# Question: The following table shows yields to maturity on U S Treasury

The following table shows yields to maturity on U.S. Treasury securities as of January 1,

2011:

Term to Maturity Yield to Maturity

1 year ........... 3.50%

2 years ............ 4.50%

3 years ............ 5.00%

4 years ............ 5.50%

5 years ............ 6.00%

10 years .......... 6.60%

a. Based on the data in the table, calculate the implied forward one-year rate of interest at January 1, 2014.

b. Describe the conditions under which the calculated forward rate would be an unbiased estimate of the one-year spot rate of interest at January 1, 2014. Assume that one year earlier, at January 1, 2010, the prevailing term structure for U.S. Treasury securities was such that the implied forward one-year rate of interest at January 1, 2014, was significantly higher than the corresponding rate implied by the term structure at January 1, 2011.

c. On the basis of the pure expectations theory of the term structure, briefly discuss two factors that could account for such a decline in the implied forward rate.

Multiple-scenario forecasting frequently makes use of information from the term structure of interest rates.

d. Briefly describe how the information conveyed by this observed decrease in the implied forward rate for 2014 could be used in making a multiple-scenario forecast.

2011:

Term to Maturity Yield to Maturity

1 year ........... 3.50%

2 years ............ 4.50%

3 years ............ 5.00%

4 years ............ 5.50%

5 years ............ 6.00%

10 years .......... 6.60%

a. Based on the data in the table, calculate the implied forward one-year rate of interest at January 1, 2014.

b. Describe the conditions under which the calculated forward rate would be an unbiased estimate of the one-year spot rate of interest at January 1, 2014. Assume that one year earlier, at January 1, 2010, the prevailing term structure for U.S. Treasury securities was such that the implied forward one-year rate of interest at January 1, 2014, was significantly higher than the corresponding rate implied by the term structure at January 1, 2011.

c. On the basis of the pure expectations theory of the term structure, briefly discuss two factors that could account for such a decline in the implied forward rate.

Multiple-scenario forecasting frequently makes use of information from the term structure of interest rates.

d. Briefly describe how the information conveyed by this observed decrease in the implied forward rate for 2014 could be used in making a multiple-scenario forecast.

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