Chapter 3: Q17BP (page 188)

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

Expert verified

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%.

$\begin{array}{rcl} 2 - Y e a r M a t u r i t y & = & \frac{(I n t e r e s t o f 1 - y e a r + I n t e r e s t o f 2 - y e a r)}{M a t u r i t y P e r i o d} \\ = & \frac{(5 % + 8 %)}{2} \\ = & 6.50 % \end{array}$

Calculation for T-bill having a maturity of 3 years

The interest rate will be 6.67%

$\begin{array}{rcl} 3 - y e a r m a t u r i t y & = & \frac{(I n t e r e s t o f 1 - y e a r + I n t e r e s t o f 2 - y e a r + I n t e r e s t o f 3 - y e a r)}{M a t u r i t y P e r i o d} \\ = & \frac{(5 % + 8 % + 7)}{3} \\ = & 6.67 % \end{array}$

Calculation for T-bill having a maturity of 4 years

The interest rate will be 7.50%

$\begin{array}{rcl} 4 - y e a r m a t u r i t y & = & \frac{(I n t e r e s t o f 1 - y e a r + I n t e r e s t o f 2 - y e a r + I n t e r e s t o f 3 - y e a r + I n t e r e s t o f 4 - y e a r)}{M a t u r i t y p e r i o d} \\ = & \frac{(5 % + 8 % + 7 % + 10 %)}{4} \\ = & 7.50 % \end{array}$

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January	\(28,000
February	\)19,000
March	\(12,000
April	\)14,000
May	\(8,000
June	\)6,000
July	\(22,000
August	\)26,000
September	\(29,000
October	\)34,000
November	\(42,000
December	\)24,000
Total annual sales	\(264,000

January	\(100,000
February	\)93,000
March	\(25,000
April	\)25,000
May	\(20,000
June	\)35,000
July	\(45,000
August	\)45,000
September	\(55,000
October	\)85,000
November	\(105,000
December	\)123,000
Total annual sales	\(756,000

Short Answer

Step by step solution

Calculation for T-bill having a maturity of 2 years

Calculation for T-bill having a maturity of 3 years

Calculation for T-bill having a maturity of 4 years

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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%