1. Assume investors expect a 2.0 percent real rate of return over the next year.

Question

1. Assume investors expect a 2.0 percent real rate of return over the next year. If inflation is expected to be 0.5 percent, what is the expected nominal interest rate for a one-year U.S. Treasury security? 2. A one-year U.S. Treasury security has a nominal interest rate of 2.25 percent. If the expected real rate of interest is 1.5 percent, what is the expected annual inflation rate? 3. A ten-year U.S. Treasury bond has a 3.5 percent interest rate, while an identical maturity corporate bond has a 5.25 percent interest rate Real interest rates and inflation rate expectations would be the same for the two bonds. If a default risk premium of 1.50 percentage points is estimated for the corporate bond, determine the liquidity premium for the corporate bond.

Explanation / Answer

1)

expected real rate of return , r1 = 2% = 0.02

expected inflation rate , i = 0.5% = 0.005

let expected nominal interest rate = n

1+n = (1+r1)*(1+i)

1+n = (1.02)*(1.005) = 1.0251

n = 1.0251-1 = 0.0251 or 2.51%

expected nominal interest rate = 2.51%

2) nominal interest rate , n = 2.25% = 0.0225

expected real rate of interest = r1 = 1.5% = 0.015

let the expected annual inflation rate = i

1+n = (1+r1)*(1+i)

1+i = (1+n)/(1+r1) = 1.0225/1.015 = 1.007389163

i = 1.007389163-1 = 0.007389163 = 0.7389163% or 0.74% ( rounding off to 2 decimal places)

expected annual inflation rate = i = 0.74%

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