Suppose the real risk-free rate is 3.50%, the average future inflation rate is 2.25%, and a maturity premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the years to maturity. What rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is NOT valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average. *
To calculate the rate of return on a 1-year Treasury security using the given information and the assumption that the pure expectations theory is not valid, you can follow these steps:
Step 1: Calculate the expected inflation rate for 1 year using the average future inflation rate.
- In this case, the average future inflation rate is provided as 2.25%. Since we are calculating the rate of return for a 1-year Treasury security, we will use the same inflation rate for the calculation.
Step 2: Calculate the maturity premium for a 1-year Treasury security using the provided formula MRP = 0.10%(t).
- For a 1-year maturity, t = 1. Substituting this value into the formula, we get: MRP = 0.10%(1) = 0.10%.
Step 3: Calculate the expected real risk-free rate by subtracting the expected inflation rate from the real risk-free rate.
- The given real risk-free rate is 3.50% and the calculated expected inflation rate is 2.25%. Subtracting the expected inflation rate from the real risk-free rate, we get: Expected real risk-free rate = 3.50% - 2.25% = 1.25%.
Step 4: Calculate the rate of return by adding the expected real risk-free rate and the maturity premium.
- The expected real risk-free rate is 1.25% and the maturity premium is 0.10%. Adding these two values together, we get: Rate of return = 1.25% + 0.10% = 1.35%.
Therefore, the rate of return you would expect on a 1-year Treasury security, assuming the pure expectations theory is NOT valid, is 1.35%.