Question

Intro

The real short-term risk-free rate is 0.5% and expected to stay constant. The inflation rate is expected to be 1.4% this year, 2% for each of the following 5 years, and 2.5% thereafter. The maturity risk premium is expected to be 0.0004 * T, where T is the number of years to maturity.

Attempt 2/5 for 10 pts.

Part 1

What is the expected yield on a 1-year Treasury bill?

Part 2

What is the expected yield on a 3-year Treasury note?

Part 3

What is the expected yield on a 30-year Treasury bond?

Answer 1

Answer 1.

Real Risk-free Rate = 0.50%
Inflation Premium = 1.40%

Maturity Risk Premium = 0.0004 * 1
Maturity Risk Premium = 0.0004 or 0.04%

Expected Yield on 1-year T-Bill = Real Risk-free Rate + Inflation Premium + Maturity Risk Premium
Expected Yield on 1-year T-Bill = 0.50% + 1.40% + 0.04%
Expected Yield on 1-year T-Bill = 1.94%

Answer 2.

Real Risk-free Rate = 0.50%

Inflation Premium = [1.40% + 2 * 2.00%] / 3
Inflation Premium = 1.80%

Maturity Risk Premium = 0.0004 * 3
Maturity Risk Premium = 0.0012 or 0.12%

Expected Yield on 1-year Treasury Note = Real Risk-free Rate + Inflation Premium + Maturity Risk Premium
Expected Yield on 1-year Treasury Note = 0.50% + 1.80% + 0.12%
Expected Yield on 1-year Treasury Note = 2.42%

Answer 3.

Real Risk-free Rate = 0.50%

Inflation Premium = [1.40% + 5 * 2.00% + 24 * 2.50%] / 30
Inflation Premium = 2.38%

Maturity Risk Premium = 0.0004 * 30
Maturity Risk Premium = 0.012 or 1.20%

Expected Yield on 30-year Treasury Bond = Real Risk-free Rate + Inflation Premium + Maturity Risk Premium
Expected Yield on 30-year Treasury Bond = 0.50% + 2.38% + 1.20%
Expected Yield on 30-year Treasury Bond = 4.08%