A 5-Year Treasury Bond Has A 4.95% Yield

Question

A 5 Year Treasury Bond Has A 495 Yield A 10 Year Treasury Bond Yiel A 5-year Treasury bond has a 4.95% yield. A 10-year Treasury bond yields 6.5%, and a 10-year corporate bond yields 9.9%. The market expects that inflation will average 2.4% over the next 10 years (IP10 = 2.4%). Assume that there is no maturity risk premium (MRP = 0) and that the annual real risk-free rate, r*, will remain constant over the next 10 years. (Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP = LP = 0.) A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond described. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. What is the yield on this 5-year corporate bond? Round your answer to two decimal places.

Dr. Jack HW Helper · Accepted Answer

The task involves calculating the yield on a 5-year corporate bond based on given information about Treasury yields, corporate yields, inflation expectations, and assumptions regarding risk premiums. This problem primarily applies the concepts of the term structure of interest rates, yield decomposition, and no-arbitrage conditions to determine the required yield. Introduction The yield on bonds can be understood as a composite of various risk and inflation expectations. For Treasury securities, the yields typically reflect the real risk-free rate and expected inflation, while corporate bond yields include additional premiums for default risk and liquidity. In this case, Treasury yields for different maturities and the corporate yield for 10 years are provided, along with the market’s inflation expectation. Our goal is to derive the yield of a 5-year corporate bond that shares the same default and liquidity premiums as the 10-year corporate bond. Step 1: Decompose the Treasury Yield Curve The 5-year and 10-year Treasury yields are given as 4.95% and 6.5%, respectively. Under the assumptions of zero maturity risk premium and a constant real risk-free rate, the yield on Treasury securities can be expressed as the sum of the real risk-free rate and expected inflation over the bond’s maturity. Since: $$ Y_{T}(n) = r^* + IP(n) $$ where $Y_T(n)$ is the yield on a Treasury bond of maturity n, $r^*$ is the real risk-free rate, and $IP(n)$ is the average inflation expectation over n years. The expected inflation over 10 years, $IP_{10}$, is provided as 2.4%. The 10-year Treasury yield appears to reflect this inflation plus the real rate: $$ 6.5\% = r^* + IP_{10} $$ Thus, $$ r^* = 6.5\% - 2.4\% = 4.1\% $$ This calculation assumes that the 10-year Treasury yield equals the real rate plus inflation, given the absence of a maturity risk premium. Step 2: Verify the Consistency with the 5-year Treasury Yield The 5-year Treasury yield (4.95%) can be expressed as: \[ Y_{T}(5

A 5-Year Treasury Bond Has A 4.95% Yield

A 5 Year Treasury Bond Has A 495 Yield A 10 Year Treasury Bond Yiel

Paper For Above instruction

Introduction

Step 1: Decompose the Treasury Yield Curve

Step 2: Verify the Consistency with the 5-year Treasury Yield

Step 3: Calculate the Expected Inflation Over the 10-Year Period

Step 4: Determine the Yield on the 10-Year Corporate Bond

Step 5: Determine the 5-Year Corporate Bond Yield

Conclusion

References