Question

We observe the following rates. The current one-year Treasury rate is 5.28% and the two-year rate is 7.37%. We believe the one year rate one year from today (E(1r2)) is 6.34%. What is the liquidity premium for year 2 (from t=1 to t=2). Enter in percent form without the percent sign.

Answer 1

The question can be answered from the concept of Term Structure of Interest Rates.

Current 1 Year Treasury Rate = 5.28%

Current 2 Year Treasury Rate = 7.37%

Hence, based on the term structure of interest rate as given below:

1 year Spot Rate 1 Year Forward Rate 1 2 (1+7.37% )2 (1+F2%) (1+5.28%)

(1 + 5.28%) * (1+ F_(1r2)) = (1 + 7.37%)^²

1 Year treasurey rate 1 Year from now = F_(1r2) = [ (1+7.37%)^² / (1+5.28%) ] - 1

_F(1r2) = 1.15283 / 1.0528 - 1

_F(1r2) = 9.501%

The liquidity risk premium for year 2 is the difference between the above derived rate less the expected rate.

Liquidity Risk Premium = F_(1r2) - E_(1r2)

E_(1r2) = 6.34% ... given

_F(1r2) = 9.50% ... Calculated above

Liquidity Risk Premium = 9.50% - 6.34%

Liquidity Risk Premium = 3.16% .... Answer