A recent edition of The Wall Street Journal reported interes

A recent edition of The Wall Street Journal reported interest rates of 7.6 percent, 7.95 percent, 8.25 percent, and 8.35 percent for three-year, four-year, five-year, and six-year Treasury notes, respectively. According to the unbiased expectations theory, what are the expected one-year rates for years 4, 5, and 6 (i.e., what are ₄f₁, ₅f₁, and ₆f₁)? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Solution

Ans (a)

For calculating expected forward rate

first add 1 to the forth-year bond\'s interest rate, i.e. , 1.0795 (or 107.95%).

Next, we take it and square it: 107.95 squared it , which gives us 1.1653.

then divide this number by the 3rd year\'s one-year interest rate plus 1.

which means 1.1653 divided by 1.076 (7.6% + 1 = 1.076), which gives 1.083%

The final step is to subtract 1 from it, which gives us the predicted one-year interest rate for next year, of 8.399%

This means that for an investor to earn an equivalent return to today\'s 4-year bond, she would have to invest in a 3-year bond today at 7.6% and hope that next year\'s one-year bond yield increased to 8.399%.

4f1 = 8.399%

Ans(B)

For calculating expected forward rate

first add 1 to the 5th-year bond\'s interest rate, i.e. , 1.0825 (or 108.25%).

Next, we take it and square it: , which gives us 1.1718%

then divide this number by the 4th year\'s one-year interest rate plus 1.

which means 1.1718 divided by 1.0795 (7.95% + 1 = 1.0795), which gives 1.0855%

The final step is to subtract 1 from it, which gives us the predicted one-year interest rate for next year, of 8.55%

This means that for an investor to earn an equivalent return to today\'s 5-year bond, she would have to invest in a 4-year bond today at 7.95% and hope that next year\'s one-year bond yield increased to 8.55%.

5f1 = 8.55%

Ans(c)

For calculating expected forward rate

first add 1 to the 6th-year bond\'s interest rate, i.e. , 1.0835 (or 108.35%).

Next, we take it and square it: , which gives us 1.1739%

then divide this number by the 5th year\'s one-year interest rate plus 1.

which means 1.1739 divided by 1.0825 (8.25% + 1 = 1.0825), which gives 1.0845%

The final step is to subtract 1 from it, which gives us the predicted one-year interest rate for next year, of 8.45%

This means that for an investor to earn an equivalent return to today\'s 6-year bond, she would have to invest in a 5-year bond today at 8.25% and hope that next year\'s one-year bond yield increased to 8.45%.

6f1 = 8.45%