Question

?(Term structure of interest rates?) You want to invest your savings of ?$26,000 in government securities for the next 2 years.? Currently, you can invest either in a security that pays interest of 8.1 percent per year for the next 2 years or in a security that matures in 1 year but pays only 6.1 percent interest. If you make the latter? choice, you would then reinvest your savings at the end of the first year for another year.

a. Why might you choose to make the investment in the 1?-year security that pays an interest rate of only 6.1 ?percent, as opposed to investing in the 2-year security paying 8.1 ?percent? Provide numerical support for your answer. Which theory of term structure have you supported in your? answer?

b. Assume your required rate of return on the? second-year investment is 11.1 ?percent; otherwise, you will choose to go with the 2?-year security. What rationale could you offer for your? preference?

Answer 1

The 2 year rate is given as 8.1% and 1 year rate is 6.1%. As per the pure expectations theory, the two year rate should essentially be 1 year rate today plus expected rate from Year 1 to 2, as below:

(1+r₂)² = (1+r₁) * (1+r_1,2). Using this equation, we find the expected Year 1 one year rate :

(1+r_1,2) = (1+8.1%)²/(1+6.1%) = 10.14%

Thus an investor might choose to invest into 1 year rate in the expectation for the Year 1 to 2 rate to be higher. However if the requires rate for second year is 11.1% then rationally investor should lock into 2 year rate today unless the investor believes that the rates 1 year hence should be higher than as predicted / expected by the above equation .