Question

The real risk-free rate of interest is 3.1%.  Inflation is expected to be 5% this year and 6% during the next 2 years.  Assume that the maturity risk premiums is zero.  What is the yield on 1-year treasury securities? Write your answer as a percent (do not type the % character - if your answer is 8.8% write 8.8 in the answer).

Answer 1

Generally, the return yield on a debt security or the quoted interest rate on a debt security is composed of the following determinant factors:-

• Real risk free rate (r*) - It is the riskless rate of return, that an investor percieves to get in an inflation free economy.
• Inflation Premium (IP) - It is also called the expected future inflation rate or the average rate of inflation expected to prevail during the lifetime of the debt security.
• Default risk Premium (DRP) is the premium that shows the default risk of the issuer that the issuer will not pay thestated interest & the principal on the stipulated date.The DRP of a US treasury security is considered zero.
• Liquidity Premium (LP) - It is the premium charged by the lender/investor of the security for the illiquidity of some securities or that some securities ca not be convesrted into cash easily in a short span of time. LP is very low for US treasury securities.
• Maturity Risk Premium (MRP) - It is significant for long term US treasury securities & other bonds, because with growing time their prices may decline due to a rise inflaton & interest rates.

Hence, the return yield on a secuirty or the quoted interest rate on a secuirty, (R) is given by the following formula :-

R = r* + IP + LP + DRP + MRP

However, since Default risk premium (DRP) & the liquidity premium (LP) is considered zero for US Treasury Security.

Therefore, the return yield on a US treasury secuirty maturing in t years is given by the following formula :-

R_t = r* + IP_t + MRP

where, R_t = treasury security rate maturing in t years or the return yield on the treasury security maturing in t years.

t = no. of years or the maturity period of the treasury security

r* = real risk free rate of return

IP_t = Inflation premium or the avg. expected inflation rate in t years.

MRP = maturity risk premium

From the above given problem, we get the following data :-

1- year treasury security i.e. the maturity period is 1 year or t =1 year

r* = 3.1%

Inflation rate for the current year = 5% for next 2 years = 6%

i.e. IP_t = IP₁ = 5%

MRP = 0

Therefore, the yield on 1- year treasury security is given by:-

R_t = r* + IP_t + MRP

or, R₁ = 3.1% + 5% + 0

or, R₁ = 8.1%

or, R₁ = 8.1

Therefore, the yield on 1-year treasury security is 8.1