Question

1) You are considering investing money in Treasury bills and wondering what the real​ risk-free rate of interest is.​ Currently, Treasury bills are yielding 4.5 % and the future inflation rate is expected to be 2.3 % per year. Ignoring the cross product between the real rate of interest and the inflation​ rate, what is the real​ risk-free rate of​ interest? 2)The CFO of your firm has asked you for an approximate answer to this​ question: What was the increase in real purchasing power associated with both​ 3-month Treasury bills and​ 30-year Treasury​ bonds? Assume that the current​ 3-month Treasury bill rate is 5.45 ​percent, the​ 30-year Treasury bond rate is 7.36 ​percent, and the inflation rate is 2.94 percent.​ Also, the chief financial officer wants a short explanation should the​ 3-month real rate turn out to be less than the​ 30-year real rate. 3)At​ present, the real​ risk-free rate of interest is 1.4​%, while inflation is expected to be 1.1​% for the next two years. If a​ 2-year Treasury note yields 4.9​%, what is the​ maturity-risk premium for this​ 2-year Treasury​ note? 4) You've just taken a job at an investment banking firm and been given the job of calculating the appropriate nominal interest rate for a number of different Treasury bonds with different maturity dates. The real​ risk-free interest rate that you have been told to use is 3.8 %​, and this rate is expected to continue on into the future without any change. Inflation is expected to be constant over the future at a rate of 1.8 %. Since these are bonds that are issued by the U.S.​ Treasury, they do not have any default risk or any liquidity risk​ (that is, there is no​ liquidity-risk premium). The​ maturity-risk premium is dependent upon how many years the bond has to maturity.

BOND MATURES​ IN:	​MATURITY-RISK PREMIUM:
​0-1 year	0.050.05​%
​ 1-2 years	0.250.25​%
​ 2-3 years	0.600.60​%
​ 3-4 years	0.850.85​%

Given this​ information, what should the nominal rate of interest on Treasury bonds maturing in​ 0-1 year,​ 1-2 years,​ 2-3 years, and​ 3-4 years​ be?

Answer 1

Since, multiple questions have been answered and each question is indpendent of each other, I have answered the first three questions.

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Question 1:

The value of the real​ risk-free rate of​ interest is determined as follows:

Real​ Risk-Free Rate of​ Interest = Treasury Bills Yield - Inflation Rate

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Here, Treasury Bills Yield = 4.5% and Inflation Rate = 2.3%

Using these values in the above formula, we get,

Real​ Risk-Free Rate of​ Interest = 4.5% - 2.3% = 2.2% or 2.20% (answer)

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Question 2:

The increase in real purchasing power associated with both​ 3-month Treasury bills and​ 30-year Treasury​ bonds is arrived as below:

Increase in Real Purchasing Power (3-Month Treasury Bill) = Current 3-Month Treasury Bill Rate - Inflation Rate = 5.45% - 2.94% = 2.51%

Increase in Real Purchasing Power (30-Year Treasury Bond) = 30-Year Treasury Bond Rate - Inflation Rate = 7.36% - 2.94% = 4.42%

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Short Explanation:

The​ 3-month real rate turn out to be less than the​ 30-year real rate because investors require a premium to be paid in order to cover the risk associated with the longer investment period.

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Question 3:

The​ maturity-risk premium for the​ 2-year Treasury​ note is calculated as follows:

Maturity-Risk Premium for 2-Year Treasury​ Note = 2-Year Treasury Note Yield - (Real​ Risk-Free Rate of Interest + Inflation Rate for Next 2 Years)

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Here, 2-Year Treasury Note Yield = 4.9%, Real​ Risk-Free Rate of Interest = 1.4​% and Inflation Rate for Next 2 Years = 1.1​%

Using these values in the above formula, we get,

Maturity-Risk Premium for 2-Year Treasury​ Note = 4.9% - (1.4% + 1.1%) = 2.4% or 2.40% (answer)