Question

State the expectations theory and explain its significance. Using the generalized equation of the expectations theory of the term structure of interest rates, calculate today's four-year rate, assuming that the current one-year, 6% rate is expected to rise by one percentage point in each of the next three years.

Answer 1

According to The Expectations Theory, long-term interest rates hold a forecast for short-term interest rates in the future.

Now, 1 year rate in Year 1 = 6%,

1 year rate in Year 2 = 7%

1 year rate in Year 3 = 8%

1 year rate in Year 4 = 9%

Assume you invest $100 in Year 1.

At the end of Year 1, total amount = $100 * (1 + 6%) = $106. This would be invested in Year 2 at 7%

At the end of Year 2, total amount = $106 * (1 + 7%) = $113.42. This would be invested in Year 3 at 8%

At the end of Year 3, total amount = $113.42 * (1 + 8%) = $122.4936. This would be invested in Year 4 at 9%

At the end of Year 4, total amount = $122.4936 * (1 + 9%) = $133.518

Now, based on expectations theory, whether you invest in a 4 year bond or invest in 1 year bonds in each of the 4 years, it is the same.

So $100 invested today, should become $133.518 in 4 years.

133.518 = 100 * (1 + r)⁴

1.33518 = (1 + r )⁴

(1 + r) = 1.07494

r = 7.494%