Question

14-2 Assume that it is now January 1, 2008. The rate of inflation is expected to be 2 percent throughout 2008. In 2009 and after, increased government deficits and renewed vigor in the economy are expected to push inflation rates higher. Investors expect the inflation rate to be 3 percent in 2009, 5 percent in 2010, and 6 percent in 2011. The real risk-free rate, r*, currently is 3 percent. Assume that no maturity risk premiums are required on bonds with five years or less to maturity. The current interest rate on five-year T-bonds is 8 percent. a. What is the average expected inflation rate over the next four years? b. What should be the prevailing interest rate on four-year T-bonds? c. What is the implied expected inflation rate in 2012, or Year 5?

Answer 1

Answer (1):

Given:

2008 Inflation rate = 2%

2009 Inflation rate = 3%

2008 Inflation rate = 5%

2008 Inflation rate = 6%

Average Inflation over next 4 years = ((1 + 2%)* (1 + 3%)* (1 + 5%)* (1 + 6%)) ^(1/4) - 1 = 3.988%

Average Inflation over next 4 years = 3.99% (rounded to two decimals)

Answer (2):

Real risk-free rate = r* = 3 percent

Average Inflation over next 4 years = 3.988%

Also given that there is no maturity risk premiums are required on bonds with five years or less to maturity.

Hence:

Expected prevailing interest rate on four-year T-bonds = 3% + 3.988% = 6.99%

Expected prevailing interest rate on four-year T-bonds = 6.99%

Answer (3):

Given that:

Interest rate on five-year T-bonds is = 8 percent

Real risk-free rate = r* = 3 percent

Expected inflation rate over next 5 years = 8% - 3% = 5%

As calculated in answer 2 above: Average Inflation over next 4 years = 3.988%

Expected inflation rate in 2012, or Year 5 = ((1 + 5%)^5 / (1 + 3.988%)) - 1 = 9.15%

Expected inflation rate in 2012, or Year 5 = 9.15%