1 year Treasury rates are 4 while 2 year Treasury rates are

1 year Treasury rates are 4%, while 2 year Treasury rates are 8%. What is the expected 1 year Treasury rate one year from today?

Solution

This needs to be calculated based on the Pure Expectations Theory, according to which short term rates are an indicator of future long term rates. According to this theory, for the question, if you invest in a 2 year bond, it would yield the same return as it would have yielded if you would have invested first in a 1 year bond and then invested in a 1 year bond, the proceeds from first.

(1 + Yield on a 2 Yr Bond)² = (1 + Yield on 1 Yr bond) * (1 + Yield on 1 Yr Bond 1 Yr later)

(1 + 8%)² = (1 + 4%) * (1 + Yield on 1 Yr Bond 1 Yr later)

1.1664 = 1.04 * (1 + Yield on 1 Yr Bond 1 Yr later)

1.1215 = (1 + Yield on 1 Yr Bond 1 Yr later)

Yield on 1 Yr Bond 1 Yr later = 0.1215

Yield on 1 Yr Bond 1 Yr later = 12.15%