re effective rates, then you use compounding. If they’re nominal rates (e.g., LIBOR), they don’t.
Be careful about overgeneralizing.