Question

Using the expectations hypothesis theory for the term structure of interest rates, determine the expected return for securities with maturities of two, three, and four years based on the following data. Do an analysis similar to that in the right-hand portion of Table 6-6.

1-year T bill at the beginning of year 1	5%
1-year T bill at the beginning of year 2	8%
1-year T bill at the beginning of year 3	7%
1-year T bill at the beginning of year 4	10%

Short answer

The interest rate will be 6.50% in the second year, 6.67% in the third year, and 7.50% in the fourth year.

Step-by-step solution

Calculation for T-bill having a maturity of 2 years

The interest rate will be 6.50%.

$\begin{array}{rcl}\mathbf{2}\mathbf{-}\mathit{Y}\mathit{e}\mathit{a}\mathit{r}\mathbf{}\mathit{M}\mathit{a}\mathit{t}\mathit{u}\mathit{r}\mathit{i}\mathit{t}\mathit{y}& \mathbf{=}& \frac{\left(Interestof1-year+Interestof2-year\right)}{\mathbf{M}\mathbf{a}\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{}\mathbf{P}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}}\\ & \mathbf{=}& \frac{\left(5\%+8\%\right)}{\mathbf{2}}\\ & \mathbf{=}& \mathbf{6}\mathbf{.}\mathbf{50}\mathbf{\%}\end{array}$

Calculation for T-bill having a maturity of 3 years

The interest rate will be 6.67%

$\begin{array}{rcl}\mathbf{3}\mathbf{-}\mathit{y}\mathit{e}\mathit{a}\mathit{r}\mathbf{}\mathit{m}\mathit{a}\mathit{t}\mathit{u}\mathit{r}\mathit{i}\mathit{t}\mathit{y}& \mathbf{=}& \frac{\left(Interestof1-year+Interestof2-year+Interestof3-year\right)}{\mathbf{M}\mathbf{a}\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{}\mathbf{P}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}}\\ & \mathbf{=}& \frac{\left(5\%+8\%+7\right)}{\mathbf{3}}\\ & \mathbf{=}& \mathbf{6}\mathbf{.}\mathbf{67}\mathbf{\%}\end{array}$

Calculation for T-bill having a maturity of 4 years

The interest rate will be 7.50%

$\begin{array}{rcl}\mathbf{4}\mathbf{-}\mathit{y}\mathit{e}\mathit{a}\mathit{r}\mathbf{}\mathit{m}\mathit{a}\mathit{t}\mathit{u}\mathit{r}\mathit{i}\mathit{t}\mathit{y}& \mathbf{=}& \frac{\left(Interestof1-year+Interestof2-year+Interestof3-year+Interestof4-year\right)}{\mathbf{M}\mathbf{a}\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}}\\ & \mathbf{=}& \frac{\left(5\%+8\%+7\%+10\%\right)}{\mathbf{4}}\\ & \mathbf{=}& \mathbf{7}\mathbf{.}\mathbf{50}\mathbf{\%}\end{array}$