Question

one year treasury bills currently earn 1.50 percent. You expect that one year from now, 1 year treasury bill rates will increase to 1.70 percent. If the unbiased expectations theory is correct, what should the current rate be on 2-year treasury securities? (Round your answe to 2 decimal places).

Answer 1

Solution :

The current rate on a 2 – year treasury securities, based on the unbiased expectations theory, is calculated using the following formula :

₀R₂ = [ ( 1 + ₀r₁ ) * ( 1 + ₁r₂) ] ^(1/2) - 1

Where

₀R₂ = Current rate on a 2 – year treasury Billi.e., Year 0 rate of a 2 year treasury bill ;

₀r₁ = Current Rate of one year treasury Bill i.e., Year 0 rate of a one year treasury bill ;

₁r₂ = Rate one year from now, of one year treasury Bill

As per the Information given in the question we have

₀r₁ = 1.50 % = 0.0150

₁r₂ = 1.70 % = 0.0170

Applying the above values in the formula we have

= [ ( 1 + 0.0150 ) * ( 1 + 0.0170 ) ] ^{( ½ )} – 1

= [ ( 1.0150 ) * ( 1.0170 ) ] ^{( ½ )} – 1

= [ 1.032255 ] ^{(1/2 )} – 1

= 1.016000 – 1

= 0.016000

= 1.6000 %

= 1.60 %

Thus, if the unbiased expectations theory is correct, the current rate on 2-year treasury securities = 1.60 %

Note : The value of [ 1.032255 ] ^{( 1/2 )}is calculated using the excel formula =SQRT(Number)

=SQRT(1.032255) = 1.016000