Due to the recession, the rate of inflation expected for the coming year is only

Question

Due to the recession, the rate of inflation expected for the coming year is only 3.5 percent. However, the rate of inflation in Year 2 and thereafter is expected to be constant at some level above 3.5 percent. Assume that the real risk-free rate is k* = 2% for all maturities and that the expectations theory fully explains the yield curve, so there are no maturity risk premiums. If 3-year Treasury bonds yield 3 percentage points (0.03) more than 1-year bonds, what rate of inflation is expected after Year 1?

Explanation / Answer

Answer: Term structure of rates Equation

K(t) = K* + IPt + DRPt + MRPt + LPt

K(t)     =             Required rate of return on a debt security.

    K*       =             Real risk-free rate.

    IP        =             Inflation premium.

DRP        =             Default risk premium.

   LP        =             Liquidity premium.

MRP      =             Maturity risk premium

If these are treasury bonds and under assumption of PEH

DRPt + MRPt + LPt = 0 for any T

So we will take care for inflation premium only

Kt = K* + IPt

IPt = Average inflation = (I1 + I2 + ......)/N

It is given in the question itself that K* = 2%

Inflation rate in year I1 = 3.5%

Yeild of 1 year bond = Kt1 = 2% + 3.5% = 5.5%

it is given in the question that yeild on 3 year bond is 3 % more than 1 year bond

Kt3 = Kt1 + 3% = 5.5% + 3% = 8.5%

Now, from the equation

Kt3 = K* + IP3

8.5% = 2% + IP3

IP3 = 6.5%

Average inflation rate is 6.5%.

Already given that rate of inflation will be constant after year 1 an will maintain above 3.5%

lets say inflation after year 1 is X

(3.5 + X + X )/3 = 6.5%

solving this

X = 8%

rate of infltion after year 1 is 8%

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