Invest in 2 yr forward rate, 4 yrs from now is equivalent with buying 4 yr zero coupon bond, reinvest after 4 yrs in a 2yrs zero coupon bond.
Is it correct?
No one?
I think i know what you are asking but not sure…
investing in a
1 year spot @ 1.05%
with a 1 year foward @ 1.09%
vs investing in a 2 year @ 1.07%
the investor would be indifferent.
No; if you do that, you aren’t locking in the forward rate today.
If there were more time, we’d go through a Socratic discussion wherein you’d create the transaction. Alas, there isn’t.
Buy a 6-year zero-coupon bond, sell a 4-year zero-coupon bond, same present value, the par of the 4-year bond being the amount you want to invest in 4 years.
Suppose that you want to invest $1,000 for 2 years starting in 4 years, the 4-year spot rate is 4% and the 6-year spot rate is 6%; everything’s compounded annually. The forward rate is:
2f4 = √[(1.06)^6 / (1.04)^4] – 1 = 10.1161%
You sell a 4-year zero-coupon bond, par value $1,000, for
$1,000 / (1.04)^4 = $854.80.
You buy a 6-year zero-coupon bond, whose market value is $854.80; you have nothing out of pocket today (as you shouldn’t).
In 4 years, you pay off the 4-year bond for $1,000; that’s your $1,000 investment 4 years from today. In 6 years, the 6-year bond pays you:
$854.80 × (1.06)^6 = $1,212.56.
The return on your $1,000 investment is $212.56 for 2 years, or
√ ($1,212.56 / $1,000.00) – 1 = 10.1161% per year.