Inflation Risk Premiums--I have answers must show all work Because of the recess
ID: 2772851 • Letter: I
Question
Inflation Risk Premiums--I have answers must show all work
Because of the recession, the inflation rate expected for the coming year is only 3%. However, the inflation rate for yer 2 and thereafter is expected to be constant at some level above 3%. Assume that the real risk-free rate is r* = 2% for all maturities and that there are no maturity premiums. If 3-year Treasury notes yield 2 percentage points more than 1 year notes, what inflation rate is expected after year 1?
Answer is 6.0%--Show all work and formulas!
Explanation / Answer
Answer:
(1 + inflation rate)(1 + real rate) = (1 + nominal rate)
First calc nominal rate for the 1 yr T-note:
1.03*1.02 = 1.0506...minus 1 = nominal rate: 0.0506
Next, as per the problem, the 3 year T-note yields 2% more than the one year...
0.0506 +0.02 = 0.0706 <3yr nominal rate
Next, solve for expected inflation....(note: the real interest rate is considered unchanged)
(1 + inflation)(1.02) = 1.0706
1.0706/1.02 = (1 + inflation)
1.049608 = (1 + inflation rate)
(expected) inflation rate = 0.049608, or about 4.96%