Question

Suppose you and most other investors expect the inflation rate to be 7% next year, to fall to 5% during the following year, and then to remain at a rate of 3% thereafter. Assume that the real risk-free rate, r , will remain at 2% and that maturity risk premiums on Treasury securities rise from zero on very short-term securities (those that mature in a few days) to a level of 0.2 percentage points for 1-year securities. Furthermore, maturity risk premiums increase 0.2 percentage points for each year to maturity, up to a limit of 1.0 percentage point on 5-year or longer-term T-notes and T-bonds.

a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities, and plot the yield curve.

b. Now suppose ExxonMobil’s bonds, rated AAA, have the same maturities as the Treasury bonds. As an approximation, plot an ExxonMobil yield curve on the same graph with the Treasury bond yield curve. (Hint: Think about the default risk premium on ExxonMobil’s long-term versus short-term bonds.)

c. Now plot the approximate yield curve of Long Island Lighting Company, a risky nuclear utility.

Answer 1

generally

(1 + real rate) = ( 1 + nominal rate ) / (1 + inflation rate)

year 1.

since nothing was mentioned lets take the difference or premium is nominal rate difference

based on above formula

premium( R_treasury- Rf )_realrate (1 + inflation rate) = 0.2% (nominal)

(R_treasury)_{real rate} = (0.2% / 1 + 7% ) + 2% = 2.187% (real)

year2

( R_treasury- Rf )_realrate (1 + i₁) (1+ i₂) = 0.4% (nominal)

R_{treasury 2nd yr} = [0.4% / (1+7%) (1+5%) ] + 2% = 2.356% (real)

year3

( R_treasury- Rf )_realrate (1 + i₁) (1+ i₂) (1+i₃) = 0.6% (nominal)

R_{3rd year treasury = [0.6% / (1+ 7%)(1+5%)(1+3%) ] + 2% = 2.5184% (real)}

_year4

( R_treasury- Rf )_realrate (1 + i₁) (1+ i₂) (1+i₃)² = 0.8% (nominal)

since from 3rd year inflation remains constant

R_{4th year treasury}  = 0.8 / (1.07)(1.05)(1.03)²  + 2%

= 2.6711% (real)

year5

( R_treasury- Rf )_realrate (1 + i₁) (1+ i₂) (1+i₃)³ = 1% (nominal)

R_{treasury 5th year = 1% / (1.07)(1.05)(1.03)³ + 2% = 2.814% (real)}

Note:-

on treasury bills, bonds and in loans only real rates are quoted.