Question

From the following information, find (a) yield on 1-year T-bonds one year from now; (b) yield on `2`-year T-bonds one year from now; and (c) yield on `1`-year T-bonds two years from now?

As on date today, interest rates on 1-year T-bonds yield `1.7%`, interest rates on `2`-year T-bonds yield `2.15%`, and interest rates on `3`-year T-bonds yield `3.8%`.

Answer 1

(a) `2.6%` - (b) `4.866%` - (c) `7.18%`

Explanation:

We are given that today, interest rates on 1-year T-bonds yield `1.7%`, interest rates on `2`-year T-bonds yield `2.15%`, and interest rates on `3`-year T-bonds yield `3.8%`.

a. It is apparent that today yield on `1`-year T-bond is `1.7%` and on a `2`-year bond is `2.15%`. Now, assume that yield on 1-year T-bonds one year from now is `x%`. Hence, if one invests today at `1.7%` for `1`-year and at the end of one year, invest the total investment at `x%`, one should get equivalent of `2.15%`.

Therefore `(1+0.017)(1+x/100)=(1+0.0215)^2`

or `1+x/100=1.04346/1.017=1.026`

or `x/100=0.026` or `x=2.6%`

b. For the yield on `2`-year T-bonds one year from now, if we invest at `1.7%` now and then let us invest in the two year bond after one year at `y%`, we should get the return equivalent to `3.8%` i.e.

`(1+0.017)(1+x/100)^2=(1.038)^3`

i.e. `(1+y/100)^2=1.11839/1.017=1.0997`

and `1+y/100=1.04866` i.e. `y/100=0.04866` or `y=4.866%`

c. For the yield on `1`-year T-bonds two years from now, one can invest now at `2.15%` for two years and then after `2` years say at `z%` and we should have the same return i.e. `3.8%` and in other words

`(1+0.0215)^2(1+z/100)=(1+0.038)^3`

or `1+z/100=1.11839/1.04346=1.0718` i.e. `z/100=0.0718`

or `z=7.18%`