# Forward rate instruments

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.