Question

Suppose you know what’s in your wallet since you landed a job on the bond trading desk of Capital One. your office ascribes to the economic “expectations theory” of interest rates that indicates the real risk-free rate is 2% and that the maturity risk premium is zero. Right now your Bloomberg terminal indicates that today’s 1-year Treasury bond yields 5% and a 2-year Treasury bond yields 7%. Your firm has a liquidity need to invest a certain portion of its portfolio in 1-year T-bills.

TASKS: Please -

[a] Based on today’s 1-year and 2-year T-bill rates, determine (infer) the annual interest rate for 1-year T-bills for Year 2. TIP … use “geometric average” logic in your calculations.

[b] Show calculations that infer what the inflation rate can be expected during Year 2.

[c]   Comment on why the average interest rate for the 2-year period differs from the 1-year interest rate expected for Year 2.

Answer 1

a) The first part is asking to find 1 year forward rate 1 year from now:

(1.07)²=(1.05)¹×(1+r₂)¹

=1.1449=1.05(1+r₂)

=1.090= (1+r₂)

=r₂=0.09=9%

b) Inflation in for Year 1:

R= risk free rate + Inflation Premium

= 5=2+ Inflation Premium

= Inflation Premium =3%

Inflation for 2 years:

R= risk free rate + Inflation Premium

= 7=2+ Inflation Premium

= Inflation Premium = 5%

This means that the average inflation for 2 years is 5 %. Therefore, expected inflation in Year 2 will be:

5*2= Expected Inflation in Year 1 + Expected Inflation in Year 2

=10=3 +Expected Inflation in Year 2

= Expected Inflation in Year 2= 7%

c) The reason why the 2 year maturity bond has a higher interest rate than 1 year bond is because inflation is expected to increase.